SMatDMatSchurExpr.h
Go to the documentation of this file.
1 //=================================================================================================
33 //=================================================================================================
34 
35 #ifndef _BLAZE_MATH_EXPRESSIONS_SMATDMATSCHUREXPR_H_
36 #define _BLAZE_MATH_EXPRESSIONS_SMATDMATSCHUREXPR_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>
77 #include <blaze/util/mpl/And.h>
78 #include <blaze/util/mpl/If.h>
79 #include <blaze/util/mpl/Maximum.h>
80 #include <blaze/util/mpl/Or.h>
81 #include <blaze/util/Types.h>
82 #include <blaze/util/Unused.h>
83 
84 
85 namespace blaze {
86 
87 //=================================================================================================
88 //
89 // CLASS SMATDMATSCHUREXPR
90 //
91 //=================================================================================================
92 
93 //*************************************************************************************************
100 template< typename MT1 // Type of the left-hand side sparse matrix
101  , typename MT2 > // Type of the right-hand side dense matrix
102 class SMatDMatSchurExpr
103  : public SchurExpr< SparseMatrix< SMatDMatSchurExpr<MT1,MT2>, false > >
104  , private Computation
105 {
106  private:
107  //**Type definitions****************************************************************************
114  //**********************************************************************************************
115 
116  //**Return type evaluation**********************************************************************
118 
123  enum : bool { returnExpr = !IsTemporary<RN1>::value && !IsTemporary<RN2>::value };
124 
127  //**********************************************************************************************
128 
129  //**Evaluation strategy*************************************************************************
131 
137  enum : bool { useAssign = ( RequiresEvaluation<MT1>::value || RequiresEvaluation<MT2>::value ) };
138 
140  template< typename VT >
142  struct UseAssign {
143  enum : bool { value = useAssign };
144  };
146  //**********************************************************************************************
147 
148  public:
149  //**Type definitions****************************************************************************
155 
158 
160  using CompositeType = const ResultType;
161 
163  using LeftOperand = If_< IsExpression<MT1>, const MT1, const MT1& >;
164 
166  using RightOperand = If_< IsExpression<MT2>, const MT2, const MT2& >;
167  //**********************************************************************************************
168 
169  //**ConstIterator class definition**************************************************************
173  {
174  public:
175  //**Type definitions*************************************************************************
178 
181 
182  using IteratorCategory = std::forward_iterator_tag;
183  using ValueType = Element;
187 
188  // STL iterator requirements
194  //*******************************************************************************************
195 
196  //**Constructor******************************************************************************
203  inline ConstIterator( LeftIterator left, RightOperand right, size_t row )
204  : left_ ( left ) // Iterator over the elements of the left-hand side sparse matrix expression
205  , right_( right ) // Right-hand side dense matrix expression
206  , row_ ( row ) // The row index of the iterator
207  {}
208  //*******************************************************************************************
209 
210  //**Prefix increment operator****************************************************************
216  ++left_;
217  return *this;
218  }
219  //*******************************************************************************************
220 
221  //**Element access operator******************************************************************
226  inline const Element operator*() const {
227  return Element( left_->value() * right_(row_,left_->index()), left_->index() );
228  }
229  //*******************************************************************************************
230 
231  //**Element access operator******************************************************************
236  inline const ConstIterator* operator->() const {
237  return this;
238  }
239  //*******************************************************************************************
240 
241  //**Value function***************************************************************************
246  inline ReturnType value() const {
247  return left_->value() * right_(row_,left_->index());
248  }
249  //*******************************************************************************************
250 
251  //**Index function***************************************************************************
256  inline size_t index() const {
257  return left_->index();
258  }
259  //*******************************************************************************************
260 
261  //**Equality operator************************************************************************
267  inline bool operator==( const ConstIterator& rhs ) const {
268  return left_ == rhs.left_;
269  }
270  //*******************************************************************************************
271 
272  //**Inequality operator**********************************************************************
278  inline bool operator!=( const ConstIterator& rhs ) const {
279  return left_ != rhs.left_;
280  }
281  //*******************************************************************************************
282 
283  //**Subtraction operator*********************************************************************
289  inline DifferenceType operator-( const ConstIterator& rhs ) const {
290  return left_ - rhs.left_;
291  }
292  //*******************************************************************************************
293 
294  private:
295  //**Member variables*************************************************************************
298  size_t row_;
299  //*******************************************************************************************
300  };
301  //**********************************************************************************************
302 
303  //**Compilation flags***************************************************************************
