#include <AnasaziGenOrthoManager.hpp>

Inheritance diagram for Anasazi::GenOrthoManager< ScalarType, MV, OP >:

Public Member Functions
Constructor/Destructor
	GenOrthoManager (Teuchos::RCP< const OP > Op=Teuchos::null)
	Default constructor. More...

virtual	~GenOrthoManager ()
	Destructor. More...

Orthogonalization methods
virtual void	projectGen (MV &S, Teuchos::Array< Teuchos::RCP< const MV > > X, Teuchos::Array< Teuchos::RCP< const MV > > Y, bool isBiOrtho, Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > > C=Teuchos::tuple(Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > >(Teuchos::null)), Teuchos::RCP< MV > MS=Teuchos::null, Teuchos::Array< Teuchos::RCP< const MV > > MX=Teuchos::tuple(Teuchos::RCP< const MV >(Teuchos::null)), Teuchos::Array< Teuchos::RCP< const MV > > MY=Teuchos::tuple(Teuchos::RCP< const MV >(Teuchos::null))) const =0
	Applies a series of generic projectors. More...

virtual int	projectAndNormalizeGen (MV &S, Teuchos::Array< Teuchos::RCP< const MV > > X, Teuchos::Array< Teuchos::RCP< const MV > > Y, bool isBiOrtho, Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > > C=Teuchos::tuple(Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > >(Teuchos::null)), Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > B=Teuchos::null, Teuchos::RCP< MV > MS=Teuchos::null, Teuchos::Array< Teuchos::RCP< const MV > > MX=Teuchos::tuple(Teuchos::RCP< const MV >(Teuchos::null)), Teuchos::Array< Teuchos::RCP< const MV > > MY=Teuchos::tuple(Teuchos::RCP< const MV >(Teuchos::null))) const =0
	Applies a series of generic projectors and returns an orthonormal basis for the residual data. More...

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

virtual	~MatOrthoManager ()
	Destructor. More...

virtual void	setOp (Teuchos::RCP< const OP > Op)
	Set operator used for inner product. More...

virtual Teuchos::RCP< const OP >	getOp () const
	Get operator used for inner product. More...

int	getOpCounter () const
	Retrieve operator counter. More...

void	resetOpCounter ()
	Reset the operator counter to zero. More...

void	innerProdMat (const MV &X, const MV &Y, Teuchos::SerialDenseMatrix< int, ScalarType > &Z, Teuchos::RCP< const MV > MX=Teuchos::null, Teuchos::RCP< const MV > MY=Teuchos::null) const
	Provides a matrix-based inner product. More...

void	normMat (const MV &X, std::vector< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType > &normvec, Teuchos::RCP< const MV > MX=Teuchos::null) const
	Provides the norm induced by the matrix-based inner product. More...

virtual void	projectMat (MV &X, Teuchos::Array< Teuchos::RCP< const MV > > Q, Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > > C=Teuchos::tuple(Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > >(Teuchos::null)), Teuchos::RCP< MV > MX=Teuchos::null, Teuchos::Array< Teuchos::RCP< const MV > > MQ=Teuchos::tuple(Teuchos::RCP< const MV >(Teuchos::null))) const =0
	Provides matrix-based projection method. More...

virtual int	normalizeMat (MV &X, Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > B=Teuchos::null, Teuchos::RCP< MV > MX=Teuchos::null) const =0
	Provides matrix-based orthonormalization method. More...

virtual int	projectAndNormalizeMat (MV &X, Teuchos::Array< Teuchos::RCP< const MV > > Q, Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > > C=Teuchos::tuple(Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > >(Teuchos::null)), Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > B=Teuchos::null, Teuchos::RCP< MV > MX=Teuchos::null, Teuchos::Array< Teuchos::RCP< const MV > > MQ=Teuchos::tuple(Teuchos::RCP< const MV >(Teuchos::null))) const =0
	Provides matrix-based projection/orthonormalization method. More...

virtual Teuchos::ScalarTraits < ScalarType >::magnitudeType	orthonormErrorMat (const MV &X, Teuchos::RCP< const MV > MX=Teuchos::null) const =0
	This method computes the error in orthonormality of a multivector. More...

