TSQR-based OrthoManager subclass implementation. More...

#include <AnasaziTsqrOrthoManagerImpl.hpp>

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

Public Types
typedef Teuchos::SerialDenseMatrix < int, Scalar >	mat_type

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	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

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

magnitude_type	relativeRankTolerance () const

Detailed Description

template<class Scalar, class MV>
class Anasazi::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 96 of file AnasaziTsqrOrthoManagerImpl.hpp.

Member Typedef Documentation

template<class Scalar , class MV >

Anasazi::TsqrOrthoManagerImpl< Scalar, MV >::mat_type

Type of the projection and normalization coefficients

Definition at line 104 of file AnasaziTsqrOrthoManagerImpl.hpp.

Constructor & Destructor Documentation

template<class Scalar , class MV >

Anasazi::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 624 of file AnasaziTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

Anasazi::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 641 of file AnasaziTsqrOrthoManagerImpl.hpp.

Member Function Documentation

template<class Scalar , class MV >

Teuchos::RCP< const Teuchos::ParameterList > Anasazi::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 1215 of file AnasaziTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

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

virtual

Set parameters from the given parameter list.

Implements Teuchos::ParameterListAcceptor.

Definition at line 565 of file AnasaziTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

Teuchos::RCP< const Teuchos::ParameterList > Anasazi::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 1280 of file AnasaziTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

void Anasazi::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 170 of file AnasaziTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

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

inline

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

Definition at line 177 of file AnasaziTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

void Anasazi::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 188 of file AnasaziTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

void Anasazi::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 658 of file AnasaziTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

void Anasazi::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 670 of file AnasaziTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

int Anasazi::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 736 of file AnasaziTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

int Anasazi::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 845 of file AnasaziTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

int Anasazi::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 277 of file AnasaziTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

int Anasazi::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. Overwritten with invalid values on output.
X_out	[out] On output: the normalized input vectors after projection against Q.
C	[out] The projection coefficients
B	[out] The 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 307 of file AnasaziTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

magnitude_type Anasazi::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 323 of file AnasaziTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

magnitude_type Anasazi::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 337 of file AnasaziTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

magnitude_type Anasazi::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 350 of file AnasaziTsqrOrthoManagerImpl.hpp.

template<class Scalar , class MV >

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

inline

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

Definition at line 354 of file AnasaziTsqrOrthoManagerImpl.hpp.

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

AnasaziTsqrOrthoManagerImpl.hpp

Public Types

Public Member Functions

Detailed Description

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

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

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