305  enum : bool { smpAssignable = false };
306  //**********************************************************************************************
307 
308  //**Constructor*********************************************************************************
314  explicit inline SMatDMatSchurExpr( const MT1& lhs, const MT2& rhs ) noexcept
315  : lhs_( lhs ) // Left-hand side sparse matrix of the Schur product expression
316  , rhs_( rhs ) // Right-hand side dense matrix of the Schur product expression
317  {
318  BLAZE_INTERNAL_ASSERT( lhs.rows() == rhs.rows() , "Invalid number of rows" );
319  BLAZE_INTERNAL_ASSERT( lhs.columns() == rhs.columns(), "Invalid number of columns" );
320  }
321  //**********************************************************************************************
322 
323  //**Access operator*****************************************************************************
330  inline ReturnType operator()( size_t i, size_t j ) const {
331  BLAZE_INTERNAL_ASSERT( i < lhs_.rows() , "Invalid row access index" );
332  BLAZE_INTERNAL_ASSERT( j < lhs_.columns(), "Invalid column access index" );
333  return lhs_(i,j) * rhs_(i,j);
334  }
335  //**********************************************************************************************
336 
337  //**At function*********************************************************************************
345  inline ReturnType at( size_t i, size_t j ) const {
346  if( i >= lhs_.rows() ) {
347  BLAZE_THROW_OUT_OF_RANGE( "Invalid row access index" );
348  }
349  if( j >= lhs_.columns() ) {
350  BLAZE_THROW_OUT_OF_RANGE( "Invalid column access index" );
351  }
352  return (*this)(i,j);
353  }
354  //**********************************************************************************************
355 
356  //**Begin function******************************************************************************
362  inline ConstIterator begin( size_t i ) const {
363  return ConstIterator( lhs_.begin(i), rhs_, i );
364  }
365  //**********************************************************************************************
366 
367  //**End function********************************************************************************
373  inline ConstIterator end( size_t i ) const {
374  return ConstIterator( lhs_.end(i), rhs_, i );
375  }
376  //**********************************************************************************************
377 
378  //**Rows function*******************************************************************************
383  inline size_t rows() const noexcept {
384  return lhs_.rows();
385  }
386  //**********************************************************************************************
387 
388  //**Columns function****************************************************************************
393  inline size_t columns() const noexcept {
394  return lhs_.columns();
395  }
396  //**********************************************************************************************
397 
398  //**NonZeros function***************************************************************************
403  inline size_t nonZeros() const {
404  return lhs_.nonZeros();
405  }
406  //**********************************************************************************************
407 
408  //**NonZeros function***************************************************************************
414  inline size_t nonZeros( size_t i ) const {
415  return lhs_.nonZeros(i);
416  }
417  //**********************************************************************************************
418 
419  //**Find function*******************************************************************************
426  inline ConstIterator find( size_t i, size_t j ) const {
428  return ConstIterator( lhs_.find( i, j ), rhs_, i );
429  }
430  //**********************************************************************************************
431 
432  //**LowerBound function*************************************************************************
439  inline ConstIterator lowerBound( size_t i, size_t j ) const {
441  return ConstIterator( lhs_.lowerBound( i, j ), rhs_, i );
442  }
443  //**********************************************************************************************
444 
445  //**UpperBound function*************************************************************************
452  inline ConstIterator upperBound( size_t i, size_t j ) const {
454  return ConstIterator( lhs_.upperBound( i, j ), rhs_, i );
455  }
456  //**********************************************************************************************
457 
458  //**Left operand access*************************************************************************
463  inline LeftOperand leftOperand() const noexcept {
464  return lhs_;
465  }
466  //**********************************************************************************************
467 
468  //**Right operand access************************************************************************
473  inline RightOperand rightOperand() const noexcept {
474  return rhs_;
475  }
476  //**********************************************************************************************
477 
478  //**********************************************************************************************
484  template< typename T >
485  inline bool canAlias( const T* alias ) const noexcept {
486  return ( lhs_.canAlias( alias ) || rhs_.canAlias( alias ) );
487  }
488  //**********************************************************************************************
489 
490  //**********************************************************************************************
496  template< typename T >
497  inline bool isAliased( const T* alias ) const noexcept {
498  return ( lhs_.isAliased( alias ) || rhs_.isAliased( alias ) );
499  }
500  //**********************************************************************************************
501 
502  private:
503  //**Member variables****************************************************************************
506  //**********************************************************************************************
507 
508  //**Assignment to dense matrices****************************************************************
520  template< typename MT // Type of the target dense matrix
521  , bool SO2 > // Storage order of the target dense matrix
522  friend inline EnableIf_< UseAssign<MT> >
523  assign( DenseMatrix<MT,SO2>& lhs, const SMatDMatSchurExpr& rhs )
524  {
