TSQR-based OrthoManager subclass implementation. More...

#include <BelosTsqrOrthoManagerImpl.hpp>

Inheritance diagram for Belos::TsqrOrthoManagerImpl< Scalar, MV >:

Public Types
typedef Scalar	scalar_type

typedef Teuchos::ScalarTraits < Scalar >::magnitudeType	magnitude_type

typedef MV	multivector_type

typedef Teuchos::SerialDenseMatrix < int, Scalar >	mat_type
	Type of the projection and normalization coefficients. More...

typedef Teuchos::RCP< mat_type >	mat_ptr

Public Member Functions
Teuchos::RCP< const Teuchos::ParameterList >	getValidParameters () const
	Default valid parameter list. More...

void	setParameterList (const Teuchos::RCP< Teuchos::ParameterList > &params)
	Set parameters from the given parameter list. More...

Teuchos::RCP< const Teuchos::ParameterList >	getFastParameters ()
	Get "fast" parameters for TsqrOrthoManagerImpl. More...

	TsqrOrthoManagerImpl (const Teuchos::RCP< Teuchos::ParameterList > &params, const std::string &label)
	Constructor (that sets user-specified parameters). More...

	TsqrOrthoManagerImpl (const std::string &label)
	Constructor (that sets default parameters). More...

void	setReorthogonalizationCallback (const Teuchos::RCP< ReorthogonalizationCallback< Scalar > > &callback)
	Set callback to be invoked on reorthogonalization. More...

void	setLabel (const std::string &label)
	Set the label for timers. More...

const std::string &	getLabel () const
	Get the label for timers (if timers are enabled). More...

void	innerProd (const MV &X, const MV &Y, mat_type &Z) const
	Euclidean inner product. More...

void	norm (const MV &X, std::vector< magnitude_type > &normVec) const
	Compute the 2-norm of each column j of X. More...

void	project (MV &X, Teuchos::Array< mat_ptr > C, Teuchos::ArrayView< Teuchos::RCP< const MV > > Q)
	Compute and . More...

int	normalize (MV &X, mat_ptr B)
	Orthogonalize the columns of X in place. More...

int	normalizeOutOfPlace (MV &X, MV &Q, mat_ptr B)
	Normalize X into Q*B, overwriting X. More...

int	projectAndNormalize (MV &X, Teuchos::Array< mat_ptr > C, mat_ptr B, Teuchos::ArrayView< Teuchos::RCP< const MV > > Q)
	Project X against Q and normalize X. More...

int	projectAndNormalizeOutOfPlace (MV &X_in, MV &X_out, Teuchos::Array< mat_ptr > C, mat_ptr B, Teuchos::ArrayView< Teuchos::RCP< const MV > > Q)
	Project and normalize X_in into X_out; overwrite X_in. More...

magnitude_type	orthonormError (const MV &X) const
	Return $\\| I - X^* \cdot X \\|_F$ . More...

magnitude_type	orthogError (const MV &X1, const MV &X2) const
	Return the Frobenius norm of the inner product of X1 with itself. More...

magnitude_type	blockReorthogThreshold () const
	Relative tolerance for triggering a block reorthogonalization. More...

magnitude_type	relativeRankTolerance () const
	Relative tolerance for determining (via the SVD) whether a block is of full numerical rank. More...

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

RCP< ParameterList >	unsetParameterList ()

RCP< const ParameterList >	getParameterList () const

Private Types
typedef Teuchos::ScalarTraits < Scalar >	SCT

typedef Teuchos::ScalarTraits < magnitude_type >	SCTM

typedef MultiVecTraits< Scalar, MV >	MVT

typedef MVT::tsqr_adaptor_type	tsqr_adaptor_type

Private Member Functions
void	raiseReorthogFault (const std::vector< magnitude_type > &normsAfterFirstPass, const std::vector< magnitude_type > &normsAfterSecondPass, const std::vector< int > &faultIndices)
	Throw an exception indicating a reorthgonalization fault. More...

void	checkProjectionDims (int &ncols_X, int &num_Q_blocks, int &ncols_Q_total, const MV &X, Teuchos::ArrayView< Teuchos::RCP< const MV > > Q) const
	Return through output arguments some relevant dimension information about X and Q. More...

