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

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 188 of file BelosTsqrOrthoManagerImpl.hpp.

Member Typedef Documentation

template<class Scalar , class MV >

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

Definition at line 191 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

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

Definition at line 192 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

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

Definition at line 193 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 195 of file BelosTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

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

Definition at line 196 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 796 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 819 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 1441 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 737 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 1506 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 274 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 286 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 303 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 314 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 842 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 854 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 933 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 1051 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 403 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 433 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 449 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 463 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 476 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 480 of file BelosTsqrOrthoManagerImpl.hpp.

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

BelosTsqrOrthoManagerImpl.hpp

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

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

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

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