526 
527  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
528  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
529 
531 
532  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
533  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side dense matrix operand
534 
535  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
536  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
537  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
538  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
539  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
540  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
541 
542  for( size_t i=0UL; i<(~lhs).rows(); ++i ) {
543  for( ConstIterator element=A.begin(i); element!=A.end(i); ++element )
544  (~lhs)(i,element->index()) = element->value() * B(i,element->index());
545  }
546  }
548  //**********************************************************************************************
549 
550  //**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 SMatDMatSchurExpr& 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  // Final memory allocation (based on the evaluated operands)
584  (~lhs).reserve( A.nonZeros() );
585 
586  // Performing the Schur product
587  for( size_t i=0UL; i<(~lhs).rows(); ++i ) {
588  for( ConstIterator element=A.begin(i); element!=A.end(i); ++element )
589  (~lhs).append( i, element->index(), element->value() * B(i,element->index()) );
590  (~lhs).finalize( i );
591  }
592  }
594  //**********************************************************************************************
595 
596  //**Assignment to column-major sparse matrices**************************************************
609  template< typename MT > // Type of the target sparse matrix
610  friend inline EnableIf_< UseAssign<MT> >
611  assign( SparseMatrix<MT,true>& lhs, const SMatDMatSchurExpr& rhs )
612  {
614 
615  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
616  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
617 
619 
620  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
621  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side dense matrix operand
622 
623  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
624  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
625  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
626  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
627  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
628  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
629 
630  const size_t m( rhs.rows() );
631  const size_t n( rhs.columns() );
632 
633  // Counting the number of elements per column
634  std::vector<size_t> nonzeros( n, 0UL );
635  for( size_t i=0UL; i<m; ++i ) {
636  const ConstIterator lend( A.end(i) );
637  for( ConstIterator l=A.begin(i); l!=lend; ++l ) {
638  ++nonzeros[l->index()];
639  }
640  }
641 
642  // Resizing the left-hand side sparse matrix
643  for( size_t j=0UL; j<n; ++j ) {
644  (~lhs).reserve( j, nonzeros[j] );
645  }
646 
647  // Performing the Schur product
648  for( size_t i=0UL; i<m; ++i ) {
649  for( ConstIterator element=A.begin(i); element!=A.end(i); ++element )
650  (~lhs).append( i, element->index(), element->value() * B(i,element->index()) );
651  }
652  }
654  //**********************************************************************************************
655 
656  //**Addition assignment to dense matrices*******************************************************
668  template< typename MT // Type of the target dense matrix
669  , bool SO2 > // Storage order of the target dense matrix
670  friend inline EnableIf_< UseAssign<MT> >
671  addAssign( DenseMatrix<MT,SO2>& lhs, const SMatDMatSchurExpr& rhs )
672  {
674 
675  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
676  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
677 
679 
680  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
681  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side dense matrix operand
682 
683  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
684  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
685  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
686  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
687  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
688  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
689 
690  for( size_t i=0UL; i<(~lhs).rows(); ++i ) {
691  for( ConstIterator element=A.begin(i); element!=A.end(i); ++element )
692  (~lhs)(i,element->index()) += element->value() * B(i,element->index());
693  }
694  }
696  //**********************************************************************************************
697 
698  //**Addition assignment to sparse matrices******************************************************
699  // No special implementation for the addition assignment to sparse matrices.
700  //**********************************************************************************************
701 
702  //**Subtraction assignment to dense matrices****************************************************
714  template< typename MT // Type of the target dense matrix
715  , bool SO2 > // Storage order of the target dense matrix
716  friend inline EnableIf_< UseAssign<MT> >
717  subAssign( DenseMatrix<MT,SO2>& lhs, const SMatDMatSchurExpr& rhs )
718  {
720 
721  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
722  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
723 
725 
726  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
727  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side dense matrix operand
728 
729  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
730  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
731  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
732  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
733  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
734  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
735 
736  for( size_t i=0UL; i<(~lhs).rows(); ++i ) {
737  for( ConstIterator element=A.begin(i); element!=A.end(i); ++element )
738  (~lhs)(i,element->index()) -= element->value() * B(i,element->index());
739  }
740  }
742  //**********************************************************************************************
743 
744  //**Subtraction assignment to sparse matrices***************************************************
745  // No special implementation for the subtraction assignment to sparse matrices.
