TSMatDMatSchurExpr.h
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1 //=================================================================================================
33 //=================================================================================================
34 
35 #ifndef _BLAZE_MATH_EXPRESSIONS_TSMATDMATSCHUREXPR_H_
36 #define _BLAZE_MATH_EXPRESSIONS_TSMATDMATSCHUREXPR_H_
37 
38 
39 //*************************************************************************************************
40 // Includes
41 //*************************************************************************************************
42 
43 #include <iterator>
44 #include <blaze/math/Aliases.h>
50 #include <blaze/math/Exception.h>
72 #include <blaze/util/Assert.h>
73 #include <blaze/util/DisableIf.h>
74 #include <blaze/util/EnableIf.h>
76 #include <blaze/util/mpl/And.h>
77 #include <blaze/util/mpl/If.h>
78 #include <blaze/util/mpl/Maximum.h>
79 #include <blaze/util/mpl/Or.h>
80 #include <blaze/util/Types.h>
81 #include <blaze/util/Unused.h>
82 
83 
84 namespace blaze {
85 
86 //=================================================================================================
87 //
88 // CLASS TSMATDMATSCHUREXPR
89 //
90 //=================================================================================================
91 
92 //*************************************************************************************************
99 template< typename MT1 // Type of the left-hand side sparse matrix
100  , typename MT2 > // Type of the right-hand side dense matrix
101 class TSMatDMatSchurExpr
102  : public SchurExpr< SparseMatrix< TSMatDMatSchurExpr<MT1,MT2>, true > >
103  , private Computation
104 {
105  private:
106  //**Type definitions****************************************************************************
113  //**********************************************************************************************
114 
115  //**Return type evaluation**********************************************************************
117 
122  enum : bool { returnExpr = !IsTemporary<RN1>::value && !IsTemporary<RN2>::value };
123 
126  //**********************************************************************************************
127 
128  //**Evaluation strategy*************************************************************************
130 
136  enum : bool { useAssign = ( RequiresEvaluation<MT1>::value || RequiresEvaluation<MT2>::value ) };
137 
139  template< typename VT >
141  struct UseAssign {
142  enum : bool { value = useAssign };
143  };
145  //**********************************************************************************************
146 
147  public:
148  //**Type definitions****************************************************************************
154 
157 
160 
162  using LeftOperand = If_< IsExpression<MT1>, const MT1, const MT1& >;
163 
165  using RightOperand = If_< IsExpression<MT2>, const MT2, const MT2& >;
166  //**********************************************************************************************
167 
168  //**ConstIterator class definition**************************************************************
172  {
173  public:
174  //**Type definitions*************************************************************************
177 
180 
181  using IteratorCategory = std::forward_iterator_tag;
182  using ValueType = Element;
186 
187  // STL iterator requirements
193  //*******************************************************************************************
194 
195  //**Constructor******************************************************************************
202  inline ConstIterator( LeftIterator left, RightOperand right, size_t column )
203  : left_ ( left ) // Iterator over the elements of the left-hand side sparse matrix expression
204  , right_( right ) // Right-hand side dense matrix expression
205  , col_ ( column ) // The column index of the iterator
206  {}
207  //*******************************************************************************************
208 
209  //**Prefix increment operator****************************************************************
215  ++left_;
216  return *this;
217  }
218  //*******************************************************************************************
219 
220  //**Element access operator******************************************************************
225  inline const Element operator*() const {
226  return Element( left_->value() * right_(left_->index(),col_), left_->index() );
227  }
228  //*******************************************************************************************
229 
230  //**Element access operator******************************************************************
235  inline const ConstIterator* operator->() const {
236  return this;
237  }
238  //*******************************************************************************************
239 
240  //**Value function***************************************************************************
245  inline ReturnType value() const {
246  return left_->value() * right_(left_->index(),col_);
247  }
248  //*******************************************************************************************
249 
250  //**Index function***************************************************************************
255  inline size_t index() const {
256  return left_->index();
257  }
258  //*******************************************************************************************
259 
260  //**Equality operator************************************************************************
266  inline bool operator==( const ConstIterator& rhs ) const {
267  return left_ == rhs.left_;
268  }
269  //*******************************************************************************************
270 
271  //**Inequality operator**********************************************************************
277  inline bool operator!=( const ConstIterator& rhs ) const {
278  return left_ != rhs.left_;
279  }
280  //*******************************************************************************************
281 
282  //**Subtraction operator*********************************************************************
288  inline DifferenceType operator-( const ConstIterator& rhs ) const {
289  return left_ - rhs.left_;
290  }
291  //*******************************************************************************************
292 
293  private:
294  //**Member variables*************************************************************************
297  size_t col_;
298  //*******************************************************************************************
299  };
300  //**********************************************************************************************
301 
302  //**Compilation flags***************************************************************************
304  enum : bool { smpAssignable = false };
305  //**********************************************************************************************
306 
307  //**Constructor*********************************************************************************
313  explicit inline TSMatDMatSchurExpr( const MT1& lhs, const MT2& rhs ) noexcept
314  : lhs_( lhs ) // Left-hand side sparse matrix of the Schur product expression
315  , rhs_( rhs ) // Right-hand side dense matrix of the Schur product expression
316  {
317  BLAZE_INTERNAL_ASSERT( lhs.rows() == rhs.rows() , "Invalid number of rows" );
318  BLAZE_INTERNAL_ASSERT( lhs.columns() == rhs.columns(), "Invalid number of columns" );
319  }
320  //**********************************************************************************************
321 
322  //**Access operator*****************************************************************************
329  inline ReturnType operator()( size_t i, size_t j ) const {
330  BLAZE_INTERNAL_ASSERT( i < lhs_.rows() , "Invalid row access index" );
