Public Member Functions | |
def | __init__ |
def | innerProd |
def | norm |
def | normalize |
def | orthonormError |
def | orthogError |
def | __init__ |
def | innerProd |
def | norm |
def | normalize |
def | orthonormError |
def | orthogError |
Anasazi's templated virtual class for providing routines for orthogonalization and orthonormalization 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. Chris Baker, Ulrich Hetmaniuk, Rich Lehoucq, and Heidi Thornquist C++ includes: AnasaziOrthoManager.hpp
def PyTrilinos::Anasazi::OrthoManagerEpetra::innerProd | ( | self, | ||
args | ||||
) |
innerProd(self, Epetra_MultiVector X, Epetra_MultiVector Y, Teuchos::SerialDenseMatrix<(int,double)> Z) virtual void Anasazi::OrthoManager< ScalarType, MV >::innerProd(const MV &X, const MV &Y, Teuchos::SerialDenseMatrix< int, ScalarType > &Z) const =0 Provides the inner product defining the orthogonality concepts. All concepts of orthogonality discussed in this class are defined with respect to this inner product. This is potentially different from MultiVecTraits::MvTransMv(). For example, it is customary in many eigensolvers to exploit a mass matrix M for the inner product: $x^HMx$. Parameters: ----------- Z: [out] Z(i,j) contains the inner product of X[i] and Y[i]: \\[ Z(i,j) = \\langle X[i], Y[i] \\rangle \\]
Reimplemented in PyTrilinos::Anasazi::MatOrthoManagerEpetra, and PyTrilinos::Anasazi::MatOrthoManagerEpetra.
def PyTrilinos::Anasazi::OrthoManagerEpetra::innerProd | ( | self, | ||
args | ||||
) |
innerProd(self, Epetra_MultiVector X, Epetra_MultiVector Y, Teuchos::SerialDenseMatrix<(int,double)> Z) virtual void Anasazi::OrthoManager< ScalarType, MV >::innerProd(const MV &X, const MV &Y, Teuchos::SerialDenseMatrix< int, ScalarType > &Z) const =0 Provides the inner product defining the orthogonality concepts. All concepts of orthogonality discussed in this class are defined with respect to this inner product. This is potentially different from MultiVecTraits::MvTransMv(). For example, it is customary in many eigensolvers to exploit a mass matrix M for the inner product: $x^HMx$. Parameters: ----------- Z: [out] Z(i,j) contains the inner product of X[i] and Y[i]: \\[ Z(i,j) = \\langle X[i], Y[i] \\rangle \\]
Reimplemented in PyTrilinos::Anasazi::MatOrthoManagerEpetra, and PyTrilinos::Anasazi::MatOrthoManagerEpetra.
def PyTrilinos::Anasazi::OrthoManagerEpetra::norm | ( | self, | ||
args | ||||
) |
norm(self, Epetra_MultiVector X, std::vector<(Teuchos::ScalarTraits<(double)>::magnitudeType,std::allocator<(Teuchos::ScalarTraits<(double)>::magnitudeType)>)> normvec) virtual void Anasazi::OrthoManager< ScalarType, MV >::norm(const MV &X, std::vector< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType > &normvec) const =0 Provides the norm induced by innerProd(). This computes the norm for each column of a multivector. This is the norm induced by innerProd(): \\[ \\|x\\| = \\sqrt{\\langle x, x \\rangle} \\] Parameters: ----------- normvec: [out] Vector of norms, whose i-th entry corresponds to the i-th column of X normvec.size() == GetNumberVecs(X)
Reimplemented in PyTrilinos::Anasazi::MatOrthoManagerEpetra, and PyTrilinos::Anasazi::MatOrthoManagerEpetra.
def PyTrilinos::Anasazi::OrthoManagerEpetra::norm | ( | self, | ||
args | ||||
) |
norm(self, Epetra_MultiVector X, std::vector<(Teuchos::ScalarTraits<(double)>::magnitudeType,std::allocator<(Teuchos::ScalarTraits<(double)>::magnitudeType)>)> normvec) virtual void Anasazi::OrthoManager< ScalarType, MV >::norm(const MV &X, std::vector< typename Teuchos::ScalarTraits< ScalarType >::magnitudeType > &normvec) const =0 Provides the norm induced by innerProd(). This computes the norm for each column of a multivector. This is the norm induced by innerProd(): \\[ \\|x\\| = \\sqrt{\\langle x, x \\rangle} \\] Parameters: ----------- normvec: [out] Vector of norms, whose i-th entry corresponds to the i-th column of X normvec.size() == GetNumberVecs(X)
Reimplemented in PyTrilinos::Anasazi::MatOrthoManagerEpetra, and PyTrilinos::Anasazi::MatOrthoManagerEpetra.
def PyTrilinos::Anasazi::OrthoManagerEpetra::normalize | ( | self, | ||
args | ||||
) |
normalize(self, Epetra_MultiVector X, Teuchos::RCP<(Teuchos::SerialDenseMatrix<(int,double)>)> B = Teuchos::null) -> int virtual int Anasazi::OrthoManager< ScalarType, MV >::normalize(MV &X, Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > B=Teuchos::null) const =0 This method takes a multivector X and attempts to compute a basis for $colspan(X)$. This basis is orthonormal 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 be modified. On output, the first rank columns of X satisfy \\[ \\langle X[i], X[j] \\rangle = \\delta_{ij}\\ . \\] Also, \\[ X_{in}(1:m,1:n) = X_{out}(1:m,1:rank) B(1:rank,1:n)\\ , \\] where m is the number of rows in X and n is the number of columns in X. B: [out] The coefficients of the original X 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 If B points to a Teuchos::SerialDenseMatrix with size inconsistent with X, then a std::invalid_argument exception will be thrown. Otherwise, if B is null, the caller will not have access to the computed coefficients. This matrix is not necessarily triangular (as in a QR factorization); see the documentation of specific orthogonalization managers. Rank of the basis computed by this method, less than or equal to the number of columns in X. This specifies how many columns in the returned X and rows in the returned B are valid.