746  //**********************************************************************************************
747 
748  //**Schur product assignment to dense matrices**************************************************
761  template< typename MT // Type of the target dense matrix
762  , bool SO2 > // Storage order of the target dense matrix
763  friend inline void schurAssign( DenseMatrix<MT,SO2>& lhs, const SMatDMatSchurExpr& rhs )
764  {
766 
767  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
768  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
769 
771 
772  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
773  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side dense matrix operand
774 
775  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
776  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
777  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
778  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
779  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
780  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
781 
782  for( size_t i=0UL; i<(~lhs).rows(); ++i )
783  {
784  const ConstIterator end( A.end(i) );
785  ConstIterator begin( A.begin(i) );
786  size_t j( 0UL );
787 
788  for( ; begin!=end; ++begin ) {
789  const size_t index( begin->index() );
790  for( ; j<index; ++j )
791  reset( (~lhs)(i,j) );
792  (~lhs)(i,index) *= begin->value() * B(i,index);
793  ++j;
794  }
795 
796  for( ; j<(~lhs).columns(); ++j )
797  reset( (~lhs)(i,j) );
798  }
799  }
801  //**********************************************************************************************
802 
803  //**Schur product assignment to sparse matrices*************************************************
804  // No special implementation for the Schur product assignment to sparse matrices.
805  //**********************************************************************************************
806 
807  //**Multiplication assignment to dense matrices*************************************************
808  // No special implementation for the multiplication assignment to dense matrices.
809  //**********************************************************************************************
810 
811  //**Multiplication assignment to sparse matrices************************************************
812  // No special implementation for the multiplication assignment to sparse matrices.
813  //**********************************************************************************************
814 
815  //**SMP assignment to dense matrices************************************************************
816  // No special implementation for the SMP assignment to dense matrices.
817  //**********************************************************************************************
818 
819  //**SMP assignment to sparse matrices***********************************************************
820  // No special implementation for the SMP assignment to sparse matrices.
821  //**********************************************************************************************
822 
823  //**SMP addition assignment to dense matrices***************************************************
824  // No special implementation for the SMP addition assignment to dense matrices.
825  //**********************************************************************************************
826 
827  //**SMP addition assignment to sparse matrices**************************************************
828  // No special implementation for the SMP addition assignment to sparse matrices.
829  //**********************************************************************************************
830 
831  //**SMP subtraction assignment to dense matrices************************************************
832  // No special implementation for the SMP subtraction assignment to dense matrices.
833  //**********************************************************************************************
834 
835  //**SMP subtraction assignment to sparse matrices***********************************************
836  // No special implementation for the SMP subtraction assignment to sparse matrices.
837  //**********************************************************************************************
838 
839  //**SMP Schur product assignment to dense matrices**********************************************
852  template< typename MT // Type of the target dense matrix
853  , bool SO > // Storage order of the target dense matrix
854  friend inline void smpSchurAssign( DenseMatrix<MT,SO>& lhs, const SMatDMatSchurExpr& rhs )
855  {
857 
858  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
859  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
860 
861  smpSchurAssign( ~lhs, rhs.lhs_ );
862  smpSchurAssign( ~lhs, rhs.rhs_ );
863  }
865  //**********************************************************************************************
866 
867  //**SMP Schur product assignment to sparse matrices*********************************************
868  // No special implementation for the SMP Schur product assignment to sparse matrices.
869  //**********************************************************************************************
870 
871  //**SMP multiplication assignment to dense matrices*********************************************
872  // No special implementation for the SMP multiplication assignment to dense matrices.
873  //**********************************************************************************************
874 
875  //**SMP multiplication assignment to sparse matrices********************************************
876  // No special implementation for the SMP multiplication assignment to sparse matrices.