331  BLAZE_INTERNAL_ASSERT( j < lhs_.columns(), "Invalid column access index" );
332  return lhs_(i,j) * rhs_(i,j);
333  }
334  //**********************************************************************************************
335 
336  //**At function*********************************************************************************
344  inline ReturnType at( size_t i, size_t j ) const {
345  if( i >= lhs_.rows() ) {
346  BLAZE_THROW_OUT_OF_RANGE( "Invalid row access index" );
347  }
348  if( j >= lhs_.columns() ) {
349  BLAZE_THROW_OUT_OF_RANGE( "Invalid column access index" );
350  }
351  return (*this)(i,j);
352  }
353  //**********************************************************************************************
354 
355  //**Begin function******************************************************************************
361  inline ConstIterator begin( size_t j ) const {
362  return ConstIterator( lhs_.begin(j), rhs_, j );
363  }
364  //**********************************************************************************************
365 
366  //**End function********************************************************************************
372  inline ConstIterator end( size_t j ) const {
373  return ConstIterator( lhs_.end(j), rhs_, j );
374  }
375  //**********************************************************************************************
376 
377  //**Rows function*******************************************************************************
382  inline size_t rows() const noexcept {
383  return lhs_.rows();
384  }
385  //**********************************************************************************************
386 
387  //**Columns function****************************************************************************
392  inline size_t columns() const noexcept {
393  return lhs_.columns();
394  }
395  //**********************************************************************************************
396 
397  //**NonZeros function***************************************************************************
402  inline size_t nonZeros() const {
403  return lhs_.nonZeros();
404  }
405  //**********************************************************************************************
406 
407  //**NonZeros function***************************************************************************
413  inline size_t nonZeros( size_t j ) const {
414  return lhs_.nonZeros(j);
415  }
416  //**********************************************************************************************
417 
418  //**Find function*******************************************************************************
425  inline ConstIterator find( size_t i, size_t j ) const {
427  return ConstIterator( lhs_.find( i, j ), rhs_, j );
428  }
429  //**********************************************************************************************
430 
431  //**LowerBound function*************************************************************************
438  inline ConstIterator lowerBound( size_t i, size_t j ) const {
440  return ConstIterator( lhs_.lowerBound( i, j ), rhs_, j );
441  }
442  //**********************************************************************************************
443 
444  //**UpperBound function*************************************************************************
451  inline ConstIterator upperBound( size_t i, size_t j ) const {
453  return ConstIterator( lhs_.upperBound( i, j ), rhs_, j );
454  }
455  //**********************************************************************************************
456 
457  //**Left operand access*************************************************************************
462  inline LeftOperand leftOperand() const noexcept {
463  return lhs_;
464  }
465  //**********************************************************************************************
466 
467  //**Right operand access************************************************************************
472  inline RightOperand rightOperand() const noexcept {
473  return rhs_;
474  }
475  //**********************************************************************************************
476 
477  //**********************************************************************************************
483  template< typename T >
484  inline bool canAlias( const T* alias ) const noexcept {
485  return ( lhs_.canAlias( alias ) || rhs_.canAlias( alias ) );
486  }
487  //**********************************************************************************************
488 
489  //**********************************************************************************************
495  template< typename T >
496  inline bool isAliased( const T* alias ) const noexcept {
497  return ( lhs_.isAliased( alias ) || rhs_.isAliased( alias ) );
498  }
499  //**********************************************************************************************
500 
501  private:
502  //**Member variables****************************************************************************
505  //**********************************************************************************************
506 
507  //**Assignment to dense matrices****************************************************************
519  template< typename MT // Type of the target dense matrix
520  , bool SO2 > // Storage order of the target dense matrix
521  friend inline EnableIf_< UseAssign<MT> >
522  assign( DenseMatrix<MT,SO2>& lhs, const TSMatDMatSchurExpr& rhs )
523  {
525 
526  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
527  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
528 
530 
531  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
532  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side dense matrix operand
533 
534  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
535  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
536  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
537  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
538  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
539  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
540 
541  for( size_t j=0UL; j<(~lhs).columns(); ++j ) {
542  for( ConstIterator element=A.begin(j); element!=A.end(j); ++element )
543  (~lhs)(element->index(),j) = element->value() * B(element->index(),j);
544  }
545  }
547  //**********************************************************************************************
548 
549  //**Assignment to row-major sparse matrices*****************************************************
562  template< typename MT > // Type of the target sparse matrix
563  friend inline EnableIf_< UseAssign<MT> >
564  assign( SparseMatrix<MT,false>& lhs, const TSMatDMatSchurExpr& rhs )
565  {
567 
568  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
569  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
570 
572 
573  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
574  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side dense matrix operand
575 
576  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
577  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
578  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
579  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
580  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
581  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
582 
583  const size_t m( rhs.rows() );
584  const size_t n( rhs.columns() );
585 
586  // Counting the number of elements per column
587  std::vector<size_t> nonzeros( m, 0UL );
588  for( size_t j=0UL; j<n; ++j ) {
589  const ConstIterator lend( A.end(j) );
590  for( ConstIterator l=A.begin(j); l!=lend; ++l ) {
591  ++nonzeros[l->index()];
592  }
593  }
594 
595  // Resizing the left-hand side sparse matrix
596  for( size_t i=0UL; i<m; ++i ) {
597  (~lhs).reserve( i, nonzeros[i] );
598  }
599 
600  // Performing the Schur product