void	allocateProjectionCoefficients (Teuchos::Array< mat_ptr > &C, Teuchos::ArrayView< Teuchos::RCP< const MV > > Q, const MV &X, const bool attemptToRecycle=true) const
	Allocate projection coefficients. More...

int	projectAndNormalizeImpl (MV &X_in, MV &X_out, const bool outOfPlace, Teuchos::Array< mat_ptr > C, mat_ptr B, Teuchos::ArrayView< Teuchos::RCP< const MV > > Q)
	Implementation of projection and normalization. More...

void	rawProject (MV &X, Teuchos::ArrayView< Teuchos::RCP< const MV > > Q, Teuchos::ArrayView< mat_ptr > C) const
	One projection pass of X against the Q[i] blocks. More...

void	rawProject (MV &X, const Teuchos::RCP< const MV > &Q, const mat_ptr &C) const
	Overload of `rawProject()` for one Q block. More...

int	rawNormalize (MV &X, MV &Q, mat_type &B)
	One out-of-place normalization pass. More...

int	normalizeOne (MV &X, mat_ptr B) const
	Normalize a "multivector" of only one column. More...

int	normalizeImpl (MV &X, MV &Q, mat_ptr B, const bool outOfPlace)
	Normalize X into Q*B, with out-of-place option. More...

Private Attributes
Teuchos::RCP < Teuchos::ParameterList >	params_
	Configuration parameters. More...

Teuchos::RCP< const Teuchos::ParameterList >	defaultParams_
	Default configuration parameters. More...

std::string	label_
	Label for timers (if timers are used). More...

tsqr_adaptor_type	tsqrAdaptor_
	Interface to TSQR implementation. More...

Teuchos::RCP< MV >	Q_
	Scratch space for TSQR. More...

magnitude_type	eps_
	Machine precision for Scalar. More...

bool	randomizeNullSpace_
	Whether to fill null space vectors with random data. More...

bool	reorthogonalizeBlocks_
	Whether to reorthogonalize blocks at all. More...

bool	throwOnReorthogFault_
	Whether to throw an exception on a orthogonalization fault. More...

magnitude_type	blockReorthogThreshold_
	Relative reorthogonalization threshold in Block Gram-Schmidt. More...

magnitude_type	relativeRankTolerance_
	Relative tolerance for measuring the numerical rank of a matrix. More...

bool	forceNonnegativeDiagonal_
	Force R factor of normalization to have a nonnegative diagonal. More...

Teuchos::RCP < ReorthogonalizationCallback < Scalar > >	reorthogCallback_
	Callback invoked if reorthogonalization is necessary. More...

Additional Inherited Members
Protected Member Functions inherited from Teuchos::ParameterListAcceptorDefaultBase
void	setMyParamList (const RCP< ParameterList > &paramList)

RCP< ParameterList >	getMyNonconstParamList ()

RCP< const ParameterList >	getMyParamList () const

Detailed Description

template<class Scalar, class MV>
class Belos::TsqrOrthoManagerImpl< Scalar, MV >

TSQR-based OrthoManager subclass implementation.

Author: Mark Hoemmen

TsqrOrthoManagerImpl implements the interface defined by OrthoManager, as well as the interface defined by OutOfPlaceNormalizerMixin. We use TsqrOrthoManagerImpl to implement TsqrOrthoManager and TsqrMatOrthoManager.

Template Parameters

Scalar	The type of matrix and (multi)vector entries.
MV	The type of (multi)vector inputs and outputs.

This class uses a combination of Tall Skinny QR (TSQR) and Block Gram-Schmidt (BGS) to orthogonalize multivectors. The Block Gram-Schmidt procedure used here is inspired by that of G. W. Stewart ("Block Gram-Schmidt Orthogonalization", SISC vol 31 #1 pp. 761–775, 2008). The difference is that we use TSQR+SVD instead of Stewart's careful Gram-Schmidt with reorthogonalization to handle the current block. "Orthogonalization faults" (as defined by Stewart) may still happen, but we do not handle them by default. Rather, we make one BGS pass, do TSQR+SVD, check the resulting column norms, and make a second BGS pass (+ TSQR+SVD) if necessary. If we then detect an orthogonalization fault, we throw TsqrOrthoFault.