877  //**********************************************************************************************
878 
879  //**Compile time checks*************************************************************************
886  //**********************************************************************************************
887 };
888 //*************************************************************************************************
889 
890 
891 
892 
893 //=================================================================================================
894 //
895 // GLOBAL BINARY ARITHMETIC OPERATORS
896 //
897 //=================================================================================================
898 
899 //*************************************************************************************************
912 template< typename MT1 // Type of the left-hand side sparse matrix
913  , typename MT2 // Type of the right-hand side dense matrix
916 inline const SMatDMatSchurExpr<MT1,MT2>
917  smatdmatschur( const SparseMatrix<MT1,false>& lhs, const DenseMatrix<MT2,false>& rhs )
918 {
920 
921  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
922  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
923 
924  return SMatDMatSchurExpr<MT1,MT2>( ~lhs, ~rhs );
925 }
927 //*************************************************************************************************
928 
929 
930 //*************************************************************************************************
943 template< typename MT1 // Type of the left-hand side sparse matrix
944  , typename MT2 // Type of the right-hand side dense matrix
945  , typename = EnableIf_< Or< And< IsUniLower<MT1>, IsUniUpper<MT2> >
946  , And< IsUniUpper<MT1>, IsUniLower<MT2> > > > >
948  smatdmatschur( const SparseMatrix<MT1,false>& lhs, const DenseMatrix<MT2,false>& rhs )
949 {
951 
952  UNUSED_PARAMETER( rhs );
953 
954  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
955  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
956 
957  return IdentityMatrix< MultTrait_< ElementType_<MT1>, ElementType_<MT2> >, false >( (~lhs).rows() );
958 }
960 //*************************************************************************************************
961 
962 
963 //*************************************************************************************************
992 template< typename MT1 // Type of the left-hand side sparse matrix
993  , typename MT2 > // Type of the right-hand side dense matrix
994 inline decltype(auto)
995  operator%( const SparseMatrix<MT1,false>& lhs, const DenseMatrix<MT2,false>& rhs )
996 {
998 
999  if( (~lhs).rows() != (~rhs).rows() || (~lhs).columns() != (~rhs).columns() ) {
1000  BLAZE_THROW_INVALID_ARGUMENT( "Matrix sizes do not match" );
1001  }
1002 
1003  return smatdmatschur( ~lhs, ~rhs );
1004 }
1005 //*************************************************************************************************
1006 
1007 
1008 //*************************************************************************************************
1021 template< typename MT1 // Type of the left-hand side sparse matrix
1022  , typename MT2 // Type of the right-hand side dense matrix
1025 inline const SMatDMatSchurExpr<MT1,MT2>
1026  smattdmatschur( const SparseMatrix<MT1,false>& lhs, const DenseMatrix<MT2,true>& rhs )
1027 {
1029 
1030  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
1031  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
1032 
1033  return SMatDMatSchurExpr<MT1,MT2>( ~lhs, ~rhs );
1034 }
1036 //*************************************************************************************************
1037 
1038 
1039 //*************************************************************************************************
1052 template< typename MT1 // Type of the left-hand side sparse matrix
1053  , typename MT2 // Type of the right-hand side dense matrix
1057  smattdmatschur( const SparseMatrix<MT1,false>& lhs, const DenseMatrix<MT2,true>& rhs )
1058 {
1060 
1061  UNUSED_PARAMETER( rhs );
1062 
1063  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
1064  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
1065 
1067 }
1069 //*************************************************************************************************
1070 
1071 
1072 //*************************************************************************************************
1102 template< typename MT1 // Type of the left-hand side sparse matrix
1103  , typename MT2 > // Type of the right-hand side dense matrix
1104 inline decltype(auto)
1105  operator%( const SparseMatrix<MT1,false>& lhs, const DenseMatrix<MT2,true>& rhs )
1106 {
1108 
1109  if( (~lhs).rows() != (~rhs).rows() || (~lhs).columns() != (~rhs).columns() ) {
1110  BLAZE_THROW_INVALID_ARGUMENT( "Matrix sizes do not match" );
1111  }
1112 
1113  return smattdmatschur( ~lhs, ~rhs );
1114 }
1115 //*************************************************************************************************
1116 
1117 
1118 
1119 
1120 //=================================================================================================
1121 //
1122 // ROWS SPECIALIZATIONS
1123 //
1124 //=================================================================================================
1125 
1126 //*************************************************************************************************
1128 template< typename MT1, typename MT2 >
1129 struct Rows< SMatDMatSchurExpr<MT1,MT2> >
1130  : public Maximum< Rows<MT1>, Rows<MT2> >
1131 {};
1133 //*************************************************************************************************
1134 
1135 
1136 
1137 
1138 //=================================================================================================
1139 //
1140 // COLUMNS SPECIALIZATIONS
1141 //
1142 //=================================================================================================
1143 
1144 //*************************************************************************************************
1146 template< typename MT1, typename MT2 >
1147 struct Columns< SMatDMatSchurExpr<MT1,MT2> >
1148  : public Maximum< Columns<MT1>, Columns<MT2> >
1149 {};
1151 //*************************************************************************************************
1152 
1153 
1154 
1155 
1156 //=================================================================================================
1157 //
1158 // ISSYMMETRIC SPECIALIZATIONS
1159 //
1160 //=================================================================================================
1161 