601  for( size_t j=0UL; j<(~lhs).columns(); ++j ) {
602  for( ConstIterator element=A.begin(j); element!=A.end(j); ++element )
603  (~lhs).append( element->index(), j, element->value() * B(element->index(),j) );
604  }
605  }
607  //**********************************************************************************************
608 
609  //**Assignment to column-major sparse matrices**************************************************
622  template< typename MT > // Type of the target sparse matrix
623  friend inline EnableIf_< UseAssign<MT> >
624  assign( SparseMatrix<MT,true>& lhs, const TSMatDMatSchurExpr& rhs )
625  {
627 
628  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
629  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
630 
632 
633  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
634  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side dense matrix operand
635 
636  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
637  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
638  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
639  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
640  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
641  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
642 
643  // Final memory allocation (based on the evaluated operands)
644  (~lhs).reserve( A.nonZeros() );
645 
646  // Performing the Schur product
647  for( size_t j=0UL; j<(~lhs).columns(); ++j ) {
648  for( ConstIterator element=A.begin(j); element!=A.end(j); ++element )
649  (~lhs).append( element->index(), j, element->value() * B(element->index(),j) );
650  (~lhs).finalize( j );
651  }
652  }
654  //**********************************************************************************************
655 
656  //**Addition assignment to dense matrices*******************************************************
669  template< typename MT // Type of the target dense matrix
670  , bool SO2 > // Storage order of the target dense matrix
671  friend inline EnableIf_< UseAssign<MT> >
672  addAssign( DenseMatrix<MT,SO2>& lhs, const TSMatDMatSchurExpr& rhs )
673  {
675 
676  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
677  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
678 
680 
681  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
682  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side dense matrix operand
683 
684  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
685  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
686  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
687  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
688  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
689  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
690 
691  for( size_t j=0UL; j<(~lhs).columns(); ++j ) {
692  for( ConstIterator element=A.begin(j); element!=A.end(j); ++element )
693  (~lhs)(element->index(),j) += element->value() * B(element->index(),j);
694  }
695  }
697  //**********************************************************************************************
698 
699  //**Addition assignment to sparse matrices******************************************************
700  // No special implementation for the addition assignment to sparse matrices.
701  //**********************************************************************************************
702 
703  //**Subtraction assignment to dense matrices****************************************************
716  template< typename MT // Type of the target dense matrix
717  , bool SO2 > // Storage order of the target dense matrix
718  friend inline EnableIf_< UseAssign<MT> >
719  subAssign( DenseMatrix<MT,SO2>& lhs, const TSMatDMatSchurExpr& rhs )
720  {
722 
723  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
724  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
725 
727 
728  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
729  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side dense matrix operand
730 
731  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
732  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
733  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
734  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
735  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
736  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
737 
738  for( size_t j=0UL; j<(~lhs).columns(); ++j ) {
739  for( ConstIterator element=A.begin(j); element!=A.end(j); ++element )
740  (~lhs)(element->index(),j) -= element->value() * B(element->index(),j);
741  }
742  }
744  //**********************************************************************************************
745 
746  //**Subtraction assignment to sparse matrices***************************************************
747  // No special implementation for the subtraction assignment to sparse matrices.
748  //**********************************************************************************************
749 
750  //**Schur product assignment to dense matrices**************************************************
763  template< typename MT // Type of the target dense matrix
764  , bool SO2 > // Storage order of the target dense matrix
765  friend inline void schurAssign( DenseMatrix<MT,SO2>& lhs, const TSMatDMatSchurExpr& rhs )
766  {
768 
769  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
770  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
771 
773 
774  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
775  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side dense matrix operand
776 
777  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
778  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
779  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
780  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
781  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
782  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
783 
784  for( size_t j=0UL; j<(~lhs).columns(); ++j )
785  {
786  const ConstIterator end( A.end(j) );
787  ConstIterator begin( A.begin(j) );
788  size_t i( 0UL );
789 
790  for( ; begin!=end; ++begin ) {
791  const size_t index( begin->index() );
792  for( ; i<index; ++i )
793  reset( (~lhs)(i,j) );
794  (~lhs)(index,j) *= begin->value() * B(index,j);
795  ++i;
796  }
797 
798  for( ; i<(~lhs).rows(); ++i )
799  reset( (~lhs)(i,j) );
800  }
801  }
803  //**********************************************************************************************
804 
805  //**Schur product assignment to sparse matrices*************************************************
806  // No special implementation for the Schur product assignment to sparse matrices.
807  //**********************************************************************************************
808 
809  //**Multiplication assignment to dense matrices*************************************************
810  // No special implementation for the multiplication assignment to dense matrices.
811  //**********************************************************************************************
812 
813  //**Multiplication assignment to sparse matrices************************************************
814  // No special implementation for the multiplication assignment to sparse matrices.
815  //**********************************************************************************************
816 
817  //**SMP assignment to dense matrices************************************************************
818  // No special implementation for the SMP assignment to dense matrices.
819  //**********************************************************************************************
820 
821  //**SMP assignment to sparse matrices***********************************************************
822  // No special implementation for the SMP assignment to sparse matrices.
