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Templated interface to vector reduction/transformation operators {abstract}. More...
#include <RTOpPack_RTOpT_decl.hpp>
Private Member Functions  
void  throwNoReductError () const 
Private Attributes  
std::string  op_name_ 
public types  
typedef PrimitiveTypeTraits < Scalar, Scalar > ::primitiveType  primitive_value_type 
Reduction object functions (NVI)  
void  get_reduct_type_num_entries (const Ptr< int > &num_values, const Ptr< int > &num_indexes, const Ptr< int > &num_chars) const 
Get the number of entries of each basic data type in the externalized state for a reduction object for this operator. More...  
Teuchos::RCP< ReductTarget >  reduct_obj_create () const 
Creates a new reduction target object initialized and ready to be used in a reduction. More...  
void  reduce_reduct_objs (const ReductTarget &in_reduct_obj, const Ptr< ReductTarget > &inout_reduct_obj) const 
Reduce intermediate reduction target objects. More...  
void  reduct_obj_reinit (const Ptr< ReductTarget > &reduct_obj) const 
Reinitialize an already created reduction object. More...  
void  extract_reduct_obj_state (const ReductTarget &reduct_obj, const ArrayView< primitive_value_type > &value_data, const ArrayView< index_type > &index_data, const ArrayView< char_type > &char_data) const 
Extract the state of an already created reduction object. More...  
void  load_reduct_obj_state (const ArrayView< const primitive_value_type > &value_data, const ArrayView< const index_type > &index_data, const ArrayView< const char_type > &char_data, const Ptr< ReductTarget > &reduct_obj) const 
Load the state of an already created reduction object given arrays of primitive objects. More...  
Operator functions (NIV)  
std::string  op_name () const 
Return the name (as a nullterminated Cstyle string) of the operator. More...  
bool  coord_invariant () const 
Returns true if this operator is coordinate invariant. More...  
Range1D  range () const 
Returns the continuous range of elements that this operator is defined over. More...  
void  apply_op (const ArrayView< const ConstSubVectorView< Scalar > > &sub_vecs, const ArrayView< const SubVectorView< Scalar > > &targ_sub_vecs, const Ptr< ReductTarget > &reduct_obj) const 
Apply the reduction/transformation operator to a set of subvectors. More...  
Protected virtual functions to be overridden by subclasses.  
virtual void  get_reduct_type_num_entries_impl (const Ptr< int > &num_values, const Ptr< int > &num_indexes, const Ptr< int > &num_chars) const 
virtual Teuchos::RCP < ReductTarget >  reduct_obj_create_impl () const 
virtual void  reduce_reduct_objs_impl (const ReductTarget &in_reduct_obj, const Ptr< ReductTarget > &inout_reduct_obj) const 
virtual void  reduct_obj_reinit_impl (const Ptr< ReductTarget > &reduct_obj) const 
virtual void  extract_reduct_obj_state_impl (const ReductTarget &reduct_obj, const ArrayView< primitive_value_type > &value_data, const ArrayView< index_type > &index_data, const ArrayView< char_type > &char_data) const 
virtual void  load_reduct_obj_state_impl (const ArrayView< const primitive_value_type > &value_data, const ArrayView< const index_type > &index_data, const ArrayView< const char_type > &char_data, const Ptr< ReductTarget > &reduct_obj) const 
virtual std::string  op_name_impl () const 
virtual bool  coord_invariant_impl () const 
virtual Range1D  range_impl () const 
virtual void  apply_op_impl (const ArrayView< const ConstSubVectorView< Scalar > > &sub_vecs, const ArrayView< const SubVectorView< Scalar > > &targ_sub_vecs, const Ptr< ReductTarget > &reduct_obj) const =0 
Nonvirtual protected functions.  
RTOpT (const std::string &op_name_base="")  
Constructor that creates an operator name appended with the type. More...  
void  setOpNameBase (const std::string &op_name_base) 
Just set the operator name. More...  
Additional Inherited Members  
Public Member Functions inherited from Teuchos::Describable  
DescribableStreamManipulatorState  describe (const Describable &describable, const EVerbosityLevel verbLevel=Describable::verbLevel_default) 
std::ostream &  operator<< (std::ostream &os, const DescribableStreamManipulatorState &d) 
virtual std::string  description () const 
virtual void  describe (FancyOStream &out, const EVerbosityLevel verbLevel=verbLevel_default) const 
void  describe (std::ostream &out, const EVerbosityLevel verbLevel=verbLevel_default) const 
virtual  ~Describable () 
LabeledObject ()  
virtual  ~LabeledObject () 
virtual void  setObjectLabel (const std::string &objectLabel) 
virtual std::string  getObjectLabel () const 
Static Public Attributes inherited from Teuchos::Describable  
static const EVerbosityLevel  verbLevel_default 
Templated interface to vector reduction/transformation operators {abstract}.
The purpose of this base class is to allow users to specify arbitrary reduction/transformation operations on vectors without requiring the vectors to reveal their implementation details. The design is motivated partly by the "Visitor" patter (Gamma, 1995).
This interface is designed to allow implementation of a distributed parallel abstract numerical algorithm without the explicit knowledge of the algorithm.
In the following discussion, v[k]
, x
, y
and z
are some abstract vector objects of dimension n
. Users can define operators to perform reduction and/or transformation operations. Reduction operations applied over all of the elements of a vector require communication between nodes in a parallel environment but do not change any of the vectors involved. Transformation operations don't require communication between nodes in a parallel environment. The targets of a transformation operation is a set of one or more vectors which are changed in some way.
The idea is that the user may want to perform reduction operations of the form:
op(v[0]...v[*],z[0]...z[*]) > reduct_obj
where reduct_obj
is a single object based on a reduction over all the elements of the vector arguments, or transformation operations of the form:
op(v[0](i)...v[*](i),z[0](i)...z[*](i)) > z[0](i)...z[*](i), for i = 0...n1
Operators can also be defined that perform reduction and transformation operations on the same vectors that that should only be done for efficiency reasons.
The tricky part though, is that the reduct_obj
object of the reduction operation may be more complex than a single scalar value. For instance, it could be a double
and an int
pair such as in the reduction operation:
min{ x(i), i = 0...n1 } > [ x(j_min), j_min ]
or it could perform several reductions at once and store several scalar values such as in:
min_max_sum{ x(i), i = 0...n1 } > [ x(j_min), j_min, x(j_max), j_max, x_sum ]
Transformation operations are much simpler to think about and to deal with. Some offthewall examples of transformation operations that this design will support are:
max{ x(i), y(i) } + z(i) > z(i), for i = 0...n1 alpha * z(i) / x(i) > z(i), for i = 0...n1 alpha * x(i) * y(i) + beta * z(i) > z(i), for i = 0...n1
Reduction operations present the more difficult technical challenge since they require information gathered from all of the elements to arrive at the final result. This design allows operator classes to be defined that can simultaneously perform reduction and transformation operations:
op(v[0](i)...v[*](i),z[0](i)...z[*](i)) > z[0](i)...z[*](i),reduct_obj, for i = 0...n1
This design is based on a few assumptions about the reduction and transformation operations and vector implementations themselves. First, we will assume that vectors are stored and manipulated as chunks of subvectors (of dimension subDim
) where each subvector is sufficiently large to overcome the inherent overhead of this design. This design supports dense strided subvectors (see ConstSubVectorView
and SubVectorView
) but is relatively flexible.
It is strictly the responsibility of the vector implementations to determine how these operators are applied. For instance, if we are performing a transformation operation of the form:
op( x(i), y(i), z(i) ) > z(i), for i = 0...n1
where x
, y
, and z
are distributed parallel vectors, then we would assume that the elements would be partitioned onto the various processors with the same local elements stored on each processor so as not to require any communication between processors.
Definition at line 137 of file RTOpPack_RTOpT_decl.hpp.
typedef PrimitiveTypeTraits<Scalar,Scalar>::primitiveType RTOpPack::RTOpT< Scalar >::primitive_value_type 
Definition at line 145 of file RTOpPack_RTOpT_decl.hpp.

