Blaze  3.6
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 <utility>
45 #include <blaze/math/Aliases.h>
53 #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/MaybeUnused.h>
78 #include <blaze/util/mpl/If.h>
79 #include <blaze/util/mpl/Max.h>
80 #include <blaze/util/Types.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  static constexpr bool returnExpr = ( !IsTemporary_v<RN1> && !IsTemporary_v<RN2> );
123 
125  using ExprReturnType = decltype( std::declval<RN1>() * std::declval<RN2>() );
126  //**********************************************************************************************
127 
128  //**Evaluation strategy*************************************************************************
130 
136  static constexpr bool useAssign = ( RequiresEvaluation_v<MT1> || RequiresEvaluation_v<MT2> );
137 
139  template< typename MT >
141  static constexpr bool UseAssign_v = useAssign;
143  //**********************************************************************************************
144 
145  public:
146  //**Type definitions****************************************************************************
153 
156 
159 
161  using LeftOperand = If_t< IsExpression_v<MT1>, const MT1, const MT1& >;
162 
164  using RightOperand = If_t< IsExpression_v<MT2>, const MT2, const MT2& >;
165  //**********************************************************************************************
166 
167  //**ConstIterator class definition**************************************************************
171  {
172  public:
173  //**Type definitions*************************************************************************
176 
179 
180  using IteratorCategory = std::forward_iterator_tag;
181  using ValueType = Element;
185 
186  // STL iterator requirements
192  //*******************************************************************************************
193 
194  //**Constructor******************************************************************************
201  inline ConstIterator( LeftIterator left, RightOperand right, size_t column )
202  : left_ ( left ) // Iterator over the elements of the left-hand side sparse matrix expression
203  , right_( right ) // Right-hand side dense matrix expression
204  , col_ ( column ) // The column index of the iterator
205  {}
206  //*******************************************************************************************
207 
208  //**Prefix increment operator****************************************************************
214  ++left_;
215  return *this;
216  }
217  //*******************************************************************************************
218 
219  //**Element access operator******************************************************************
224  inline const Element operator*() const {
225  return Element( left_->value() * right_(left_->index(),col_), left_->index() );
226  }
227  //*******************************************************************************************
228 
229  //**Element access operator******************************************************************
234  inline const ConstIterator* operator->() const {
235  return this;
236  }
237  //*******************************************************************************************
238 
239  //**Value function***************************************************************************
244  inline ReturnType value() const {
245  return left_->value() * right_(left_->index(),col_);
246  }
247  //*******************************************************************************************
248 
249  //**Index function***************************************************************************
254  inline size_t index() const {
255  return left_->index();
256  }
257  //*******************************************************************************************
258 
259  //**Equality operator************************************************************************
265  inline bool operator==( const ConstIterator& rhs ) const {
266  return left_ == rhs.left_;
267  }
268  //*******************************************************************************************
269 
270  //**Inequality operator**********************************************************************
276  inline bool operator!=( const ConstIterator& rhs ) const {
277  return left_ != rhs.left_;
278  }
279  //*******************************************************************************************
280 
281  //**Subtraction operator*********************************************************************
287  inline DifferenceType operator-( const ConstIterator& rhs ) const {
288  return left_ - rhs.left_;
289  }
290  //*******************************************************************************************
291 
292  private:
293  //**Member variables*************************************************************************
296  size_t col_;
297  //*******************************************************************************************
298  };
299  //**********************************************************************************************
300 
301  //**Compilation flags***************************************************************************
303  static constexpr bool smpAssignable = false;
304  //**********************************************************************************************
305 
306  //**Constructor*********************************************************************************
312  explicit inline TSMatDMatSchurExpr( const MT1& lhs, const MT2& rhs ) noexcept
313  : lhs_( lhs ) // Left-hand side sparse matrix of the Schur product expression
314  , rhs_( rhs ) // Right-hand side dense matrix of the Schur product expression
315  {
316  BLAZE_INTERNAL_ASSERT( lhs.rows() == rhs.rows() , "Invalid number of rows" );
317  BLAZE_INTERNAL_ASSERT( lhs.columns() == rhs.columns(), "Invalid number of columns" );
318  }
319  //**********************************************************************************************
320 
321  //**Access operator*****************************************************************************
328  inline ReturnType operator()( size_t i, size_t j ) const {
329  BLAZE_INTERNAL_ASSERT( i < lhs_.rows() , "Invalid row access index" );
330  BLAZE_INTERNAL_ASSERT( j < lhs_.columns(), "Invalid column access index" );
331  return lhs_(i,j) * rhs_(i,j);
332  }
333  //**********************************************************************************************
334 
335  //**At function*********************************************************************************
343  inline ReturnType at( size_t i, size_t j ) const {
344  if( i >= lhs_.rows() ) {
345  BLAZE_THROW_OUT_OF_RANGE( "Invalid row access index" );
346  }
347  if( j >= lhs_.columns() ) {
348  BLAZE_THROW_OUT_OF_RANGE( "Invalid column access index" );
349  }
350  return (*this)(i,j);
351  }