823  //**********************************************************************************************
824 
825  //**SMP addition assignment to dense matrices***************************************************
826  // No special implementation for the SMP addition assignment to dense matrices.
827  //**********************************************************************************************
828 
829  //**SMP addition assignment to sparse matrices**************************************************
830  // No special implementation for the SMP addition assignment to sparse matrices.
831  //**********************************************************************************************
832 
833  //**SMP subtraction assignment to dense matrices************************************************
834  // No special implementation for the SMP subtraction assignment to dense matrices.
835  //**********************************************************************************************
836 
837  //**SMP subtraction assignment to sparse matrices***********************************************
838  // No special implementation for the SMP subtraction assignment to sparse matrices.
839  //**********************************************************************************************
840 
841  //**SMP Schur product assignment to dense matrices**********************************************
854  template< typename MT // Type of the target dense matrix
855  , bool SO > // Storage order of the target dense matrix
856  friend inline void smpSchurAssign( DenseMatrix<MT,SO>& lhs, const TSMatDMatSchurExpr& rhs )
857  {
859 
860  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
861  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
862 
863  smpSchurAssign( ~lhs, rhs.lhs_ );
864  smpSchurAssign( ~lhs, rhs.rhs_ );
865  }
867  //**********************************************************************************************
868 
869  //**SMP Schur product assignment to sparse matrices*********************************************
870  // No special implementation for the SMP Schur product assignment to sparse matrices.
871  //**********************************************************************************************
872 
873  //**SMP multiplication assignment to dense matrices*********************************************
874  // No special implementation for the SMP multiplication assignment to dense matrices.
875  //**********************************************************************************************
876 
877  //**SMP multiplication assignment to sparse matrices********************************************
878  // No special implementation for the SMP multiplication assignment to sparse matrices.
879  //**********************************************************************************************
880 
881  //**Compile time checks*************************************************************************
888  //**********************************************************************************************
889 };
890 //*************************************************************************************************
891 
892 
893 
894 
895 //=================================================================================================
896 //
897 // GLOBAL BINARY ARITHMETIC OPERATORS
898 //
899 //=================================================================================================
900 
901 //*************************************************************************************************
914 template< typename MT1 // Type of the left-hand side sparse matrix
915  , typename MT2 // Type of the right-hand side dense matrix
918 inline const TSMatDMatSchurExpr<MT1,MT2>
919  tsmatdmatschur( const SparseMatrix<MT1,true>& lhs, const DenseMatrix<MT2,false>& rhs )
920 {
922 
923  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
924  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
925 
926  return TSMatDMatSchurExpr<MT1,MT2>( ~lhs, ~rhs );
927 }
929 //*************************************************************************************************
930 
931 
932 //*************************************************************************************************
945 template< typename MT1 // Type of the left-hand side sparse matrix
946  , typename MT2 // Type of the right-hand side dense matrix
947  , typename = EnableIf_< Or< And< IsUniLower<MT1>, IsUniUpper<MT2> >
948  , And< IsUniUpper<MT1>, IsUniLower<MT2> > > > >
950  tsmatdmatschur( const SparseMatrix<MT1,true>& lhs, const DenseMatrix<MT2,false>& rhs )
951 {
953 
954  UNUSED_PARAMETER( rhs );
955 
956  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
957  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
958 
959  return IdentityMatrix< MultTrait_< ElementType_<MT1>, ElementType_<MT2> >, true >( (~lhs).rows() );
960 }
962 //*************************************************************************************************
963 
964 
965 //*************************************************************************************************
995 template< typename MT1 // Type of the left-hand side sparse matrix
996  , typename MT2 > // Type of the right-hand side dense matrix
997 inline decltype(auto)
998  operator%( const SparseMatrix<MT1,true>& lhs, const DenseMatrix<MT2,false>& rhs )
999 {
1001 
1002  if( (~lhs).rows() != (~rhs).rows() || (~lhs).columns() != (~rhs).columns() ) {
1003  BLAZE_THROW_INVALID_ARGUMENT( "Matrix sizes do not match" );
1004  }
1005 
1006  return tsmatdmatschur( ~lhs, ~rhs );
1007 }
1008 //*************************************************************************************************
1009 
1010 
1011 //*************************************************************************************************
1024 template< typename MT1 // Type of the left-hand side sparse matrix
1025  , typename MT2 // Type of the right-hand side dense matrix
1028 inline const TSMatDMatSchurExpr<MT1,MT2>
1029  tsmattdmatschur( const SparseMatrix<MT1,true>& lhs, const DenseMatrix<MT2,true>& rhs )
1030 {
1032 
1033  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
1034  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
1035 
1036  return TSMatDMatSchurExpr<MT1,MT2>( ~lhs, ~rhs );
1037 }
1039 //*************************************************************************************************
1040 
1041 
1042 //*************************************************************************************************
1055 template< typename MT1 // Type of the left-hand side sparse matrix
1056  , typename MT2 // Type of the right-hand side dense matrix
1060  tsmattdmatschur( const SparseMatrix<MT1,true>& lhs, const DenseMatrix<MT2,true>& rhs )
1061 {
1063 
1064  UNUSED_PARAMETER( rhs );
1065 
1066  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
1067  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
1068 
1070 }
1072 //*************************************************************************************************
1073 
1074 
