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Anasazi::GenOrthoManager< ScalarType, MV, OP > Class Template Referenceabstract

#include <AnasaziGenOrthoManager.hpp>

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

Public Member Functions

Constructor/Destructor
 GenOrthoManager (Teuchos::RCP< const OP > Op=Teuchos::null)
 Default constructor.
 
virtual ~GenOrthoManager ()
 Destructor.
 
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.
 
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.
 
- Public Member Functions inherited from Anasazi::MatOrthoManager< ScalarType, MV, OP >
 MatOrthoManager (Teuchos::RCP< const OP > Op=Teuchos::null)
 Default constructor.
 
virtual ~MatOrthoManager ()
 Destructor.
 
virtual void setOp (Teuchos::RCP< const OP > Op)
 Set operator used for inner product.
 
virtual Teuchos::RCP< const OP > getOp () const
 Get operator used for inner product.
 
int getOpCounter () const
 Retrieve operator counter.
 
void resetOpCounter ()
 Reset the operator counter to zero.
 
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.
 
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.
 
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.
 
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.
 
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.
 
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.
 
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.
 
void innerProd (const MV &X, const MV &Y, Teuchos::SerialDenseMatrix< int, ScalarType > &Z) const
 Implements the interface OrthoManager::innerProd().
 
void norm (const MV &X, std::vector< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType > &normvec) const
 Implements the interface OrthoManager::norm().
 
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().
 
int normalize (MV &X, Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > B=Teuchos::null) const
 Implements the interface OrthoManager::normalize().
 
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().
 
Teuchos::ScalarTraits< ScalarType >::magnitudeType orthonormError (const MV &X) const
 Implements the interface OrthoManager::orthonormError().
 
Teuchos::ScalarTraits< ScalarType >::magnitudeType orthogError (const MV &X1, const MV &X2) const
 Implements the interface OrthoManager::orthogError().
 
- Public Member Functions inherited from Anasazi::OrthoManager< ScalarType, MV >
 OrthoManager ()
 Default constructor.
 
virtual ~OrthoManager ()
 Destructor.
 

Additional Inherited Members

- Protected Attributes inherited from Anasazi::MatOrthoManager< ScalarType, MV, OP >
Teuchos::RCP< const OP > _Op
 
bool _hasOp
 
int _OpCounter
 

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 72 of file AnasaziGenOrthoManager.hpp.

Constructor & Destructor Documentation

◆ GenOrthoManager()

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 289 of file AnasaziGenOrthoManager.hpp.

◆ ~GenOrthoManager()

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

Destructor.

Definition at line 80 of file AnasaziGenOrthoManager.hpp.

Member Function Documentation

◆ projectGen()

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))
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.
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 $xc_i$ columns and S has $sc$ columns, then C[i] if specified must be $xc_i \times sc$.

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

◆ projectAndNormalizeGen()

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 );
void innerProd(const MV &X, const MV &Y, Teuchos::SerialDenseMatrix< int, ScalarType > &Z) const
Implements the interface OrthoManager::innerProd().
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 $xc_i$ columns and S has $sc$ columns, then C[i] if specified must be $xc_i \times sc$.
  • If S has $sc$ 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: