## Classes | |

class | Anasazi::HelperTraits< ScalarType > |

Class which defines basic traits for working with different scalar types. More... | |

class | Anasazi::MultiVecTraits< ScalarType, MV > |

Virtual base class which defines basic traits for the multi-vector type. More... | |

class | Anasazi::OperatorTraits< ScalarType, MV, OP > |

Virtual base class which defines basic traits for the operator type. More... |

Anasazi utilizes abstract interfaces for operators and multivectors to enable the leveraging of existing linear algebra libraries. The choice in linear algebra is made through templating, and access to the functionality of the underlying objects is provided via the traits classes Anasazi::MultiVecTraits and Anasazi::OperatorTraits.

Anasazi::MultiVecTraits requires two template arguments:

- a scalar class (
`ScalarType`

), describing the field over which the multivectors are defined, and - a multivector class (
`MV`

).

Because Anasazi implements block eigensolvers, the underlying primitive is a collection of column vectors (a multivector) instead of a single column vector. The purpose of Anasazi::MultiVecTraits is to provide an interface for performing multivector operations (e.g., multivector `AXPY`

). An example illustrating the manipulation of an Epetra_MultiVector using Anasazi::MultiVecTraits follows:

// build some Epetra_MultiVector objects... Epetra_MultiVector A(...), B(...), C(...); // ...and a Teuchos::SerialDenseMatrix Teuchos::SerialDenseMatrix<int,double> D(...); // perform C <- 1.0*A + 0.5*B; Anasazi::MultiVecTraits<double,Epetra_MultiVector>::MvAddMv(1.0, A, 0.5, B, C); // perform C <- -2.0*A*D + 1.0*C Anasazi::MultiVecTraits<double,Epetra_MultiVector>::MvTimesMatAddMv(-2.0, A, D, 1.0, C);

As is customary among large-scale eigenvalue software, Anasazi assumes matrix-free access to the problem operators, i.e., only matrix-vector products are needed. Therefore, Anasazi::OperatorTraits requires three template arguments:

- a scalar class (
`ScalarType`

), describing the field over which the multivectors are defined, - a multivector class (
`MV`

), describing the domain and range of the operator, and - an operator class (
`OP`

).

The Anasazi::OperatorTraits interface provides a single mechanism: the ability to apply an operator of type `OP`

to a multivector of type `MV`

, yielding another multivector of type `MV`

. This is performed as follows:

// build some Epetra_MultiVector objects... Epetra_MultiVector A(...), B(...); // ...and an Epetra operator Epetra_Operator Op(...); // apply the operation B <- Op*A Anasazi::OperatorTraits<double,Epetra_MultiVector,Epetra_Operator>::Apply(Op,A,B);

These interfaces are used throughout Anasazi to manipulate multivectors and apply operators, so that no low-level access to the underlying objects are needed. Hence, Anasazi is independent of the underlying linear algebra data structures (e.g., serial or parallel, real or complex). This allows the generic programming of algorithms for the solution of eigenvalue problems.

Calling methods of MultiVecTraits<ScalarType,MV> requires that a specialization of MultiVecTraits has been implemented for classes `ScalarType`

and `MV`

. In the case of Epetra_MultiVector and Epetra_Operator (which are both defined on the field of doubles), this specialization is provided by the Anasazi adapters to Epetra. Specializations of these traits classes provided by Anasazi are:

- Epetra_MultiVector and Epetra_Operator (with scalar type
`double`

) - Thyra::MultiVectorBase and Thyra::LinearOpBase (with arbitrary scalar type)

This allows Anasazi to be used with any classes that implement the abstract interfaces provided by the Thyra package. - Tpetra::MultiVector and Tpetra::Operator (with arbitrary scalar type)

Tpetra is a templated implementation of Epetra. Tpetra is currently available only in the limited release of Trilinos. - Anasazi::MultiVec and Anasazi::Operator (with arbitrary scalar type)

This allows Anasazi to be used with any classes that implement the abstract base classes Anasazi::MultiVec and Anasazi::Operator.

Additional specializations of Anasazi::MultiVecTraits and Anasazi::OperatorTraits may be created by the user for any other multivector and operator class.

Generated on Wed Apr 13 09:56:59 2011 for Anasazi by 1.6.3