1075 //*************************************************************************************************
1104 template< typename MT1 // Type of the left-hand side sparse matrix
1105  , typename MT2 > // Type of the right-hand side dense matrix
1106 inline decltype(auto)
1107  operator%( const SparseMatrix<MT1,true>& lhs, const DenseMatrix<MT2,true>& rhs )
1108 {
1110 
1111  if( (~lhs).rows() != (~rhs).rows() || (~lhs).columns() != (~rhs).columns() ) {
1112  BLAZE_THROW_INVALID_ARGUMENT( "Matrix sizes do not match" );
1113  }
1114 
1115  return tsmattdmatschur( ~lhs, ~rhs );
1116 }
1117 //*************************************************************************************************
1118 
1119 
1120 
1121 
1122 //=================================================================================================
1123 //
1124 // SIZE SPECIALIZATIONS
1125 //
1126 //=================================================================================================
1127 
1128 //*************************************************************************************************
1130 template< typename MT1, typename MT2 >
1131 struct Size< TSMatDMatSchurExpr<MT1,MT2>, 0UL >
1132  : public Maximum< Size<MT1,0UL>, Size<MT2,0UL> >
1133 {};
1134 
1135 template< typename MT1, typename MT2 >
1136 struct Size< TSMatDMatSchurExpr<MT1,MT2>, 1UL >
1137  : public Maximum< Size<MT1,1UL>, Size<MT2,1UL> >
1138 {};
1140 //*************************************************************************************************
1141 
1142 
1143 
1144 
1145 //=================================================================================================
1146 //
1147 // ISSYMMETRIC SPECIALIZATIONS
1148 //
1149 //=================================================================================================
1150 
1151 //*************************************************************************************************
1153 template< typename MT1, typename MT2 >
1154 struct IsSymmetric< TSMatDMatSchurExpr<MT1,MT2> >
1155  : public And< IsSymmetric<MT1>, IsSymmetric<MT2> >
1156 {};
1158 //*************************************************************************************************
1159 
1160 
1161 
1162 
1163 //=================================================================================================
1164 //
1165 // ISHERMITIAN SPECIALIZATIONS
1166 //
1167 //=================================================================================================
1168 
1169 //*************************************************************************************************
1171 template< typename MT1, typename MT2 >
1172 struct IsHermitian< TSMatDMatSchurExpr<MT1,MT2> >
1173  : public And< IsHermitian<MT1>, IsHermitian<MT2> >
1174 {};
1176 //*************************************************************************************************
1177 
1178 
1179 
1180 
1181 //=================================================================================================
1182 //
1183 // ISLOWER SPECIALIZATIONS
1184 //
1185 //=================================================================================================
1186 
1187 //*************************************************************************************************
1189 template< typename MT1, typename MT2 >
1190 struct IsLower< TSMatDMatSchurExpr<MT1,MT2> >
1191  : public Or< IsLower<MT1>, IsLower<MT2> >
1192 {};
1194 //*************************************************************************************************
1195 
1196 
1197 
1198 
1199 //=================================================================================================
1200 //
1201 // ISUNILOWER SPECIALIZATIONS
1202 //
1203 //=================================================================================================
1204 
1205 //*************************************************************************************************
1207 template< typename MT1, typename MT2 >
1208 struct IsUniLower< TSMatDMatSchurExpr<MT1,MT2> >
1209  : public And< IsUniLower<MT1>, IsUniLower<MT2> >
1210 {};
1212 //*************************************************************************************************
1213 
1214 
1215 
1216 
1217 //=================================================================================================
1218 //
1219 // ISSTRICTLYLOWER SPECIALIZATIONS
1220 //
1221 //=================================================================================================
1222 
1223 //*************************************************************************************************
1225 template< typename MT1, typename MT2 >
1226 struct IsStrictlyLower< TSMatDMatSchurExpr<MT1,MT2> >
1227  : public Or< IsStrictlyLower<MT1>, IsStrictlyLower<MT2> >
1228 {};
1230 //*************************************************************************************************
1231 
1232 
1233 
1234 
1235 //=================================================================================================
1236 //
1237 // ISUPPER SPECIALIZATIONS
1238 //
1239 //=================================================================================================
1240 
1241 //*************************************************************************************************
1243 template< typename MT1, typename MT2 >
1244 struct IsUpper< TSMatDMatSchurExpr<MT1,MT2> >
1245  : public Or< IsUpper<MT1>, IsUpper<MT2> >
1246 {};
1248 //*************************************************************************************************
1249 
1250 
1251 
1252 
1253 //=================================================================================================
1254 //
1255 // ISUNIUPPER SPECIALIZATIONS
1256 //
1257 //=================================================================================================
1258 
1259 //*************************************************************************************************
1261 template< typename MT1, typename MT2 >
1262 struct IsUniUpper< TSMatDMatSchurExpr<MT1,MT2> >
1263  : public And< IsUniUpper<MT1>, IsUniUpper<MT2> >
1264 {};
1266 //*************************************************************************************************
1267 
1268 
1269 
1270 
1271 //=================================================================================================
1272 //
1273 // ISSTRICTLYUPPER SPECIALIZATIONS
1274 //
1275 //=================================================================================================
1276 
1277 //*************************************************************************************************
1279 template< typename MT1, typename MT2 >
1280 struct IsStrictlyUpper< TSMatDMatSchurExpr<MT1,MT2> >
1281  : public Or< IsStrictlyUpper<MT1>, IsStrictlyUpper<MT2> >
1282 {};
1284 //*************************************************************************************************
1285 
1286 } // namespace blaze
1287 
1288 #endif
#define BLAZE_THROW_INVALID_ARGUMENT(MESSAGE)
Macro for the emission of a std::invalid_argument exception.This macro encapsulates the default way o...