Note: Despite the "Impl" part of the name of this class, we don't actually use it for the "pImpl" C++ idiom. We just separate out the TSQR implementation to make it easier to implement the OrthoManager and MatOrthoManager interfaces for the case where the inner product operator is not the identity matrix.

Definition at line 156 of file BelosTsqrOrthoManagerImpl.hpp.

Member Typedef Documentation

template<class Scalar , class MV >

typedef Scalar Belos::TsqrOrthoManagerImpl< Scalar, MV >::scalar_type

Definition at line 159 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

typedef Teuchos::ScalarTraits<Scalar>::magnitudeType Belos::TsqrOrthoManagerImpl< Scalar, MV >::magnitude_type

Definition at line 160 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

typedef MV Belos::TsqrOrthoManagerImpl< Scalar, MV >::multivector_type

Definition at line 161 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

typedef Teuchos::SerialDenseMatrix<int, Scalar> Belos::TsqrOrthoManagerImpl< Scalar, MV >::mat_type

Type of the projection and normalization coefficients.

Definition at line 163 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

typedef Teuchos::RCP<mat_type> Belos::TsqrOrthoManagerImpl< Scalar, MV >::mat_ptr

Definition at line 164 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

typedef Teuchos::ScalarTraits<Scalar> Belos::TsqrOrthoManagerImpl< Scalar, MV >::SCT

private

Definition at line 167 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

typedef Teuchos::ScalarTraits<magnitude_type> Belos::TsqrOrthoManagerImpl< Scalar, MV >::SCTM

private

Definition at line 168 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

typedef MultiVecTraits<Scalar, MV> Belos::TsqrOrthoManagerImpl< Scalar, MV >::MVT

private

Definition at line 169 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

typedef MVT::tsqr_adaptor_type Belos::TsqrOrthoManagerImpl< Scalar, MV >::tsqr_adaptor_type

private

Definition at line 170 of file BelosTsqrOrthoManagerImpl.hpp.

Constructor & Destructor Documentation

template<class Scalar , class MV >

Belos::TsqrOrthoManagerImpl< Scalar, MV >::TsqrOrthoManagerImpl	(	const Teuchos::RCP< Teuchos::ParameterList > &	params,
		const std::string &	label
	)

Constructor (that sets user-specified parameters).

Parameters

params	[in/out] Configuration parameters, both for this orthogonalization manager, and for TSQR itself (as the "TSQR implementation" sublist). This can be null, in which case default parameters will be set for now; you can always call `setParameterList()` later to change these.
label	[in] Label for timers. This only matters if the compile-time option for enabling timers is set.

Call getValidParameters() for default parameters and their documentation, including TSQR implementation parameters. Call getFastParameters() to get documented parameters for faster computation, possibly at the expense of accuracy and robustness.

Definition at line 764 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

Belos::TsqrOrthoManagerImpl< Scalar, MV >::TsqrOrthoManagerImpl ( const std::string & label )

Constructor (that sets default parameters).

Parameters

label [in] Label for timers. This only matters if the compile-time option for enabling timers is set.

Definition at line 787 of file BelosTsqrOrthoManagerImpl.hpp.

Member Function Documentation

template<class Scalar , class MV >

Teuchos::RCP< const Teuchos::ParameterList > Belos::TsqrOrthoManagerImpl< Scalar, MV >::getValidParameters ( ) const

virtual

Default valid parameter list.

Get a (pointer to a) default list of parameters for configuring a TsqrOrthoManagerImpl instance.

Note: TSQR implementation configuration options are stored under "TSQR implementation" as a sublist.

Reimplemented from Teuchos::ParameterListAcceptor.

Definition at line 1409 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

void Belos::TsqrOrthoManagerImpl< Scalar, MV >::setParameterList ( const Teuchos::RCP< Teuchos::ParameterList > & params )

virtual

Set parameters from the given parameter list.

Implements Teuchos::ParameterListAcceptor.

Definition at line 705 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

Teuchos::RCP< const Teuchos::ParameterList > Belos::TsqrOrthoManagerImpl< Scalar, MV >::getFastParameters ( )

Get "fast" parameters for TsqrOrthoManagerImpl.

Get a (pointer to a) list of parameters for configuring a TsqrOrthoManager or TsqrMatOrthoManager instance for maximum speed, at the cost of accuracy (no block reorthogonalization) and robustness to rank deficiency (no randomization of the null space basis).

