Anasazi Operator/Vector Interfaces

Classes
class	Anasazi::HelperTraits< ScalarType >
	Class which defines basic traits for working with different scalar types. More...
class	Anasazi::MultiVecTraits< ScalarType, MV >
	Traits class which defines basic operations on multivectors. More...
class	Anasazi::OperatorTraits< ScalarType, MV, OP >
	Virtual base class which defines basic traits for the operator type. More...

Detailed Description

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(...);

typedef Anasazi::MultiVecTraits<double, Epetra_MultiVector> MVT;

// perform C <- 1.0*A + 0.5*B;
MVT::MvAddMv(1.0, A, 0.5, B, C);

// perform C <- -2.0*A*D + 1.0*C
MVT::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
typedef Anasazi::OperatorTraits<double, Epetra_MultiVector, Epetra_Operator> OPT;
OPT::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).
• 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.