1162 //*************************************************************************************************
1164 template< typename MT1, typename MT2 >
1165 struct IsSymmetric< SMatDMatSchurExpr<MT1,MT2> >
1166  : public BoolConstant< IsSymmetric<MT1>::value && IsSymmetric<MT2>::value >
1167 {};
1169 //*************************************************************************************************
1170 
1171 
1172 
1173 
1174 //=================================================================================================
1175 //
1176 // ISHERMITIAN SPECIALIZATIONS
1177 //
1178 //=================================================================================================
1179 
1180 //*************************************************************************************************
1182 template< typename MT1, typename MT2 >
1183 struct IsHermitian< SMatDMatSchurExpr<MT1,MT2> >
1184  : public BoolConstant< IsHermitian<MT1>::value && IsHermitian<MT2>::value >
1185 {};
1187 //*************************************************************************************************
1188 
1189 
1190 
1191 
1192 //=================================================================================================
1193 //
1194 // ISLOWER SPECIALIZATIONS
1195 //
1196 //=================================================================================================
1197 
1198 //*************************************************************************************************
1200 template< typename MT1, typename MT2 >
1201 struct IsLower< SMatDMatSchurExpr<MT1,MT2> >
1202  : public BoolConstant< Or< IsLower<MT1>, IsLower<MT2> >::value >
1203 {};
1205 //*************************************************************************************************
1206 
1207 
1208 
1209 
1210 //=================================================================================================
1211 //
1212 // ISUNILOWER SPECIALIZATIONS
1213 //
1214 //=================================================================================================
1215 
1216 //*************************************************************************************************
1218 template< typename MT1, typename MT2 >
1219 struct IsUniLower< SMatDMatSchurExpr<MT1,MT2> >
1220  : public BoolConstant< And< IsUniLower<MT1>, IsUniLower<MT2> >::value >
1221 {};
1223 //*************************************************************************************************
1224 
1225 
1226 
1227 
1228 //=================================================================================================
1229 //
1230 // ISSTRICTLYLOWER SPECIALIZATIONS
1231 //
1232 //=================================================================================================
1233 
1234 //*************************************************************************************************
1236 template< typename MT1, typename MT2 >
1237 struct IsStrictlyLower< SMatDMatSchurExpr<MT1,MT2> >
1238  : public BoolConstant< Or< IsStrictlyLower<MT1>, IsStrictlyLower<MT2> >::value >
1239 {};
1241 //*************************************************************************************************
1242 
1243 
1244 
1245 
1246 //=================================================================================================
1247 //
1248 // ISUPPER SPECIALIZATIONS
1249 //
1250 //=================================================================================================
1251 
1252 //*************************************************************************************************
1254 template< typename MT1, typename MT2 >
1255 struct IsUpper< SMatDMatSchurExpr<MT1,MT2> >
1256  : public BoolConstant< Or< IsUpper<MT1>, IsUpper<MT2> >::value >
1257 {};
1259 //*************************************************************************************************
1260 
1261 
1262 
1263 
1264 //=================================================================================================
1265 //
1266 // ISUNIUPPER SPECIALIZATIONS
1267 //
1268 //=================================================================================================
1269 
1270 //*************************************************************************************************
1272 template< typename MT1, typename MT2 >
1273 struct IsUniUpper< SMatDMatSchurExpr<MT1,MT2> >
1274  : public BoolConstant< And< IsUniUpper<MT1>, IsUniUpper<MT2> >::value >
1275 {};
1277 //*************************************************************************************************
1278 
1279 
1280 
1281 
1282 //=================================================================================================
1283 //
1284 // ISSTRICTLYUPPER SPECIALIZATIONS
1285 //
1286 //=================================================================================================
1287 
1288 //*************************************************************************************************
1290 template< typename MT1, typename MT2 >
1291 struct IsStrictlyUpper< SMatDMatSchurExpr<MT1,MT2> >
1292  : public BoolConstant< Or< IsStrictlyUpper<MT1>, IsStrictlyUpper<MT2> >::value >
1293 {};
1295 //*************************************************************************************************
1296 
1297 } // namespace blaze
1298 
1299 #endif
LeftOperand leftOperand() const noexcept
Returns the left-hand side sparse matrix operand.
Definition: SMatDMatSchurExpr.h:463
ElementType_< ResultType > ElementType
Resulting element type.
Definition: SMatDMatSchurExpr.h:154
#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.
RightOperand rightOperand() const noexcept
Returns the right-hand side dense matrix operand.
Definition: SMatDMatSchurExpr.h:473
Header file for auxiliary alias declarations.
size_t rows() const noexcept
Returns the current number of rows of the matrix.
Definition: SMatDMatSchurExpr.h:383
Header file for the Schur product trait.
Compile time check whether the given type is a temporary vector or matrix type.This type trait class ...
Definition: IsTemporary.h:70
Header file for the Rows type trait.
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
ResultType_< MT2 > RT2
Result type of the right-hand side dense matrix expression.
Definition: SMatDMatSchurExpr.h:109
ConstIterator find(size_t i, size_t j) const
Searches for a specific matrix element.
Definition: SMatDMatSchurExpr.h:426
Header file for basic type definitions.
bool operator!=(const ConstIterator &rhs) const
Inequality comparison between two ConstIterator objects.
Definition: SMatDMatSchurExpr.h:278
Header file for the serial shim.
