While the use of the RTOpPack::RTOpT interface class and the single Thyra::VectorBase::applyOp() function provide an elegant and efficient solution for the interoperability of vector interfaces, it is not the easiest API for developing ANAs. However, a number of easy to use C++ wrapper functions for many different vector and multi-vector operations is already provided:
These C++ wrapper functions rely on pre-implemented RTOpPack::RTOpT subclasses. Adding new RTOpPack::RTOpT subclasses and new wrapper functions for new vector and multi-vector reduction/transformation operations is an easy matter for an experienced C++ developer who understands RTOpPack::RTOpT (please contact rabartl@sandia.gov if you need a new vector or multi-vector operation that is not already supported).
Warning! using the utility classes below it is very easy to obtain direct access to vector and multi-vector elements but in general, this is a very bad idea. However, as described in this report, there are some types of ANAs that require direct element access to certain kinds of vectors and multi-vectors (for example, vectors and multi-vectors that lie is the domain space of a multi-vector). The following utility classes streamline creating and using explicit views.
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Thyra::ExplicitVectorViewcreates a (const) non-mutable explicit view of aconst Thyra::VectorBaseobject, allows direct access to vector elements and then frees the view in the destructor. -
Thyra::ExplicitMutableVectorViewcreates a (non-const) mutable explicit view of aThyra::VectorBaseobject, allows direct access to vector elements and then frees the view in the destructor. -
Thyra::ExplicitMultiVectorViewcreates a (const) non-mutable explicit view of aconst Thyra::MultiVectorBaseobject, allows direct access to multi-vector elements and then frees the view in the destructor. -
Thyra::ExplicitMutableMultiVectorViewcreates a (non-const) mutable explicit view of aThyra::MultiVectorBaseobject, allows direct access to multi-vector elements and then frees the view in the destructor.
One of the big advantages of using the above utility classes in addition to their convenience is that views are freed in destructors and these view will be freed even in the event that an exception is thrown. The use of these view classes is quite straightforward.
One of the big advantages of having a set of abstract interfaces to operators and vectors is that it is quite easy to define some very useful aggregate subclasses that allow one or more individual objects be treated as a single object (see the "Composite" and "Decorator" design patterns in the GoF's "Design Patterns" book).
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Product vector spaces, vectors and multi-vectors
One particularly useful category of composite linear algebra objects is the product vector space
where 
, for 
, are different constituent vector spaces. Product vector spaces give rise to product vectors![\[ x = \left[\begin{array}{c} v_1 \\ v_2 \\ \vdots \\ v_m \end{array}\right] \]](form_3.png)
(where
) and product multi-vectors![\[ X = \left[\begin{array}{c} V_1 \\ V_2 \\ \vdots \\ V_m \end{array}\right]. \]](form_5.png)
(where
and 
is the domain space for the multi-vectors).Very general concrete implementations of the product vector space, vector and multi-vector interfaces described here are provided and are shown below:
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Thyra::ProductVectorSpaceis a general concrete implementation ofThyra::ProductVectorSpaceBasethat should be sufficient for most use cases. -
Thyra::ProductVectoris a general concrete implementation ofThyra::ProductVectorBasethat should be sufficient for most use cases. -
Thyra::ProductMultiVectoris a general concrete implementation ofThyra::ProductMultiVectorBasethat should be sufficient for most use cases. (ToDo: This needs to be implemented!)
Note that the above concrete subclasses are very efficient for must, but not all, possible use cases for such composite objects.
When using product vector spaces, product vectors and product multi-vectors it is generally the case where a concrete
Thyra::ProductVectorSpaceobject is first created and thenThyra::ProductVectorandThyra::ProductMultiVectorobjects are created by the functionsThyra::ProductVectorSpace::createMember()andThyra::ProductVectorSpace::createMembers(). See this example of how product vector spaces are used. -
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Miscellaneous aggregate linear operators
There are several different types of useful composite
Thyra::LinearOpBasesubclasses that one can define. A few useful composite linear operator subclasses are shown below:-
Thyra::DiagonalLinearOpis a simple concrete subclass that defines a diagonalThyra::LinearOpBase
out of any Thyra::VectorBaseobject for the diagonal
. -
Thyra::ScaledAdjointLinearOpis a simple concrete decorator subclass that defines an implicit scaled and/or adjoined (or transposed) linear operator
. -
Thyra::MultiplicativeLinearOpis a simple concrete composite subclass that defines a composite multiplicativeThyra::LinearOpBaseof the form
composed out of one or more constituent linear operators 
.
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This is basic testing software for Thyra:
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Thyra::LinearOpTesteris a unit testing class that validates the implementation of aThyra::LinearOpBaseobject by checking its linear properties, and/or its adjoint, and/or symmetry. In addition, it can check if two linear operators are the same. -
Thyra::MultiVectorTesteris a unit testing class that validates the implementation of aThyra::MultiVectorBaseobject. This class exposes aThyra::LinearOpTesterobject for testing theLinearOpBasebase interface ofThyra::MultiVectorBase. -
Thyra::VectorTesteris a unit testing class that validates the implementation of aThyra::VectorBaseobject. This class exposes aThyra::MultiVectorTesterobject for testing theMultiVectorBasebase interface ofThyra::VectorBase. -
Thyra::VectorSpaceTesteris a unit testing class that accepts anyThyra::VectorSpaceBaseobject and then proceeds to create a number ofThyra::VectorBaseandThyra::MultiVectorBaseobjects and then and validates all of these objects. This class class, therefore, is a unit testing class for all three interfacesThyra::VectorSpaceBase,Thyra::VectorBase, andThyra::MultiVectorBase. -
Thyra::VectorStdOpsTesteris a unit testing class that accepts anyThyra::VectorSpaceBaseobject and then tests all of the standard vector RTOp wrappers documented here. -
Thyra::MultiVectorStdOpsTesteris a unit testing class that accepts anyThyra::VectorSpaceBaseobject and then tests all of the standard multi-vector RTOp wrappers documented here.
There is software included in the Thyra package to support basic testing and debugging.
First, 100/% general output stream operators for any Thyra::VectorBase or Thyra::LinearOpBase object are provided in the following operator functions:
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Thyra::operator<<(std::ostream& o, const Thyra::VectorBase<Scalar>& v)is an output stream operator for printingThyra::VectorBaseobjects. -
Thyra::operator<<(std::ostream& o, const Thyra::LinearOpBase<Scalar>& M)is an output stream operator for printingThyra::LinearOpBase(and therefore alsoThyra::MultiVectorBase) objects.