Note: TSQR implementation configuration options are stored under "TSQR implementation" as a sublist.

Definition at line 1474 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

void Belos::TsqrOrthoManagerImpl< Scalar, MV >::setReorthogonalizationCallback ( const Teuchos::RCP< ReorthogonalizationCallback< Scalar > > & callback )

inline

Set callback to be invoked on reorthogonalization.

This callback is invoked right after the first projection step, and only if reorthogonalization will be necessary. It is called before actually reorthogonalizing. The first argument is a Teuchos::ArrayView of the norms of the columns of the input multivector before the first projection pass, and the second argument is a Teuchos::ArrayView of their norms after the first projection pass.

The callback is null by default. If the callback is null, no callback will be invoked.

For details and suggested uses, please refer to the documentation of ReorthogonalizationCallback.

Warning: We assume that the input arguments of the callback's operator() are only valid views within the scope of the function. Your callback should not keep the views.

Definition at line 242 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

void Belos::TsqrOrthoManagerImpl< Scalar, MV >::setLabel ( const std::string & label )

inline

Set the label for timers.

This only matters if timers are enabled. If timers are enabled and the label changes, this method will clear the old timers and replace them with new ones. The old timers will not appear in the list of timers shown by Teuchos::TimeMonitor::summarize().

Definition at line 254 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

const std::string& Belos::TsqrOrthoManagerImpl< Scalar, MV >::getLabel ( ) const

inline

Get the label for timers (if timers are enabled).

Definition at line 271 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

void Belos::TsqrOrthoManagerImpl< Scalar, MV >::innerProd	(	const MV &	X,
		const MV &	Y,
		mat_type &	Z
	)		const

inline

Euclidean inner product.

Compute the Euclidean block inner product X^* Y, and store the result in Z.

Parameters

X	[in]
Y	[in]
Z	[out] On output,

Definition at line 282 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

void Belos::TsqrOrthoManagerImpl< Scalar, MV >::norm	(	const MV &	X,
		std::vector< magnitude_type > &	normVec
	)		const

Compute the 2-norm of each column j of X.

Parameters

X	[in] Multivector for which to compute column norms.
normVec	[out] On output: normvec[j] is the 2-norm of column j of X. normVec is resized if necessary so that it has at least as many entries as there are columns of X.

Note: Performance of this method depends on how MultiVecTraits implements column norm computation for the given multivector type MV. It may or may not be the case that a reduction is performed for every column of X. Furthermore, whether or not the columns of X are contiguous (as opposed to a view of noncontiguous columns) may also affect performance. The computed results should be the same regardless, except perhaps for small rounding differences due to a different order of operations.

Definition at line 810 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

void Belos::TsqrOrthoManagerImpl< Scalar, MV >::project	(	MV &	X,
		Teuchos::Array< mat_ptr >	C,
		Teuchos::ArrayView< Teuchos::RCP< const MV > >	Q
	)

Compute $C := Q^* X$ and $X := X - Q C$ .

Project X against the span of the (Euclidean) orthogonal vectors Q, and store the resulting coefficients in C.

Parameters

X	[in/out] On input: the vectors to project. On output: where .
C	[out] The projection coefficients
Q	[in] The orthogonal basis against which to project

Definition at line 822 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

int Belos::TsqrOrthoManagerImpl< Scalar, MV >::normalize	(	MV &	X,
		mat_ptr	B
	)

Orthogonalize the columns of X in place.

Orthogonalize the columns of X in place, storing the resulting coefficients in B. Return the rank of X. If X is full rank, then X*B on output is a QR factorization of X on input. If X is not full rank, then the first rank columns of X on output form a basis for the column space of X (on input). Additional options control randomization of the null space basis.

Parameters

X	[in/out]
B	[out]

Returns: Rank of X

Definition at line 901 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

int Belos::TsqrOrthoManagerImpl< Scalar, MV >::normalizeOutOfPlace	(	MV &	X,
		MV &	Q,
		mat_ptr	B
	)

Normalize X into Q*B, overwriting X.

Normalize X into Q*B, overwriting X with invalid values.