Definition: Exception.h:235
Pointer difference type of the Blaze library.
CompositeType_< MT1 > CT1
Composite type of the left-hand side sparse matrix expression.
Definition: TSMatDMatSchurExpr.h:111
Header file for auxiliary alias declarations.
decltype(auto) column(Matrix< MT, SO > &matrix, RCAs... args)
Creating a view on a specific column of the given matrix.
Definition: Column.h:131
Header file for the Schur product trait.
size_t nonZeros(size_t j) const
Returns the number of non-zero elements in the specified column.
Definition: TSMatDMatSchurExpr.h:413
Compile time check whether the given type is a temporary vector or matrix type.This type trait class ...
Definition: IsTemporary.h:69
Header file for the UNUSED_PARAMETER function template.
Header file for the IsUniUpper type trait.
EnableIf_< IsDenseMatrix< MT1 > > smpSchurAssign(Matrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs)
Default implementation of the SMP Schur product assignment of a matrix to dense matrix.
Definition: DenseMatrix.h:196
Expression object for transpose sparse matrix-dense matrix Schur product.The TSMatDMatSchurExpr class...
Definition: Forward.h:161
Header file for basic type definitions.
LeftOperand lhs_
Left-hand side sparse matrix of the Schur product expression.
Definition: TSMatDMatSchurExpr.h:503
ReturnType at(size_t i, size_t j) const
Checked access to the matrix elements.
Definition: TSMatDMatSchurExpr.h:344
CompositeType_< MT2 > CT2
Composite type of the right-hand side dense matrix expression.
Definition: TSMatDMatSchurExpr.h:112
Header file for the serial shim.
#define BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE(T)
Constraint on the data type.In case the given data type T is not a dense, N-dimensional matrix type...
Definition: DenseMatrix.h:61
void reset(const DiagonalProxy< MT > &proxy)
Resetting the represented element to the default initial values.
Definition: DiagonalProxy.h:588
ConstIterator upperBound(size_t i, size_t j) const
Returns an iterator to the first index greater then the given index.
Definition: TSMatDMatSchurExpr.h:451
typename DisableIf< Condition, T >::Type DisableIf_
Auxiliary type for the DisableIf class template.The DisableIf_ alias declaration provides a convenien...
Definition: DisableIf.h:224
ConstIterator lowerBound(size_t i, size_t j) const
Returns an iterator to the first index not less then the given index.
Definition: TSMatDMatSchurExpr.h:438
ResultType_< MT2 > RT2
Result type of the right-hand side dense matrix expression.
Definition: TSMatDMatSchurExpr.h:108
Header file for the And class template.
Compile time value evaluation.The Maximum alias declaration selects the larger of the two given templ...
Definition: Maximum.h:73
Compile time check for lower triangular matrices.This type trait tests whether or not the given templ...
Definition: IsLower.h:87
Header file for the Computation base class.
Compile time check for upper triangular matrices.This type trait tests whether or not the given templ...
Definition: IsUpper.h:87
ReturnType value() const
Access to the current value of the sparse element.
Definition: TSMatDMatSchurExpr.h:245
ReturnType_< MT1 > RN1
Return type of the left-hand side sparse matrix expression.
Definition: TSMatDMatSchurExpr.h:109
Header file for the IsUniLower type trait.
typename T::ResultType ResultType_
Alias declaration for nested ResultType type definitions.The ResultType_ alias declaration provides a...
Definition: Aliases.h:343
ConstIterator(LeftIterator left, RightOperand right, size_t column)
Constructor for the ConstIterator class.
Definition: TSMatDMatSchurExpr.h:202
#define BLAZE_CONSTRAINT_MUST_FORM_VALID_SCHUREXPR(T1, T2)
Constraint on the data type.In case the given data types T1 and T2 do not form a valid matrix/matrix ...
Definition: SchurExpr.h:107
Base class for dense matrices.The DenseMatrix class is a base class for all dense matrix classes...
Definition: DenseMatrix.h:80
Base class for sparse matrices.The SparseMatrix class is a base class for all sparse matrix classes...
Definition: Forward.h:129
Header file for all forward declarations for sparse vectors and matrices.
MultExprTrait_< RN1, RN2 > ExprReturnType
Expression return type for the subscript operator.
Definition: TSMatDMatSchurExpr.h:125
typename IfTrue< Condition, T1, T2 >::Type IfTrue_
Auxiliary alias declaration for the IfTrue class template.The IfTrue_ alias declaration provides a co...
Definition: If.h:109
DifferenceType operator-(const ConstIterator &rhs) const
Calculating the number of elements between two expression iterators.
Definition: TSMatDMatSchurExpr.h:288
typename T::ReturnType ReturnType_
Alias declaration for nested ReturnType type definitions.The ReturnType_ alias declaration provides a...
Definition: Aliases.h:363
Header file for the SparseMatrix base class.
ConstIterator_< RemoveReference_< LeftOperand > > LeftIterator
Iterator type of the sparse matrix expression.
Definition: TSMatDMatSchurExpr.h:179
const ConstIterator * operator->() const
Direct access to the sparse matrix element at the current iterator position.