protected 
Constructor that creates an operator name appended with the type.
Definition at line 113 of file RTOpPack_RTOpT_def.hpp.

inline 
Get the number of entries of each basic data type in the externalized state for a reduction object for this operator.
Note that a specific reduction object is not passed in as an argument. This is because the structure of a reduction object is completely determined by its associated operator object and this structure can not change as a result of a reduction operation (this is needed to simplify global communication code when used * with MPI).
The default implementation returns zeros for *num_values
, *num_indexes
and *num_chars
(i.e. by default there is no reduction operation performed).
Definition at line 167 of file RTOpPack_RTOpT_decl.hpp.

inline 
Creates a new reduction target object initialized and ready to be used in a reduction.
The default implementation returns returnVal.get()==NULL
(i.e. by default there is no reduction operation performed).
Definition at line 182 of file RTOpPack_RTOpT_decl.hpp.

inline 
Reduce intermediate reduction target objects.
The default implementation does not do anything (i.e. by default there is no reduction operation performed).
Definition at line 192 of file RTOpPack_RTOpT_decl.hpp.

inline 
Reinitialize an already created reduction object.
The default implementation does nothing (i.e. by default there is no reduction operation performed).
reduct_obj  [in/out] Reduction object is reinitialized on output. 
Definition at line 206 of file RTOpPack_RTOpT_decl.hpp.

inline 
Extract the state of an already created reduction object.
This method allows the state of a reduction target object to be externalized so that it can be passed over a heterogeneous network of computers.
The default implementation does nothing (i.e. by default there is no reduction operation performed).
Definition at line 220 of file RTOpPack_RTOpT_decl.hpp.

inline 
Load the state of an already created reduction object given arrays of primitive objects.
The default implementation does nothing.
Definition at line 236 of file RTOpPack_RTOpT_decl.hpp.

inline 
Return the name (as a nullterminated Cstyle string) of the operator.
This name is used to differentiate an operator subclass from all other operator subclasses. This is an important property needed for a client/server or master/slave runtime configuration.
The default implementation uses the value created in the constructor RTOpT()
.
Definition at line 260 of file RTOpPack_RTOpT_decl.hpp.

inline 
Returns true
if this operator is coordinate invariant.
The default implementation returns true
as most vector operators are coordinate invariant.
Definition at line 274 of file RTOpPack_RTOpT_decl.hpp.

inline 
Returns the continuous range of elements that this operator is defined over.
Vector client implementations are free to ignore this but they can use this information to optimize rare operators that only interact with a subset of elements.
The default implementation return Range1D()
which means all of the elements.
Definition at line 289 of file RTOpPack_RTOpT_decl.hpp.

inline 
Apply the reduction/transformation operator to a set of subvectors.
op(sub_vecs[], targ_sub_vecs[], reduct_obj) > targ_sub_vecs[], reduct_obj
.
This is the bread and butter of the whole design. Through this method, a vector implementation applies a reduction/transformation operator to a set of subvectors.
sub_vecs  [in] Array (length num_vecs ) of nonmutable vectors to apply the operator over. The ordering of these subvectors sub_vecs[k], for k = 0...num_vecs1 , is significant to the this operator object. If num_vecs==0 then sub_vecs can be NULL . 
targ_sub_vecs  [in/out] Array (length num_targ_vecs ) of mutable vectors to apply the operator over and be mutated. The ordering of these subvectors targ_sub_vecs[k], for k = 0...num_targ_vecs1 , is significant to this operator object. If num_targ_vecs==0 then targ_sub_vecs can be NULL . 
reduct_obj  [in/out] This reduction object must have been created by a this>reduct_obj_create() call and it may have * already passed through one or more other reduction operations (accumulating the reductions along the way). If this>get_reduct_type_num_entries() returns num_values==0 , num_indexes==0 and num_chars==0 , then reduct_obj should be set to NULL as no reduction will be performed. 
Preconditions:
globalOffset==sub_vecs[k].globalOffset
, for k = 0,...,sub_vecs.subDim()1
globalOffset==targ_sub_vecs[k].globalOffset
, for k = 0,...,targ_vecs.subDim()1
subDim==sub_vecs[k].subDim()
, for k = 0,...,sub_vecs.subDim()1
subDim==targ_sub_vecs[k].subDim()
, for k = 0,...,targ_vecs.subDim()1
If nonnull(reduct_obj)==true
then the reduction operation will be accumulated as:
op(sub_vecs[], targ_sub_vecs[], reduct_obj) > reduct_obj
By allowing an in/out reduct_obj
and an accumulation of the reduction, the maximum reuse of memory is achieved. If this>reduct_obj_create()
or this>reduct_obj_reinit()
(passing in reduct_obj
) was called immediately before this function, then on return, reduct_obj
will contain only the reduction from this function call.
If the sizes of sub_vecs
and targ_sub_vecs
is incompatible with the underlying operator object then InvalidNumVecs
is thrown. If the subvectors are not compatible (i.e. globalOffset
and/or subDim
not the same) then IncompatibleVecs
is thrown.
Definition at line 362 of file RTOpPack_RTOpT_decl.hpp.

protectedvirtual 
Reimplemented in RTOpPack::ROpScalarReductionWithOpBase< Scalar, ConcreteReductObj, ReductObjReduction >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, Scalar, SumScalarReductObjReduction< Scalar > >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, ReductScalar, ReductObjReduction >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, ScalarIndex< Scalar >, ROpMaxIndexReductObjReductionOp< Scalar > >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, ScalarIndex< Scalar >, ROpMinIndexReductObjReductionOp< Scalar > >, RTOpPack::RTOpSubRangeDecorator< Scalar >, and RTOpPack::ROpGetSubVector< Scalar >.
Definition at line 27 of file RTOpPack_RTOpT_def.hpp.

protectedvirtual 
Reimplemented in RTOpPack::ROpScalarReductionWithOpBase< Scalar, ConcreteReductObj, ReductObjReduction >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, Scalar, SumScalarReductObjReduction< Scalar > >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, ReductScalar, ReductObjReduction >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, ScalarIndex< Scalar >, ROpMaxIndexReductObjReductionOp< Scalar > >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, ScalarIndex< Scalar >, ROpMinIndexReductObjReductionOp< Scalar > >, RTOpPack::RTOpSubRangeDecorator< Scalar >, and RTOpPack::ROpGetSubVector< Scalar >.
Definition at line 41 of file RTOpPack_RTOpT_def.hpp.

protectedvirtual 
Reimplemented in RTOpPack::ROpScalarReductionWithOpBase< Scalar, ConcreteReductObj, ReductObjReduction >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, Scalar, SumScalarReductObjReduction< Scalar > >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, ReductScalar, ReductObjReduction >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, ScalarIndex< Scalar >, ROpMaxIndexReductObjReductionOp< Scalar > >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, ScalarIndex< Scalar >, ROpMinIndexReductObjReductionOp< Scalar > >, RTOpPack::RTOpSubRangeDecorator< Scalar >, and RTOpPack::ROpGetSubVector< Scalar >.
Definition at line 48 of file RTOpPack_RTOpT_def.hpp.

protectedvirtual 
Reimplemented in RTOpPack::ROpScalarReductionWithOpBase< Scalar, ConcreteReductObj, ReductObjReduction >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, Scalar, SumScalarReductObjReduction< Scalar > >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, ReductScalar, ReductObjReduction >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, ScalarIndex< Scalar >, ROpMaxIndexReductObjReductionOp< Scalar > >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, ScalarIndex< Scalar >, ROpMinIndexReductObjReductionOp< Scalar > >, RTOpPack::RTOpSubRangeDecorator< Scalar >, and RTOpPack::ROpGetSubVector< Scalar >.
Definition at line 57 of file RTOpPack_RTOpT_def.hpp.