Parameters

X	[in/out] Vector(s) to normalize
Q	[out] Normalized vector(s)
B	[out] Normalization coefficients

Returns: Rank of X

Note: Q must have at least as many columns as X. It may have more columns than X; those columns are ignored.; We expose this interface to applications because TSQR is not able to compute an orthogonal basis in place; it needs scratch space. Applications can exploit this interface to avoid excessive copying of vectors when using TSQR for orthogonalization.

Definition at line 1019 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

int Belos::TsqrOrthoManagerImpl< Scalar, MV >::projectAndNormalize	(	MV &	X,
		Teuchos::Array< mat_ptr >	C,
		mat_ptr	B,
		Teuchos::ArrayView< Teuchos::RCP< const MV > >	Q
	)

inline

Project X against Q and normalize X.

This method is equivalent (in exact arithmetic) to project(X,C,Q) followed by normalize(X,B). However, the interface allows this method to implement reorthogonalization more efficiently and accurately.

Parameters

X	[in/out] The vectors to project against Q and normalize
C	[out] The projection coefficients
B	[out] The normalization coefficients
Q	[in] The orthogonal basis against which to project

Returns: Rank of X after projection

Definition at line 371 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

int Belos::TsqrOrthoManagerImpl< Scalar, MV >::projectAndNormalizeOutOfPlace	(	MV &	X_in,
		MV &	X_out,
		Teuchos::Array< mat_ptr >	C,
		mat_ptr	B,
		Teuchos::ArrayView< Teuchos::RCP< const MV > >	Q
	)

inline

Project and normalize X_in into X_out; overwrite X_in.

Project X_in against Q, storing projection coefficients in C, and normalize X_in into X_out, storing normalization coefficients in B. On output, X_out has the resulting orthogonal vectors and X_in is overwritten with invalid values.

Parameters

X_in	[in/out] On input: The vectors to project against Q and normalize. On output: Overwritten with invalid values.
X_out	[out] The normalized input vectors after projection against Q.
C	[out] Projection coefficients
B	[out] Normalization coefficients
Q	[in] The orthogonal basis against which to project

Returns: Rank of X_in after projection

Note: We expose this interface to applications for the same reason that we expose normalizeOutOfPlace().

Definition at line 401 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

magnitude_type Belos::TsqrOrthoManagerImpl< Scalar, MV >::orthonormError ( const MV & X ) const

inline

Return $\| I - X^* \cdot X \|_F$ .

Return the Frobenius norm of I - X^* X, which is an absolute measure of the orthogonality of the columns of X.

Definition at line 417 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

magnitude_type Belos::TsqrOrthoManagerImpl< Scalar, MV >::orthogError	(	const MV &	X1,
		const MV &	X2
	)		const

inline

Return the Frobenius norm of the inner product of X1 with itself.

Definition at line 431 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

magnitude_type Belos::TsqrOrthoManagerImpl< Scalar, MV >::blockReorthogThreshold ( ) const

inline

Relative tolerance for triggering a block reorthogonalization.

If any column norm in a block decreases by this amount, then we reorthogonalize.

Definition at line 444 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

magnitude_type Belos::TsqrOrthoManagerImpl< Scalar, MV >::relativeRankTolerance ( ) const

inline

Relative tolerance for determining (via the SVD) whether a block is of full numerical rank.

Definition at line 448 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

void Belos::TsqrOrthoManagerImpl< Scalar, MV >::raiseReorthogFault	(	const std::vector< magnitude_type > &	normsAfterFirstPass,
		const std::vector< magnitude_type > &	normsAfterSecondPass,
		const std::vector< int > &	faultIndices
	)

private

Throw an exception indicating a reorthgonalization fault.

Definition at line 1388 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

void Belos::TsqrOrthoManagerImpl< Scalar, MV >::checkProjectionDims	(	int &	ncols_X,
		int &	num_Q_blocks,
		int &	ncols_Q_total,
		const MV &	X,
		Teuchos::ArrayView< Teuchos::RCP< const MV > >	Q
	)		const

private

Return through output arguments some relevant dimension information about X and Q.