Reimplemented in PyTrilinos::Anasazi::MatOrthoManagerEpetra, and PyTrilinos::Anasazi::MatOrthoManagerEpetra.
def PyTrilinos::Anasazi::OrthoManagerEpetra::normalize | ( | self, | ||
args | ||||
) |
normalize(self, Epetra_MultiVector X, Teuchos::RCP<(Teuchos::SerialDenseMatrix<(int,double)>)> B = Teuchos::null) -> int virtual int Anasazi::OrthoManager< ScalarType, MV >::normalize(MV &X, Teuchos::RCP< Teuchos::SerialDenseMatrix< int, ScalarType > > B=Teuchos::null) const =0 This method takes a multivector X and attempts to compute a basis for $colspan(X)$. This basis is orthonormal 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 be modified. On output, the first rank columns of X satisfy \\[ \\langle X[i], X[j] \\rangle = \\delta_{ij}\\ . \\] Also, \\[ X_{in}(1:m,1:n) = X_{out}(1:m,1:rank) B(1:rank,1:n)\\ , \\] where m is the number of rows in X and n is the number of columns in X. B: [out] The coefficients of the original X 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 If B points to a Teuchos::SerialDenseMatrix with size inconsistent with X, then a std::invalid_argument exception will be thrown. Otherwise, if B is null, the caller will not have access to the computed coefficients. This matrix is not necessarily triangular (as in a QR factorization); see the documentation of specific orthogonalization managers. Rank of the basis computed by this method, less than or equal to the number of columns in X. This specifies how many columns in the returned X and rows in the returned B are valid.
Reimplemented in PyTrilinos::Anasazi::MatOrthoManagerEpetra, and PyTrilinos::Anasazi::MatOrthoManagerEpetra.
def PyTrilinos::Anasazi::OrthoManagerEpetra::orthogError | ( | self, | ||
args | ||||
) |
orthogError(self, Epetra_MultiVector X1, Epetra_MultiVector X2) -> magnitudeType virtual Teuchos::ScalarTraits<ScalarType>::magnitudeType Anasazi::OrthoManager< ScalarType, MV >::orthogError(const MV &X1, const MV &X2) const =0 This method computes the error in orthogonality of two multivectors. This method return some measure of $\\| \\langle X1, X2 \\rangle \\| $. See the documentation of specific orthogonalization managers.
Reimplemented in PyTrilinos::Anasazi::MatOrthoManagerEpetra, and PyTrilinos::Anasazi::MatOrthoManagerEpetra.
def PyTrilinos::Anasazi::OrthoManagerEpetra::orthogError | ( | self, | ||
args | ||||
) |
orthogError(self, Epetra_MultiVector X1, Epetra_MultiVector X2) -> magnitudeType virtual Teuchos::ScalarTraits<ScalarType>::magnitudeType Anasazi::OrthoManager< ScalarType, MV >::orthogError(const MV &X1, const MV &X2) const =0 This method computes the error in orthogonality of two multivectors. This method return some measure of $\\| \\langle X1, X2 \\rangle \\| $. See the documentation of specific orthogonalization managers.
Reimplemented in PyTrilinos::Anasazi::MatOrthoManagerEpetra, and PyTrilinos::Anasazi::MatOrthoManagerEpetra.
def PyTrilinos::Anasazi::OrthoManagerEpetra::orthonormError | ( | self, | ||
args | ||||
) |
orthonormError(self, Epetra_MultiVector X) -> magnitudeType virtual Teuchos::ScalarTraits< ScalarType >::magnitudeType Anasazi::OrthoManager< ScalarType, MV >::orthonormError(const MV &X) const =0 This method computes the error in orthonormality of a multivector. This method return some measure of $\\| \\langle X, X \\rangle - I \\| $. See the documentation of specific orthogonalization managers.
Reimplemented in PyTrilinos::Anasazi::MatOrthoManagerEpetra, and PyTrilinos::Anasazi::MatOrthoManagerEpetra.
def PyTrilinos::Anasazi::OrthoManagerEpetra::orthonormError | ( | self, | ||
args | ||||
) |
orthonormError(self, Epetra_MultiVector X) -> magnitudeType virtual Teuchos::ScalarTraits< ScalarType >::magnitudeType Anasazi::OrthoManager< ScalarType, MV >::orthonormError(const MV &X) const =0 This method computes the error in orthonormality of a multivector. This method return some measure of $\\| \\langle X, X \\rangle - I \\| $. See the documentation of specific orthogonalization managers.
Reimplemented in PyTrilinos::Anasazi::MatOrthoManagerEpetra, and PyTrilinos::Anasazi::MatOrthoManagerEpetra.