protectedvirtual 
Reimplemented in RTOpPack::ROpScalarReductionWithOpBase< Scalar, ConcreteReductObj, ReductObjReduction >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, Scalar, SumScalarReductObjReduction< Scalar > >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, ReductScalar, ReductObjReduction >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, ScalarIndex< Scalar >, ROpMaxIndexReductObjReductionOp< Scalar > >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, ScalarIndex< Scalar >, ROpMinIndexReductObjReductionOp< Scalar > >, RTOpPack::RTOpSubRangeDecorator< Scalar >, and RTOpPack::ROpGetSubVector< Scalar >.
Definition at line 65 of file RTOpPack_RTOpT_def.hpp.

protectedvirtual 
Reimplemented in RTOpPack::ROpScalarReductionWithOpBase< Scalar, ConcreteReductObj, ReductObjReduction >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, Scalar, SumScalarReductObjReduction< Scalar > >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, ReductScalar, ReductObjReduction >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, ScalarIndex< Scalar >, ROpMaxIndexReductObjReductionOp< Scalar > >, RTOpPack::ROpScalarReductionWithOpBase< Scalar, ScalarIndex< Scalar >, ROpMinIndexReductObjReductionOp< Scalar > >, RTOpPack::RTOpSubRangeDecorator< Scalar >, and RTOpPack::ROpGetSubVector< Scalar >.
Definition at line 77 of file RTOpPack_RTOpT_def.hpp.

protectedvirtual 
Reimplemented in RTOpPack::RTOpSubRangeDecorator< Scalar >.
Definition at line 89 of file RTOpPack_RTOpT_def.hpp.

protectedvirtual 
Reimplemented in RTOpPack::TOp_0_1_CoordVariantBase< Scalar, EleWiseTransformation >, RTOpPack::TOp_0_1_CoordVariantBase< Scalar, TOpSetElementEleWiseTransformation< Scalar > >, RTOpPack::TOp_0_1_CoordVariantBase< Scalar, TOpSetAssendingValuesEleWiseTransformation< Scalar > >, RTOpPack::ROp_1_CoordVariantScalarReduction< Scalar, ReductScalar, EleWiseReduction, ReductObjReduction >, RTOpPack::ROp_1_CoordVariantScalarReduction< Scalar, ScalarIndex< Scalar >, ROpMaxIndexLessThanBoundEleWiseReductionOp< Scalar >, ROpMaxIndexReductObjReductionOp< Scalar > >, RTOpPack::ROp_1_CoordVariantScalarReduction< Scalar, ScalarIndex< Scalar >, ROpMinIndexEleWiseReductionOp< Scalar >, ROpMinIndexReductObjReductionOp< Scalar > >, RTOpPack::ROp_1_CoordVariantScalarReduction< Scalar, ScalarIndex< Scalar >, ROpMaxIndexEleWiseReductionOp< Scalar >, ROpMaxIndexReductObjReductionOp< Scalar > >, RTOpPack::ROp_1_CoordVariantScalarReduction< Scalar, ScalarIndex< Scalar >, ROpMinIndexGreaterThanBoundEleWiseReductionOp< Scalar >, ROpMinIndexReductObjReductionOp< Scalar > >, RTOpPack::ROp_1_CoordVariantScalarReduction< Scalar, Scalar, ROpGetElementEleWiseReductionOp< Scalar > >, RTOpPack::RTOpSubRangeDecorator< Scalar >, RTOpPack::ROpGetSubVector< Scalar >, and RTOpPack::TOpSetSubVector< Scalar >.
Definition at line 96 of file RTOpPack_RTOpT_def.hpp.

protectedvirtual 
Reimplemented in RTOpPack::ROpGetElement< Scalar >, and RTOpPack::TOpSetElement< Scalar >.
Definition at line 103 of file RTOpPack_RTOpT_def.hpp.

