Anasazi::OrthoManager< ScalarType, MV > Class Template Reference

Anasazi's templated virtual class for providing routines for orthogonalization and orthonormzalition of multivectors. More...

#include <AnasaziOrthoManager.hpp>

Inheritance diagram for Anasazi::OrthoManager< ScalarType, MV >:

Anasazi::MatOrthoManager< ScalarType, MV, OP > Anasazi::BasicOrthoManager< ScalarType, MV, OP > Anasazi::SVQBOrthoManager< ScalarType, MV, OP > List of all members.

Public Member Functions

Constructor/Destructor
 OrthoManager ()
 Default constructor.
virtual ~OrthoManager ()
 Destructor.
Orthogonalization methods
virtual void innerProd (const MV &X, const MV &Y, Teuchos::SerialDenseMatrix< int, ScalarType > &Z) const =0
 Provides the inner product defining the orthogonality concepts.
virtual void norm (const MV &X, std::vector< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType > *normvec) const =0
 Provides the norm induced by innerProd().
virtual void project (MV &X, Teuchos::Array< Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > > C, Teuchos::Array< Teuchos::RefCountPtr< const MV > > Q) const =0
 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().
virtual int normalize (MV &X, Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > B) const =0
 This method takes a multivector X and attempts to compute an orthonormal basis for $colspan(X)$, with respect to innerProd().
virtual 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 =0
 Given a set of bases Q[i] and a multivector X, this method computes an orthonormal basis for $colspan(X) - \sum_i colspan(Q[i])$.
Error methods
virtual Teuchos::ScalarTraits<
ScalarType >::magnitudeType 
orthonormError (const MV &X) const =0
 This method computes the error in orthonormality of a multivector.
virtual Teuchos::ScalarTraits<
ScalarType >::magnitudeType 
orthogError (const MV &X1, const MV &X2) const =0
 This method computes the error in orthogonality of two multivectors.

Detailed Description

template<class ScalarType, class MV>
class Anasazi::OrthoManager< ScalarType, MV >

Anasazi's templated virtual class for providing routines for orthogonalization and orthonormzalition of multivectors.

This class defines concepts of orthogonality through the definition of an inner product. It also provides computational routines for orthogonalization.

A concrete implementation of this class is necessary. The user can create their own implementation if those supplied are not suitable for their needs.

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

Definition at line 74 of file AnasaziOrthoManager.hpp.


Constructor & Destructor Documentation

template<class ScalarType, class MV>
Anasazi::OrthoManager< ScalarType, MV >::OrthoManager  )  [inline]
 

Default constructor.

Definition at line 79 of file AnasaziOrthoManager.hpp.

template<class ScalarType, class MV>
virtual Anasazi::OrthoManager< ScalarType, MV >::~OrthoManager  )  [inline, virtual]
 

Destructor.

Definition at line 82 of file AnasaziOrthoManager.hpp.


Member Function Documentation

template<class ScalarType, class MV>
virtual void Anasazi::OrthoManager< ScalarType, MV >::innerProd const MV &  X,
const MV &  Y,
Teuchos::SerialDenseMatrix< int, ScalarType > &  Z
const [pure virtual]
 

Provides the inner product defining the orthogonality concepts.

All concepts of orthogonality discussed in this class are with respect to this inner product.

Note:
This can be different than the MvTransMv method from the multivector class. For example, if there is a mass matrix M, then this might be the M inner product ($x^HMx$).

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

template<class ScalarType, class MV>
virtual void Anasazi::OrthoManager< ScalarType, MV >::norm const MV &  X,
std::vector< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType > *  normvec
const [pure virtual]
 

Provides the norm induced by innerProd().

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

template<class ScalarType, class MV>
virtual void Anasazi::OrthoManager< ScalarType, MV >::project MV &  X,
Teuchos::Array< Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > > >  C,
Teuchos::Array< Teuchos::RefCountPtr< const MV > >  Q
const [pure 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].

Parameters:
X [in/out] The multivector to be modified. On output, X will be orthogonal to Q[i] with respect to innerProd().
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.

Implemented in Anasazi::BasicOrthoManager< ScalarType, MV, OP >, Anasazi::MatOrthoManager< ScalarType, MV, OP >, and Anasazi::SVQBOrthoManager< ScalarType, MV, OP >.

template<class ScalarType, class MV>
virtual int Anasazi::OrthoManager< ScalarType, MV >::normalize MV &  X,
Teuchos::RefCountPtr< Teuchos::SerialDenseMatrix< int, ScalarType > >  B
const [pure virtual]
 

This method takes a multivector X and attempts to compute an orthonormal basis for $colspan(X)$, with respect to innerProd().

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.

Parameters:
X [in/out] The multivector to the modified. On output, X will have some number of orthonormal columns (with respect to innerProd()).
B [out] The coefficients of the original X with respect to the computed basis. This matrix is not necessarily triangular; see the documentation for specific orthogonalization managers.
Returns:
Rank of the basis computed by this method.

Implemented in Anasazi::BasicOrthoManager< ScalarType, MV, OP >, Anasazi::MatOrthoManager< ScalarType, MV, OP >, and Anasazi::SVQBOrthoManager< ScalarType, MV, OP >.

template<class ScalarType, class MV>
virtual int Anasazi::OrthoManager< ScalarType, MV >::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 [pure 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.

Note:
This routine guarantees both the orthgonality constraints against the Q[i] as well as the orthonormality constraints. Therefore, this method is not necessarily equivalent to calling project() followed by a call to normalize(); see the documentation for specific orthogonalization managers.
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()).
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. This matrix is not necessarily triangular; see the documentation for specific orthogonalization managers.
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.

Implemented in Anasazi::BasicOrthoManager< ScalarType, MV, OP >, Anasazi::MatOrthoManager< ScalarType, MV, OP >, and Anasazi::SVQBOrthoManager< ScalarType, MV, OP >.

template<class ScalarType, class MV>
virtual Teuchos::ScalarTraits< ScalarType >::magnitudeType Anasazi::OrthoManager< ScalarType, MV >::orthonormError const MV &  X  )  const [pure virtual]
 

This method computes the error in orthonormality of a multivector.

Implemented in Anasazi::BasicOrthoManager< ScalarType, MV, OP >, Anasazi::MatOrthoManager< ScalarType, MV, OP >, and Anasazi::SVQBOrthoManager< ScalarType, MV, OP >.

template<class ScalarType, class MV>
virtual Teuchos::ScalarTraits<ScalarType>::magnitudeType Anasazi::OrthoManager< ScalarType, MV >::orthogError const MV &  X1,
const MV &  X2
const [pure virtual]
 

This method computes the error in orthogonality of two multivectors.

Implemented in Anasazi::BasicOrthoManager< ScalarType, MV, OP >, Anasazi::MatOrthoManager< ScalarType, MV, OP >, and Anasazi::SVQBOrthoManager< ScalarType, MV, OP >.


The documentation for this class was generated from the following file:
Generated on Thu Sep 18 12:31:39 2008 for Anasazi by doxygen 1.3.9.1