Definition: TSMatDMatSchurExpr.h:235
bool operator==(const ConstIterator &rhs) const
Equality comparison between two ConstIterator objects.
Definition: TSMatDMatSchurExpr.h:266
Constraint on the data type.
Constraint on the data type.
size_t columns() const noexcept
Returns the current number of columns of the matrix.
Definition: TSMatDMatSchurExpr.h:392
Header file for the Maximum class template.
typename MultExprTrait< T1, T2 >::Type MultExprTrait_
Auxiliary alias declaration for the MultExprTrait class template.The MultExprTrait_ alias declaration...
Definition: MultExprTrait.h:112
size_t rows() const noexcept
Returns the current number of rows of the matrix.
Definition: TSMatDMatSchurExpr.h:382
Header file for the MultExprTrait class template.
Compile time check to query the requirement to evaluate an expression.Via this type trait it is possi...
Definition: RequiresEvaluation.h:71
typename T::CompositeType CompositeType_
Alias declaration for nested CompositeType type definitions.The CompositeType_ alias declaration prov...
Definition: Aliases.h:83
Compile time check for upper unitriangular matrices.This type trait tests whether or not the given te...
Definition: IsUniUpper.h:86
Header file for the ValueIndexPair class.
Efficient implementation of an identity matrix.The IdentityMatrix class template is the representati...
Definition: Forward.h:49
Header file for the DisableIf class template.
Header file for the IsTemporary type trait class.
Header file for the multiplication trait.
Header file for the IsStrictlyUpper type trait.
If_< IsExpression< MT1 >, const MT1, const MT1 &> LeftOperand
Composite type of the left-hand side sparse matrix expression.
Definition: TSMatDMatSchurExpr.h:162
ConstIterator & operator++()
Pre-increment operator.
Definition: TSMatDMatSchurExpr.h:214
Header file for the IsSymmetric type trait.
OppositeType_< ResultType > OppositeType
Result type with opposite storage order for expression template evaluations.
Definition: TSMatDMatSchurExpr.h:151
Namespace of the Blaze C++ math library.
Definition: Blaze.h:58
Header file for the If class template.
#define BLAZE_CONSTRAINT_MUST_BE_COLUMN_MAJOR_MATRIX_TYPE(T)
Constraint on the data type.In case the given data type T is not a column-major dense or sparse matri...
Definition: ColumnMajorMatrix.h:61
Header file for the Or class template.
#define BLAZE_THROW_OUT_OF_RANGE(MESSAGE)
Macro for the emission of a std::out_of_range exception.This macro encapsulates the default way of Bl...
Definition: Exception.h:331
ElementType_< ResultType > ElementType
Resulting element type.
Definition: TSMatDMatSchurExpr.h:153
const Element * ConstIterator
Iterator over constant elements.
Definition: CompressedMatrix.h:3085
typename T::ElementType ElementType_
Alias declaration for nested ElementType type definitions.The ElementType_ alias declaration provides...
Definition: Aliases.h:163
RightOperand rightOperand() const noexcept
Returns the right-hand side dense matrix operand.
Definition: TSMatDMatSchurExpr.h:472
Header file for the IsLower type trait.
typename SchurTrait< T1, T2 >::Type SchurTrait_
Auxiliary alias declaration for the SchurTrait class template.The SchurTrait_ alias declaration provi...
Definition: SchurTrait.h:208
ResultType_< MT1 > RT1
Result type of the left-hand side sparse matrix expression.
Definition: TSMatDMatSchurExpr.h:107
LeftOperand leftOperand() const noexcept
Returns the left-hand side transpose sparse matrix operand.
Definition: TSMatDMatSchurExpr.h:462
Compile time check for symmetric matrices.This type trait tests whether or not the given template par...
Definition: IsSymmetric.h:85
bool operator!=(const ConstIterator &rhs) const
Inequality comparison between two ConstIterator objects.
Definition: TSMatDMatSchurExpr.h:277
Header file for the exception macros of the math module.
Compile time check for strictly upper triangular matrices.This type trait tests whether or not the gi...
Definition: IsStrictlyUpper.h:86
size_t col_
The column index of the iterator.
Definition: TSMatDMatSchurExpr.h:297
ConstIterator end(size_t j) const
Returns an iterator just past the last non-zero element of column j.
Definition: TSMatDMatSchurExpr.h:372
Constraint on the data type.
IfTrue_< useAssign, const ResultType, const TSMatDMatSchurExpr &> CompositeType
Data type for composite expression templates.
Definition: TSMatDMatSchurExpr.h:159
Header file for all forward declarations for expression class templates.
TransposeType_< ResultType > TransposeType
Transpose type for expression template evaluations.
Definition: TSMatDMatSchurExpr.h:152
Header file for the EnableIf class template.
Header file for the IsStrictlyLower type trait.
Compile time check for lower unitriangular matrices.This type trait tests whether or not the given te...
Definition: IsUniLower.h:86
ReturnType_< MT2 > RN2
Return type of the right-hand side dense matrix expression.
Definition: TSMatDMatSchurExpr.h:110
std::forward_iterator_tag IteratorCategory
The iterator category.
Definition: TSMatDMatSchurExpr.h:181
If_< IsExpression< MT2 >, const MT2, const MT2 &> RightOperand
Composite type of the right-hand side dense matrix expression.