virtual Teuchos::ScalarTraits < ScalarType >::magnitudeType	orthogErrorMat (const MV &X, const MV &Y, Teuchos::RCP< const MV > MX=Teuchos::null, Teuchos::RCP< const MV > MY=Teuchos::null) const =0
	This method computes the error in orthogonality of two multivectors. More...

void	innerProd (const MV &X, const MV &Y, Teuchos::SerialDenseMatrix< int, ScalarType > &Z) const
	Implements the interface OrthoManager::innerProd(). More...

void	norm (const MV &X, std::vector< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType > &normvec) const
	Implements the interface OrthoManager::norm(). More...

void	project (MV &X, Teuchos::Array< Teuchos::RCP< const MV > > Q, Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > > C=Teuchos::tuple(Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > >(Teuchos::null))) const
	Implements the interface OrthoManager::project(). More...

int	normalize (MV &X, Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > B=Teuchos::null) const
	Implements the interface OrthoManager::normalize(). More...

int	projectAndNormalize (MV &X, Teuchos::Array< Teuchos::RCP< const MV > > Q, Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > > C=Teuchos::tuple(Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > >(Teuchos::null)), Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > B=Teuchos::null) const
	Implements the interface OrthoManager::projectAndNormalize(). More...

Teuchos::ScalarTraits < ScalarType >::magnitudeType	orthonormError (const MV &X) const
	Implements the interface OrthoManager::orthonormError(). More...

Teuchos::ScalarTraits < ScalarType >::magnitudeType	orthogError (const MV &X1, const MV &X2) const
	Implements the interface OrthoManager::orthogError(). More...

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

virtual	~OrthoManager ()
	Destructor. More...

Detailed Description

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

This class provides an interface for orthogonalization managers to provide oblique projectors of the form:

$P_{X,Y} S = S - X \langle Y, X \rangle^{-1} \langle Y, S \rangle\ .$

Such a projector modifies the input in the range on $X$ in order to make the output orthogonal to the range of $Y$ .

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

Definition at line 40 of file AnasaziGenOrthoManager.hpp.

Constructor & Destructor Documentation

template<class ScalarType , class MV , class OP >

Anasazi::GenOrthoManager< ScalarType, MV, OP >::GenOrthoManager ( Teuchos::RCP< const OP > Op = Teuchos::null )

Default constructor.

Definition at line 257 of file AnasaziGenOrthoManager.hpp.

template<class ScalarType , class MV , class OP >

virtual Anasazi::GenOrthoManager< ScalarType, MV, OP >::~GenOrthoManager ( )

inlinevirtual

Destructor.

Definition at line 48 of file AnasaziGenOrthoManager.hpp.

Member Function Documentation

template<class ScalarType , class MV , class OP >

virtual void Anasazi::GenOrthoManager< ScalarType, MV, OP >::projectGen	(	MV &	S,
		Teuchos::Array< Teuchos::RCP< const MV > >	X,
		Teuchos::Array< Teuchos::RCP< const MV > >	Y,
		bool	isBiOrtho,
		Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > >	C = `Teuchos::tuple(Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > >(Teuchos::null))`,
		Teuchos::RCP< MV >	MS = `Teuchos::null`,
		Teuchos::Array< Teuchos::RCP< const MV > >	MX = `Teuchos::tuple(Teuchos::RCP< const MV >(Teuchos::null))`,
		Teuchos::Array< Teuchos::RCP< const MV > >	MY = `Teuchos::tuple(Teuchos::RCP< const MV >(Teuchos::null))`
	)		const

pure virtual

Applies a series of generic projectors.

Given a list of bases X[i] and Y[i] (a projection pair), this method takes a multivector S and applies the projectors

$P_{X[i],Y[i]} S = S - X[i] \langle Y[i], X[i] \rangle^{-1} \langle Y[i], S \rangle\ .$

This operation projects S onto the space orthogonal to the Y[i], along the range of the X[i]. The inner product specified by $\langle \cdot, \cdot \rangle$ is given by innerProd().