Parameters

ncols_X	[out] Number of columns in X
num_Q_blocks	[out] Number of entries in the Q array
ncols_Q_total	[out] Total number of columns in all the entries of Q
X	[in] Multivector to project against the Q[i]
Q	[in] Array of multivectors against which to project X

Definition at line 1877 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

void Belos::TsqrOrthoManagerImpl< Scalar, MV >::allocateProjectionCoefficients	(	Teuchos::Array< mat_ptr > &	C,
		Teuchos::ArrayView< Teuchos::RCP< const MV > >	Q,
		const MV &	X,
		const bool	attemptToRecycle = `true`
	)		const

private

Allocate projection coefficients.

Parameters

C	[out] Array of projection coefficient matrices
Q	[in] Array of MV against which to project
X	[in] MV to project against the entries of Q
attemptToRecycle	[in] Hint whether to check the existing entries of C to see if they have already been allocated and have the right dimensions. This function will do the right thing regardless, but the hint might improve performance by avoiding unnecessary allocations or checks.

Definition at line 979 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

int Belos::TsqrOrthoManagerImpl< Scalar, MV >::projectAndNormalizeImpl	(	MV &	X_in,
		MV &	X_out,
		const bool	outOfPlace,
		Teuchos::Array< mat_ptr >	C,
		mat_ptr	B,
		Teuchos::ArrayView< Teuchos::RCP< const MV > >	Q
	)

private

Implementation of projection and normalization.

Implementation of projectAndNormalize() (in which case X_out is not read or written, so it may alias X_in, and outOfPlace==false) and projectAndNormalizeOutOfPlace() (in which case X_out is written, and outOfPlace==true).

Returns: Rank of X_in after projection

Definition at line 1052 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

void Belos::TsqrOrthoManagerImpl< Scalar, MV >::rawProject	(	MV &	X,
		Teuchos::ArrayView< Teuchos::RCP< const MV > >	Q,
		Teuchos::ArrayView< mat_ptr >	C
	)		const

private

One projection pass of X against the Q[i] blocks.

Perform one projection pass (Modified Block Gram-Schmidt) of X against the Q[i] blocks. Does not allocate C[i] coefficients, and does not reorthogonalize.

template<class Scalar , class MV >

void Belos::TsqrOrthoManagerImpl< Scalar, MV >::rawProject	(	MV &	X,
		const Teuchos::RCP< const MV > &	Q,
		const mat_ptr &	C
	)		const

private

Overload of rawProject() for one Q block.

template<class Scalar , class MV >

int Belos::TsqrOrthoManagerImpl< Scalar, MV >::rawNormalize	(	MV &	X,
		MV &	Q,
		mat_type &	B
	)

private

One out-of-place normalization pass.

Compute one normalization pass of X into Q*B. Overwrite X with invalid values.

Parameters

X	[in/out] On input: multivector whose columns are to be orthogonalized ("normalized"). On output: overwritten with invalid values.
Q	[out] The orthogonalized ("normalized") columns of X. If X on input had (numerical) rank r, the first r columns are a column space basis for X, and the remaining columns are a null space basis for X.
B	[out] Normalization coefficients: X = QB. If X on input had full (numerical) rank, B is upper triangular. Otherwise, B may not be upper triangular, but the factorization X = QB is still valid.

Returns: The rank of the input X

Warning: Q must have exactly as many columns as X.; B must have been allocated and must have the right dimensions (square, with number of rows/columns equal to the number of columns in X).

Definition at line 1502 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

int Belos::TsqrOrthoManagerImpl< Scalar, MV >::normalizeOne	(	MV &	X,
		mat_ptr	B
	)		const

private

Normalize a "multivector" of only one column.

Special case of normalize() when X has only one column. The operation is done in place in X. We assume that B(0,0) makes sense, since we're going to assign to it.

Parameters

X	[in/out] On input: multivector of one column. On output: if that column has nonzero 2-norm, the column scaled by its 2-norm; otherwise, if the column has zero 2-norm, it is not modified.
B	[out] Matrix of dimension 1 x 1. On output, the 2-norm of X.

Returns: One if X has nonzero 2-norm, else zero.

Warning: We do no checking of the dimensions of X or B, and we do not resize B if it has dimensions other than 1 x 1.

Definition at line 1524 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

int Belos::TsqrOrthoManagerImpl< Scalar, MV >::normalizeImpl	(	MV &	X,
		MV &	Q,
		mat_ptr	B,
		const bool	outOfPlace
	)

private

Normalize X into Q*B, with out-of-place option.