protectedpure virtual 
Implemented in RTOpPack::TOp_3_1_Base< Scalar, EleWiseTransformation >, RTOpPack::TOp_2_1_Base< Scalar, EleWiseTransformation >, RTOpPack::TOp_2_1_Base< Scalar, TOpEleWiseConjProdEleWiseTransformation< Scalar > >, RTOpPack::TOp_2_1_Base< Scalar, TOpEleWiseDivideEleWiseTransformation< Scalar > >, RTOpPack::TOp_2_1_Base< Scalar, TOpEleWiseProdEleWiseTransformation< Scalar > >, RTOpPack::TOp_2_1_Base< Scalar, TOpPairWiseMaxPairWiseTransformation< Scalar > >, RTOpPack::TOp_1_1_Base< Scalar, EleWiseTransformation >, RTOpPack::TOp_1_1_Base< Scalar, TOpEleWiseScaleEleWiseTransformation< Scalar > >, RTOpPack::TOp_1_1_Base< Scalar, TOpPairWiseMaxUpdatePairWiseTransformation< Scalar > >, RTOpPack::TOp_1_1_Base< Scalar, TOpAXPYEleWiseTransformation< Scalar > >, RTOpPack::TOp_1_1_Base< Scalar, TOpEleWiseProdUpdateEleWiseTransformation< Scalar > >, RTOpPack::TOp_0_1_CoordVariantBase< Scalar, EleWiseTransformation >, RTOpPack::TOp_0_1_CoordVariantBase< Scalar, TOpSetElementEleWiseTransformation< Scalar > >, RTOpPack::TOp_0_1_CoordVariantBase< Scalar, TOpSetAssendingValuesEleWiseTransformation< Scalar > >, RTOpPack::TOp_0_1_Base< Scalar, EleWiseTransformation >, RTOpPack::TOp_0_1_Base< Scalar, TOpScaleVectorEleWiseTransformation< Scalar > >, RTOpPack::TOp_0_1_Base< Scalar, TOpAddScalarEleWiseTransformation< Scalar > >, RTOpPack::TOp_0_1_Base< Scalar, TOpAssignScalarEleWiseTransformation< Scalar > >, RTOpPack::ROp_2_ScalarReduction< Scalar, ReductScalar, EleWiseReduction, ReductObjReduction >, RTOpPack::ROp_2_ScalarReduction< Scalar, Scalar, ROpWeightedNorm2EleWiseReduction< Scalar > >, RTOpPack::ROp_1_CoordVariantScalarReduction< Scalar, ReductScalar, EleWiseReduction, ReductObjReduction >, RTOpPack::ROp_1_CoordVariantScalarReduction< Scalar, ScalarIndex< Scalar >, ROpMaxIndexLessThanBoundEleWiseReductionOp< Scalar >, ROpMaxIndexReductObjReductionOp< Scalar > >, RTOpPack::ROp_1_CoordVariantScalarReduction< Scalar, ScalarIndex< Scalar >, ROpMinIndexEleWiseReductionOp< Scalar >, ROpMinIndexReductObjReductionOp< Scalar > >, RTOpPack::ROp_1_CoordVariantScalarReduction< Scalar, ScalarIndex< Scalar >, ROpMaxIndexEleWiseReductionOp< Scalar >, ROpMaxIndexReductObjReductionOp< Scalar > >, RTOpPack::ROp_1_CoordVariantScalarReduction< Scalar, ScalarIndex< Scalar >, ROpMinIndexGreaterThanBoundEleWiseReductionOp< Scalar >, ROpMinIndexReductObjReductionOp< Scalar > >, RTOpPack::ROp_1_CoordVariantScalarReduction< Scalar, Scalar, ROpGetElementEleWiseReductionOp< Scalar > >, RTOpPack::ROp_1_ScalarReduction< Scalar, ConcreteReductObj, EleWiseReduction, ReductObjReduction >, RTOpPack::ROp_1_ScalarReduction< Scalar, Scalar, ROpNorm2EleWiseReduction< Scalar > >, RTOpPack::RTOpSubRangeDecorator< Scalar >, RTOpPack::ROpGetSubVector< Scalar >, RTOpPack::TOpRandomize< Scalar >, RTOpPack::TOpLinearCombination< Scalar >, and RTOpPack::TOpSetSubVector< Scalar >.

protected 
Just set the operator name.
Definition at line 120 of file RTOpPack_RTOpT_def.hpp.

private 
Definition at line 130 of file RTOpPack_RTOpT_def.hpp.

private 
Definition at line 447 of file RTOpPack_RTOpT_decl.hpp.