Anasazi::BasicOrthoManager< ScalarType, MV, OP > Class Template Reference

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

#include <AnasaziBasicOrthoManager.hpp>

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

List of all members.


Public Member Functions
Constructor/Destructor
	BasicOrthoManager (Teuchos::RefCountPtr< const OP > Op=Teuchos::null, const MagnitudeType kappa=SCT::magnitude(1.5625))
	Constructor specifying re-orthogonalization tolerance.
	~BasicOrthoManager ()
	Destructor.
Accessor routines
void	setKappa (const MagnitudeType kappa)
	Set parameter for re-orthogonalization threshhold.
MagnitudeType	getKappa () const
	Return parameter for re-orthogonalization threshhold.
Orthogonalization methods
void	project (MV &X, Teuchos::RefCountPtr< MV > MX, Teuchos::Array< Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::Array< Teuchos::RefCountPtr< 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().
void	project (MV &X, Teuchos::Array< Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::Array< Teuchos::RefCountPtr< const MV > > Q) const
	This method calls project(X,Teuchos::null,C,Q); see documentation for that function.
int	normalize (MV &X, Teuchos::RefCountPtr< MV > MX, Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > B) const
	This method takes a multivector `X` and attempts to compute an orthonormal basis for , with respect to innerProd().
int	normalize (MV &X, Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > B) const
	This method calls normalize(X,Teuchos::null,B); see documentation for that function.
int	projectAndNormalize (MV &X, Teuchos::RefCountPtr< MV > MX, Teuchos::Array< Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > B, Teuchos::Array< Teuchos::RefCountPtr< const MV > > Q) const
	Given a set of bases `Q[i]` and a multivector `X`, this method computes an orthonormal basis for $colspan(X) - \sum_i colspan(Q[i])$ .
int	projectAndNormalize (MV &X, Teuchos::Array< Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > B, Teuchos::Array< Teuchos::RefCountPtr< const MV > > Q) const
	This method calls projectAndNormalize(X,Teuchos::null,C,B,Q); see documentation for that function.
Error methods
Teuchos::ScalarTraits< ScalarType >::magnitudeType	orthonormError (const MV &X) const
	This method computes the error in orthonormality of a multivector, measured as the Frobenius norm of the difference `innerProd(X,Y) - I`.
Teuchos::ScalarTraits< ScalarType >::magnitudeType	orthonormError (const MV &X, Teuchos::RefCountPtr< const MV > MX) const
	This method computes the error in orthonormality of a multivector, measured as the Frobenius norm of the difference `innerProd(X,Y) - I`. The method has the option of exploiting a caller-provided `MX`.
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)`.
Teuchos::ScalarTraits< ScalarType >::magnitudeType	orthogError (const MV &X1, Teuchos::RefCountPtr< 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`.

Detailed Description

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

An implementation of the Anasazi::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 55 of file AnasaziBasicOrthoManager.hpp.

Constructor & Destructor Documentation

template<class ScalarType, class MV, class OP>

Anasazi::BasicOrthoManager< ScalarType, MV, OP >::BasicOrthoManager ( Teuchos::RefCountPtr< const OP > Op = Teuchos::null,

const MagnitudeType kappa = SCT::magnitude(1.5625)

)

Constructor specifying re-orthogonalization tolerance.

Definition at line 272 of file AnasaziBasicOrthoManager.hpp.

template<class ScalarType, class MV, class OP>

Anasazi::BasicOrthoManager< ScalarType, MV, OP >::~BasicOrthoManager ( ) [inline]

Destructor.

Definition at line 72 of file AnasaziBasicOrthoManager.hpp.

Member Function Documentation

template<class ScalarType, class MV, class OP>

void Anasazi::BasicOrthoManager< ScalarType, MV, OP >::setKappa ( const MagnitudeType kappa ) [inline]

Set parameter for re-orthogonalization threshhold.

Definition at line 80 of file AnasaziBasicOrthoManager.hpp.

template<class ScalarType, class MV, class OP>

MagnitudeType Anasazi::BasicOrthoManager< ScalarType, MV, OP >::getKappa ( ) const [inline]

Return parameter for re-orthogonalization threshhold.

Definition at line 83 of file AnasaziBasicOrthoManager.hpp.

template<class ScalarType, class MV, class OP>

void Anasazi::BasicOrthoManager< ScalarType, MV, OP >::project ( MV & X,

Teuchos::RefCountPtr< MV > MX,

Teuchos::Array< Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > > C,

Teuchos::Array< Teuchos::RefCountPtr< 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 $ MX != 0$ : On input, this is expected to be consistent with X. On output, this is updated consistent with updates to X. If $ MX == 0$ or $ Op == 0$ : 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 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 Anasazi::MatOrthoManager< ScalarType, MV, OP >.
Definition at line 464 of file AnasaziBasicOrthoManager.hpp.

