Anasazi Version of the Day

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 multivector 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:
ScalarType
), describing the field over which the multivectors are defined, andMV
).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 largescale eigenvalue software, Anasazi assumes matrixfree access to the problem operators, i.e., only matrixvector products are needed. Therefore, Anasazi::OperatorTraits requires three template arguments:
ScalarType
), describing the field over which the multivectors are defined,MV
), describing the domain and range of the operator, andOP
).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 lowlevel 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:
double
)Additional specializations of Anasazi::MultiVecTraits and Anasazi::OperatorTraits may be created by the user for any other multivector and operator class.