Note: The call
projectGen(S, tuple(X1,X2), tuple(Y1,Y2))

is equivalent to the call
projectGen(S, tuple(X2,X1), tuple(Y2,Y1))

The method also returns the coefficients C[i] associated with each projection pair, so that

$S_{in} = S_{out} + \sum_i X[i] C[i]$

and therefore

$C[i] = \langle Y[i], X[i] \rangle^{-1} \langle Y[i], S \rangle\ .$

Lastly, for reasons of efficiency, the user must specify whether the projection pairs are bi-orthonormal with respect to innerProd(), i.e., whether $\langle Y[i], X[i] \rangle = I$ . In the case that the bases are specified to be biorthogonal, the inverse $\langle Y, X \rangle^{-1}$ will not be computed. Furthermore, the user may optionally specifiy the image of S and the projection pairs under the inner product operator getOp().

Parameters

S	[in/out] The multivector to be modified. On output, the columns of `S` will be orthogonal to each `Y[i]`, satisfying $\langle Y[i], S_{out} \rangle = 0$ Also, $S_{in} = S_{out} + \sum_i X[i] C[i]$
X	[in] Multivectors for bases under which $S_{in}$ is modified.
Y	[in] Multivectors for bases to which $S_{out}$ should be orthogonal.
isBiortho	[in] A flag specifying whether the bases `X[i]` and `Y[i]` are biorthonormal, i.e,. whether $\langle Y[i], X[i]\rangle == I$ .
C	[out] Coefficients for reconstructing $S_{in}$ via the bases `X[i]`. If `C[i]` is a non-null pointer and `C[i]` matches the dimensions of `S` and `X[i]`, then the coefficients computed during the orthogonalization routine will be stored in the matrix `C[i]`. If `C[i]` points to a Teuchos::SerialDenseMatrix with size inconsistent with `S` and `X[i]`, then a std::invalid_argument exception will be thrown. Otherwise, if `C.size() < i` or `C[i]` is a null pointer, the caller will not have access to the computed coefficients `C[i]`.
MS	[in/out] If specified by the user, on input `MS` is required to be the image of `S` under the operator getOp(). On output, `MS` will be updated to reflect the changes in `S`.
MX	[in] If specified by the user, `MX[i]` is required to be the image of `X[i]` under the operator getOp().
MY	[in] If specified by the user, `MY[i]` is required to be the image of `Y[i]` under the operator getOp().

Precondition

If X[i] != Teuchos::null or Y[i] != Teuchos::null, then X[i] and Y[i] are required to have the same number of columns, and each should have the same number of rows as S.
For any i != j, $\langle Y[i], X[j] \rangle == 0$ .
If biOrtho == true, $\langle Y[i], X[i]\rangle == I$
Otherwise, if biOrtho == false, then $\langle Y[i], X[i]\rangle$ should be Hermitian positive-definite.
If X[i] and Y[i] have columns and S has columns, then C[i] if specified must be $xc_i \times sc$ .

Implemented in Anasazi::ICGSOrthoManager< ScalarType, MV, OP >.

template<class ScalarType , class MV , class OP >

virtual int Anasazi::GenOrthoManager< ScalarType, MV, OP >::projectAndNormalizeGen	(	MV &	S,
		Teuchos::Array< Teuchos::RCP< const MV > >	X,
		Teuchos::Array< Teuchos::RCP< const MV > >	Y,
		bool	isBiOrtho,
		Teuchos::Array< Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > >	C = `Teuchos::tuple(Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > >(Teuchos::null))`,
		Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > >	B = `Teuchos::null`,
		Teuchos::RCP< MV >	MS = `Teuchos::null`,
		Teuchos::Array< Teuchos::RCP< const MV > >	MX = `Teuchos::tuple(Teuchos::RCP< const MV >(Teuchos::null))`,
		Teuchos::Array< Teuchos::RCP< const MV > >	MY = `Teuchos::tuple(Teuchos::RCP< const MV >(Teuchos::null))`
	)		const

pure virtual

Applies a series of generic projectors and returns an orthonormal basis for the residual data.