Definition: TSMatDMatSchurExpr.h:165
TSMatDMatSchurExpr(const MT1 &lhs, const MT2 &rhs) noexcept
Constructor for the TSMatDMatSchurExpr class.
Definition: TSMatDMatSchurExpr.h:313
const Element operator*() const
Direct access to the sparse matrix element at the current iterator position.
Definition: TSMatDMatSchurExpr.h:225
Header file for run time assertion macros.
const IfTrue_< returnExpr, ExprReturnType, ElementType > ReturnType
Return type for expression template evaluations.
Definition: TSMatDMatSchurExpr.h:156
size_t nonZeros() const
Returns the number of non-zero elements in the sparse matrix.
Definition: TSMatDMatSchurExpr.h:402
Header file for the SchurExpr base class.
typename If< T1, T2, T3 >::Type If_
Auxiliary alias declaration for the If class template.The If_ alias declaration provides a convenient...
Definition: If.h:154
RightOperand right_
Right-hand side dense matrix expression.
Definition: TSMatDMatSchurExpr.h:296
#define BLAZE_FUNCTION_TRACE
Function trace macro.This macro can be used to reliably trace function calls. In case function tracin...
Definition: FunctionTrace.h:94
Iterator over the elements of the sparse matrix/dense matrix Schur product expression.
Definition: TSMatDMatSchurExpr.h:171
Compile time check for Hermitian matrices.This type trait tests whether or not the given template par...
Definition: IsHermitian.h:85
RightOperand rhs_
Right-hand side dense matrix of the Schur product expression.
Definition: TSMatDMatSchurExpr.h:504
Constraints on the storage order of matrix types.
decltype(auto) serial(const DenseMatrix< MT, SO > &dm)
Forces the serial evaluation of the given dense matrix expression dm.
Definition: DMatSerialExpr.h:816
ConstIterator begin(size_t j) const
Returns an iterator to the first non-zero element of column j.
Definition: TSMatDMatSchurExpr.h:361
#define BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION(T)
Constraint on the data type.In case the given data type T requires an intermediate evaluation within ...
Definition: RequiresEvaluation.h:81
typename EnableIf< Condition, T >::Type EnableIf_
Auxiliary alias declaration for the EnableIf class template.The EnableIf_ alias declaration provides ...
Definition: EnableIf.h:224
typename T::OppositeType OppositeType_
Alias declaration for nested OppositeType type definitions.The OppositeType_ alias declaration provid...
Definition: Aliases.h:263
Compile time check for strictly lower triangular matrices.This type trait tests whether or not the gi...
Definition: IsStrictlyLower.h:86
typename T::ConstIterator ConstIterator_
Alias declaration for nested ConstIterator type definitions.The ConstIterator_ alias declaration prov...
Definition: Aliases.h:103
Index-value-pair for sparse vectors and matrices.The ValueIndexPair class represents a single index-v...
Definition: ValueIndexPair.h:73
LeftIterator left_
Iterator over the elements of the left-hand side sparse matrix expression.
Definition: TSMatDMatSchurExpr.h:295
IteratorCategory iterator_category
The iterator category.
Definition: TSMatDMatSchurExpr.h:188
Compile time logical &#39;or&#39; evaluation.The Or alias declaration performs at compile time a logical &#39;or&#39;...
Definition: Or.h:76
bool isAliased(const T *alias) const noexcept
Returns whether the expression is aliased with the given address alias.
Definition: TSMatDMatSchurExpr.h:496
Compile time evaluation of the size of vectors and matrices.The Size type trait evaluates the size of...
Definition: Size.h:80
SchurTrait_< RT1, RT2 > ResultType
Result type for expression template evaluations.
Definition: TSMatDMatSchurExpr.h:150
Compile time logical &#39;and&#39; evaluation.The And alias declaration performs at compile time a logical &#39;a...
Definition: And.h:76
typename T::TransposeType TransposeType_
Alias declaration for nested TransposeType type definitions.The TransposeType_ alias declaration prov...
Definition: Aliases.h:423
Header file for the IsUpper type trait.
void UNUSED_PARAMETER(const Args &...)
Suppression of unused parameter warnings.
Definition: Unused.h:81
ReturnType operator()(size_t i, size_t j) const
2D-access to the matrix elements.
Definition: TSMatDMatSchurExpr.h:329
Header file for the IsHermitian type trait.
ConstIterator find(size_t i, size_t j) const
Searches for a specific matrix element.
Definition: TSMatDMatSchurExpr.h:425
Header file for the Size type trait.
bool canAlias(const T *alias) const noexcept
Returns whether the expression can alias with the given address alias.
Definition: TSMatDMatSchurExpr.h:484
#define BLAZE_INTERNAL_ASSERT(expr, msg)
Run time assertion macro for internal checks.In case of an invalid run time expression, the program execution is terminated. The BLAZE_INTERNAL_ASSERT macro can be disabled by setting the BLAZE_USER_ASSERTION flag to zero or by defining NDEBUG during the compilation.
Definition: Assert.h:101
size_t index() const
Access to the current index of the sparse element.
Definition: TSMatDMatSchurExpr.h:255
#define BLAZE_CONSTRAINT_MUST_BE_SPARSE_MATRIX_TYPE(T)
Constraint on the data type.In case the given data type T is not a sparse, N-dimensional matrix type...
Definition: SparseMatrix.h:61
Header file for the IsExpression type trait class.
Header file for the function trace functionality.
Constraint on the data type.