ReturnType at(size_t i, size_t j) const
Checked access to the matrix elements.
Definition: SMatDMatSchurExpr.h:345
size_t columns() const noexcept
Returns the current number of columns of the matrix.
Definition: SMatDMatSchurExpr.h:393
Generic wrapper for a compile time constant integral value.The IntegralConstant class template repres...
Definition: IntegralConstant.h:71
#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
DifferenceType operator-(const ConstIterator &rhs) const
Calculating the number of elements between two expression iterators.
Definition: SMatDMatSchurExpr.h:289
bool operator==(const ConstIterator &rhs) const
Equality comparison between two ConstIterator objects.
Definition: SMatDMatSchurExpr.h:267
SMatDMatSchurExpr(const MT1 &lhs, const MT2 &rhs) noexcept
Constructor for the SMatDMatSchurExpr class.
Definition: SMatDMatSchurExpr.h:314
ResultType_< MT1 > RT1
Result type of the left-hand side sparse matrix expression.
Definition: SMatDMatSchurExpr.h:108
void reset(const DiagonalProxy< MT > &proxy)
Resetting the represented element to the default initial values.
Definition: DiagonalProxy.h:560
typename DisableIf< Condition, T >::Type DisableIf_
Auxiliary type for the DisableIf class template.The DisableIf_ alias declaration provides a convenien...
Definition: DisableIf.h:224
CompositeType_< MT1 > CT1
Composite type of the left-hand side sparse matrix expression.
Definition: SMatDMatSchurExpr.h:112
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:88
Header file for the Computation base class.
ConstIterator_< RemoveReference_< LeftOperand > > LeftIterator
Iterator type of the sparse matrix expression.
Definition: SMatDMatSchurExpr.h:180
Compile time check for upper triangular matrices.This type trait tests whether or not the given templ...
Definition: IsUpper.h:88
Constraints on the storage order of matrix types.
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
size_t index() const
Access to the current index of the sparse element.
Definition: SMatDMatSchurExpr.h:256
#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:108
Base class for dense matrices.The DenseMatrix class is a base class for all dense matrix classes...
Definition: DenseMatrix.h:78
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.
RightOperand rhs_
Right-hand side dense matrix of the Schur product expression.
Definition: SMatDMatSchurExpr.h:505
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
typename T::ReturnType ReturnType_
Alias declaration for nested ReturnType type definitions.The ReturnType_ alias declaration provides a...
Definition: Aliases.h:363
MultExprTrait_< RN1, RN2 > ExprReturnType
Expression return type for the subscript operator.
Definition: SMatDMatSchurExpr.h:126
Header file for the SparseMatrix base class.
Row< MT > row(Matrix< MT, SO > &matrix, size_t index)
Creating a view on a specific row of the given matrix.
Definition: Row.h:124
LeftIterator left_
Iterator over the elements of the left-hand side sparse matrix expression.
Definition: SMatDMatSchurExpr.h:296
If_< IsExpression< MT1 >, const MT1, const MT1 &> LeftOperand
Composite type of the left-hand side sparse matrix expression.
Definition: SMatDMatSchurExpr.h:163
Constraint on the data type.
Constraint on the data type.
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
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:72
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.
size_t row_
The row index of the iterator.
Definition: SMatDMatSchurExpr.h:298
Header file for the IsStrictlyUpper type trait.
Header file for the IsSymmetric type trait.
ReturnType value() const
Access to the current value of the sparse element.
Definition: SMatDMatSchurExpr.h:246
Namespace of the Blaze C++ math library.
Definition: Blaze.h:57
std::forward_iterator_tag IteratorCategory
The iterator category.
Definition: SMatDMatSchurExpr.h:182
Header file for the If class template.
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
Header file for the Columns type trait.
const Element * ConstIterator
Iterator over constant elements.
Definition: CompressedMatrix.h:3087
typename T::ElementType ElementType_
Alias declaration for nested ElementType type definitions.The ElementType_ alias declaration provides...
Definition: Aliases.h:163
Header file for the IsLower type trait.
ConstIterator upperBound(size_t i, size_t j) const
Returns an iterator to the first index greater then the given index.
Definition: SMatDMatSchurExpr.h:452
typename SchurTrait< T1, T2 >::Type SchurTrait_
Auxiliary alias declaration for the SchurTrait class template.The SchurTrait_ alias declaration provi...
Definition: SchurTrait.h:167
LeftOperand lhs_
Left-hand side sparse matrix of the Schur product expression.
Definition: SMatDMatSchurExpr.h:504
bool isAliased(const T *alias) const noexcept
Returns whether the expression is aliased with the given address alias.
Definition: SMatDMatSchurExpr.h:497
Compile time check for symmetric matrices.This type trait tests whether or not the given template par...