template<class ScalarType, class MV, class OP>

void Anasazi::BasicOrthoManager< ScalarType, MV, OP >::project ( MV & X,

Teuchos::Array< Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > > C,

Teuchos::Array< Teuchos::RefCountPtr< const MV > > Q

) const [inline, virtual]

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

Reimplemented from Anasazi::MatOrthoManager< ScalarType, MV, OP >.
Definition at line 125 of file AnasaziBasicOrthoManager.hpp.

template<class ScalarType, class MV, class OP>

int Anasazi::BasicOrthoManager< ScalarType, MV, OP >::normalize ( MV & X,

Teuchos::RefCountPtr< MV > MX,

Teuchos::RefCountPtr< 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 $ MX != 0$ : On input, this is expected to be consistent with X. On output, this is updated consistent with updates to X. If $ MX == 0$ or $ Op == 0$ : 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 Anasazi::MatOrthoManager< ScalarType, MV, OP >.
Definition at line 453 of file AnasaziBasicOrthoManager.hpp.

template<class ScalarType, class MV, class OP>

int Anasazi::BasicOrthoManager< ScalarType, MV, OP >::normalize ( MV & X,

Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > B

) const [inline, virtual]

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

Reimplemented from Anasazi::MatOrthoManager< ScalarType, MV, OP >.
Definition at line 163 of file AnasaziBasicOrthoManager.hpp.

template<class ScalarType, class MV, class OP>

int Anasazi::BasicOrthoManager< ScalarType, MV, OP >::projectAndNormalize ( MV & X,

Teuchos::RefCountPtr< MV > MX,

Teuchos::Array< Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > > C,

Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > B,

Teuchos::Array< Teuchos::RefCountPtr< const MV > > Q

) const [virtual]

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 $ MX != 0$ : On input, this is expected to be consistent with X. On output, this is updated consistent with updates to X. If $ MX == 0$ or $ Op == 0$ : 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 a std::invalid_argument 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.

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 Anasazi::MatOrthoManager< ScalarType, MV, OP >.
Definition at line 310 of file AnasaziBasicOrthoManager.hpp.

template<class ScalarType, class MV, class OP>

int Anasazi::BasicOrthoManager< ScalarType, MV, OP >::projectAndNormalize ( MV & X,

Teuchos::Array< Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > > C,

Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > B,

Teuchos::Array< Teuchos::RefCountPtr< const MV > > Q

) const [inline, virtual]

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

Reimplemented from Anasazi::MatOrthoManager< ScalarType, MV, OP >.
Definition at line 207 of file AnasaziBasicOrthoManager.hpp.

template<class ScalarType, class MV, class OP>

Teuchos::ScalarTraits<ScalarType>::magnitudeType Anasazi::BasicOrthoManager< ScalarType, MV, OP >::orthonormError ( const MV & X ) const [inline, virtual]

This method computes the error in orthonormality of a multivector, measured as the Frobenius norm of the difference innerProd(X,Y) - I.

Reimplemented from Anasazi::MatOrthoManager< ScalarType, MV, OP >.
Definition at line 223 of file AnasaziBasicOrthoManager.hpp.

template<class ScalarType, class MV, class OP>

Teuchos::ScalarTraits< ScalarType >::magnitudeType Anasazi::BasicOrthoManager< ScalarType, MV, OP >::orthonormError ( const MV & X,

Teuchos::RefCountPtr< const MV > MX

) const [virtual]

This method computes the error in orthonormality of a multivector, measured as the Frobenius norm of the difference innerProd(X,Y) - I. The method has the option of exploiting a caller-provided MX.

Implements Anasazi::MatOrthoManager< ScalarType, MV, OP >.
Definition at line 284 of file AnasaziBasicOrthoManager.hpp.

template<class ScalarType, class MV, class OP>

Teuchos::ScalarTraits<ScalarType>::magnitudeType Anasazi::BasicOrthoManager< ScalarType, MV, OP >::orthogError ( const MV & X1,

const MV & X2

) const [inline, virtual]

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

Reimplemented from Anasazi::MatOrthoManager< ScalarType, MV, OP >.
Definition at line 238 of file AnasaziBasicOrthoManager.hpp.

template<class ScalarType, class MV, class OP>

Teuchos::ScalarTraits< ScalarType >::magnitudeType Anasazi::BasicOrthoManager< ScalarType, MV, OP >::orthogError ( const MV & X1,

Teuchos::RefCountPtr< 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 Anasazi::MatOrthoManager< ScalarType, MV, OP >.
Definition at line 299 of file AnasaziBasicOrthoManager.hpp.

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

AnasaziBasicOrthoManager.hpp

Generated on Thu Sep 18 12:31:38 2008 for Anasazi by

1.3.9.1

Anasazi::BasicOrthoManager< ScalarType, MV, OP > Class Template Reference

Public Member Functions

Detailed Description

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

Constructor & Destructor Documentation

Member Function Documentation

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