If outOfPlace is true, write the normalized vectors to Q, leaving the contents of X invalid. Otherwise, write the normalized vectors to X, leaving the contents of Q invalid. Regardless, if X on input had (numerical) rank r, the first r normalized vectors are a column space basis for X, and the remaining vectors are a null space basis for X.

Parameters

X	[in/out] On input: multivector whose columns are to be orthogonalized ("normalized"). On output: if outOfPlace, overwritten with invalid values; else, the normalized vector(s).
Q	[out] If outOfPlace, overwritten with invalid values; else, the normalized vector(s).
B	[out] Normalization coefficients: X = QB. If X on input had full (numerical) rank, B is upper triangular. Otherwise, B may not be upper triangular, but the factorization X = QB is still valid.

Returns: The rank of X

Note: Q must have at least as many columns as X. It may have more columns than X. This routine doesn't try to allocate space for Q if it is too small.

Definition at line 1641 of file BelosTsqrOrthoManagerImpl.hpp.

Member Data Documentation

template<class Scalar , class MV >

Teuchos::RCP<Teuchos::ParameterList> Belos::TsqrOrthoManagerImpl< Scalar, MV >::params_

private

Configuration parameters.

Definition at line 452 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

Teuchos::RCP<const Teuchos::ParameterList> Belos::TsqrOrthoManagerImpl< Scalar, MV >::defaultParams_

mutableprivate

Default configuration parameters.

Definition at line 455 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

std::string Belos::TsqrOrthoManagerImpl< Scalar, MV >::label_

private

Label for timers (if timers are used).

Definition at line 458 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

tsqr_adaptor_type Belos::TsqrOrthoManagerImpl< Scalar, MV >::tsqrAdaptor_

private

Interface to TSQR implementation.

Definition at line 461 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

Teuchos::RCP<MV> Belos::TsqrOrthoManagerImpl< Scalar, MV >::Q_

private

Scratch space for TSQR.

This multivector scratch space is allocated lazily, only if normalize() is called with a multivector input having more than one column. We do our best to avoid reallocation and recycle this space whenever possible. The normalizeOutOfPlace() method does not allocate Q_, which you can use to your advantage if you already have scratch space allocated.

Definition at line 472 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

magnitude_type Belos::TsqrOrthoManagerImpl< Scalar, MV >::eps_

private

Machine precision for Scalar.

Definition at line 475 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

bool Belos::TsqrOrthoManagerImpl< Scalar, MV >::randomizeNullSpace_

private

Whether to fill null space vectors with random data.

If so, this happens after normalization.

Definition at line 480 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

bool Belos::TsqrOrthoManagerImpl< Scalar, MV >::reorthogonalizeBlocks_

private

Whether to reorthogonalize blocks at all.

Reorthogonalization is conditional, based on the block reorthogonalization threshold. Tests for reorthogonalization only happen if this Boolean is set.

Definition at line 487 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

bool Belos::TsqrOrthoManagerImpl< Scalar, MV >::throwOnReorthogFault_

private

Whether to throw an exception on a orthogonalization fault.

Recovery is possible, but expensive.

Definition at line 492 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

magnitude_type Belos::TsqrOrthoManagerImpl< Scalar, MV >::blockReorthogThreshold_

private

Relative reorthogonalization threshold in Block Gram-Schmidt.

Definition at line 495 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

magnitude_type Belos::TsqrOrthoManagerImpl< Scalar, MV >::relativeRankTolerance_

private

Relative tolerance for measuring the numerical rank of a matrix.

Definition at line 498 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

bool Belos::TsqrOrthoManagerImpl< Scalar, MV >::forceNonnegativeDiagonal_

private

Force R factor of normalization to have a nonnegative diagonal.

If true, then (if necessary) do extra work (modifying both the Q and R factors) in the normalization step in order to force the R factor of the current block to have a nonnegative diagonal.

Definition at line 506 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

Teuchos::RCP<ReorthogonalizationCallback<Scalar> > Belos::TsqrOrthoManagerImpl< Scalar, MV >::reorthogCallback_

private

Callback invoked if reorthogonalization is necessary.

Definition at line 520 of file BelosTsqrOrthoManagerImpl.hpp.

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