Given a list of bases X[i] and Y[i] (a projection pair), this method takes a multivector S and applies the projectors

$P_{X[i],Y[i]} S = S - X[i] \langle Y[i], X[i] \rangle^{-1} \langle Y[i], S \rangle\ .$

These operation project S onto the space orthogonal to the range of the Y[i], along the range of X[i]. The inner product specified by $\langle \cdot, \cdot \rangle$ is given by innerProd().

The method returns in S an orthonormal basis for the residual

$\left( \prod_{i} P_{X[i],Y[i]} \right) S_{in} = S_{out} B\ ,$

where B contains the (not necessarily triangular) coefficients of the residual with respect to the new basis.

The method also returns the coefficients C[i] and B associated with each projection pair, so that

$S_{in} = S_{out} B + \sum_i X[i] C[i]$

and

$C[i] = \langle Y[i], X[i] \rangle^{-1} \langle Y[i], S \rangle\ .$

Lastly, for reasons of efficiency, the user must specify whether the projection pairs are bi-orthonormal with respect to innerProd(), i.e., whether $\langle Y[i], X[i] \rangle = I$ . Furthermore, the user may optionally specifiy the image of S and the projection pairs under the inner product operator getOp().

Parameters

S	[in/out] The multivector to be modified. On output, the columns of `S` will be orthogonal to each `Y[i]`, satisfying $\langle Y[i], S_{out} \rangle = 0$ Also, $S_{in}(1:m,1:n) = S_{out}(1:m,1:rank) B(1:rank,1:n) + \sum_i X[i] C[i]\ ,$ where `m` is the number of rows in `S`, `n` is the number of columns in `S`, and `rank` is the value returned from the method.
X	[in] Multivectors for bases under which $S_{in}$ is modified.
Y	[in] Multivectors for bases to which $S_{out}$ should be orthogonal.
isBiortho	[in] A flag specifying whether the bases `X[i]` and `Y[i]` are biorthonormal, i.e,. whether $\langle Y[i], X[i]\rangle == I$ .
C	[out] Coefficients for reconstructing $S_{in}$ via the bases `X[i]`. 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]` points to a Teuchos::SerialDenseMatrix with size inconsistent with `S` and `X[i]`, then a std::invalid_argument exception will be thrown. Otherwise, if `C.size() < i` or `C[i]` is a null pointer, the caller will not have access to the computed coefficients `C[i]`.
B	[out] The coefficients of the original `S` with respect to the computed basis. If `B` is a non-null pointer and `B` matches the dimensions of `B`, then the coefficients computed during the orthogonalization routine will be stored in `B`, similar to calling innerProd( Sout, Sin, B ); If `B` points to a Teuchos::SerialDenseMatrix with size inconsistent with `S`, then a std::invalid_argument exception will be thrown. Otherwise, if `B` is null, the caller will not have access to the computed coefficients.
MS	[in/out] If specified by the user, on input `MS` is required to be the image of `S` under the operator getOp(). On output, `MS` will be updated to reflect the changes in `S`.
MX	[in] If specified by the user, `MX[i]` is required to be the image of `X[i]` under the operator getOp().
MY	[in] If specified by the user, `MY[i]` is required to be the image of `Y[i]` under the operator getOp().

Note: The matrix B is not necessarily triangular (as in a QR factorization); see the documentation of specific orthogonalization managers.

Precondition

If X[i] != Teuchos::null or Y[i] != Teuchos::null, then X[i] and Y[i] are required to have the same number of columns, and each should have the same number of rows as S.
For any i != j, $\langle Y[i], X[j] \rangle == 0$ .
If biOrtho == true, $\langle Y[i], X[i]\rangle == I$
Otherwise, if biOrtho == false, then $\langle Y[i], X[i]\rangle$ should be Hermitian positive-definite.
If X[i] and Y[i] have columns and S has columns, then C[i] if specified must be $xc_i \times sc$ .
If S has columns, then B if specified must be $sc \times sc$ .

Returns: Rank of the basis computed by this method.

Implemented in Anasazi::ICGSOrthoManager< ScalarType, MV, OP >.

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

AnasaziGenOrthoManager.hpp

Public Member Functions

Detailed Description

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

Constructor & Destructor Documentation

Member Function Documentation

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