Definition: IsSymmetric.h:85
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
RightOperand right_
Right-hand side dense matrix expression.
Definition: SMatDMatSchurExpr.h:297
Constraint on the data type.
Header file for all forward declarations for expression class templates.
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
If_< IsExpression< MT2 >, const MT2, const MT2 &> RightOperand
Composite type of the right-hand side dense matrix expression.
Definition: SMatDMatSchurExpr.h:166
const ConstIterator * operator->() const
Direct access to the sparse matrix element at the current iterator position.
Definition: SMatDMatSchurExpr.h:236
CompositeType_< MT2 > CT2
Composite type of the right-hand side dense matrix expression.
Definition: SMatDMatSchurExpr.h:113
#define BLAZE_CONSTRAINT_MUST_BE_ROW_MAJOR_MATRIX_TYPE(T)
Constraint on the data type.In case the given data type T is not a row-major dense or sparse matrix t...
Definition: RowMajorMatrix.h:61
size_t nonZeros() const
Returns the number of non-zero elements in the sparse matrix.
Definition: SMatDMatSchurExpr.h:403
Header file for run time assertion macros.
ConstIterator(LeftIterator left, RightOperand right, size_t row)
Constructor for the ConstIterator class.
Definition: SMatDMatSchurExpr.h:203
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
OppositeType_< ResultType > OppositeType
Result type with opposite storage order for expression template evaluations.
Definition: SMatDMatSchurExpr.h:152
ConstIterator end(size_t i) const
Returns an iterator just past the last non-zero element of row i.
Definition: SMatDMatSchurExpr.h:373
ReturnType_< MT1 > RN1
Return type of the left-hand side sparse matrix expression.
Definition: SMatDMatSchurExpr.h:110
ReturnType_< MT2 > RN2
Return type of the right-hand side dense matrix expression.
Definition: SMatDMatSchurExpr.h:111
#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
TransposeType_< ResultType > TransposeType
Transpose type for expression template evaluations.
Definition: SMatDMatSchurExpr.h:153
const IfTrue_< returnExpr, ExprReturnType, ElementType > ReturnType
Return type for expression template evaluations.
Definition: SMatDMatSchurExpr.h:157
Compile time check for Hermitian matrices.This type trait tests whether or not the given template par...
Definition: IsHermitian.h:85
ConstIterator & operator++()
Pre-increment operator.
Definition: SMatDMatSchurExpr.h:215
const ResultType CompositeType
Data type for composite expression templates.
Definition: SMatDMatSchurExpr.h:160
decltype(auto) serial(const DenseMatrix< MT, SO > &dm)
Forces the serial evaluation of the given dense matrix expression dm.
Definition: DMatSerialExpr.h:819
const Element operator*() const
Direct access to the sparse matrix element at the current iterator position.
Definition: SMatDMatSchurExpr.h:226
#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
Iterator over the elements of the sparse matrix/dense matrix Schur product expression.
Definition: SMatDMatSchurExpr.h:172
Index-value-pair for sparse vectors and matrices.The ValueIndexPair class represents a single index-v...
Definition: ValueIndexPair.h:73
Header file for the IntegralConstant class template.
Compile time evaluation of the number of columns of a matrix.The Columns type trait evaluates the num...
Definition: Columns.h:75
size_t nonZeros(size_t i) const
Returns the number of non-zero elements in the specified row.
Definition: SMatDMatSchurExpr.h:414
Compile time evaluation of the number of rows of a matrix.The Rows type trait evaluates the number of...
Definition: Rows.h:75
bool canAlias(const T *alias) const noexcept
Returns whether the expression can alias with the given address alias.
Definition: SMatDMatSchurExpr.h:485
Compile time logical and evaluation.The And alias declaration performs at compile time a logical and ...
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
Header file for the IsHermitian type trait.
IteratorCategory iterator_category
The iterator category.
Definition: SMatDMatSchurExpr.h:189
Expression object for sparse matrix-dense matrix Schur product.The SMatDMatSchurExpr class represents...
Definition: Forward.h:108
ConstIterator begin(size_t i) const
Returns an iterator to the first non-zero element of row i.
Definition: SMatDMatSchurExpr.h:362
SchurTrait_< RT1, RT2 > ResultType
Result type for expression template evaluations.
Definition: SMatDMatSchurExpr.h:151
#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
ReturnType operator()(size_t i, size_t j) const
2D-access to the matrix elements.
Definition: SMatDMatSchurExpr.h:330
#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.
ConstIterator lowerBound(size_t i, size_t j) const
Returns an iterator to the first index not less then the given index.
Definition: SMatDMatSchurExpr.h:439