352  //**********************************************************************************************
353 
354  //**Begin function******************************************************************************
360  inline ConstIterator begin( size_t j ) const {
361  return ConstIterator( lhs_.begin(j), rhs_, j );
362  }
363  //**********************************************************************************************
364 
365  //**End function********************************************************************************
371  inline ConstIterator end( size_t j ) const {
372  return ConstIterator( lhs_.end(j), rhs_, j );
373  }
374  //**********************************************************************************************
375 
376  //**Rows function*******************************************************************************
381  inline size_t rows() const noexcept {
382  return lhs_.rows();
383  }
384  //**********************************************************************************************
385 
386  //**Columns function****************************************************************************
391  inline size_t columns() const noexcept {
392  return lhs_.columns();
393  }
394  //**********************************************************************************************
395 
396  //**NonZeros function***************************************************************************
401  inline size_t nonZeros() const {
402  return lhs_.nonZeros();
403  }
404  //**********************************************************************************************
405 
406  //**NonZeros function***************************************************************************
412  inline size_t nonZeros( size_t j ) const {
413  return lhs_.nonZeros(j);
414  }
415  //**********************************************************************************************
416 
417  //**Find function*******************************************************************************
424  inline ConstIterator find( size_t i, size_t j ) const {
426  return ConstIterator( lhs_.find( i, j ), rhs_, j );
427  }
428  //**********************************************************************************************
429 
430  //**LowerBound function*************************************************************************
437  inline ConstIterator lowerBound( size_t i, size_t j ) const {
439  return ConstIterator( lhs_.lowerBound( i, j ), rhs_, j );
440  }
441  //**********************************************************************************************
442 
443  //**UpperBound function*************************************************************************
450  inline ConstIterator upperBound( size_t i, size_t j ) const {
452  return ConstIterator( lhs_.upperBound( i, j ), rhs_, j );
453  }
454  //**********************************************************************************************
455 
456  //**Left operand access*************************************************************************
461  inline LeftOperand leftOperand() const noexcept {
462  return lhs_;
463  }
464  //**********************************************************************************************
465 
466  //**Right operand access************************************************************************
471  inline RightOperand rightOperand() const noexcept {
472  return rhs_;
473  }
474  //**********************************************************************************************
475 
476  //**********************************************************************************************
482  template< typename T >
483  inline bool canAlias( const T* alias ) const noexcept {
484  return ( lhs_.canAlias( alias ) || rhs_.isAliased( alias ) );
485  }
486  //**********************************************************************************************
487 
488  //**********************************************************************************************
494  template< typename T >
495  inline bool isAliased( const T* alias ) const noexcept {
496  return ( lhs_.isAliased( alias ) || rhs_.isAliased( alias ) );
497  }
498  //**********************************************************************************************
499 
500  private:
501  //**Member variables****************************************************************************
504  //**********************************************************************************************
505 
506  //**Assignment to dense matrices****************************************************************
518  template< typename MT // Type of the target dense matrix
519  , bool SO2 > // Storage order of the target dense matrix
520  friend inline auto assign( DenseMatrix<MT,SO2>& lhs, const TSMatDMatSchurExpr& rhs )
522  {
524 
525  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
526  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
527 
528  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
529  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side dense matrix operand
530 
531  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
532  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
533  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
534  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
535  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
536  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
537 
538  for( size_t j=0UL; j<(~lhs).columns(); ++j ) {
539  for( auto element=A.begin(j); element!=A.end(j); ++element )
540  (~lhs)(element->index(),j) = element->value() * B(element->index(),j);
541  }
542  }
544  //**********************************************************************************************
545 
546  //**Assignment to row-major sparse matrices*****************************************************
559  template< typename MT > // Type of the target sparse matrix
560  friend inline auto assign( SparseMatrix<MT,false>& lhs, const TSMatDMatSchurExpr& rhs )
562  {
564 
565  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
566  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
567 
568  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
569  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side dense matrix operand
570 
571  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
572  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
573  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
574  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
575  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
576  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
577 
578  const size_t m( rhs.rows() );
579  const size_t n( rhs.columns() );
580 
581  // Counting the number of elements per column
582  std::vector<size_t> nonzeros( m, 0UL );
583  for( size_t j=0UL; j<n; ++j ) {
584  const auto lend( A.end(j) );
585  for( auto l=A.begin(j); l!=lend; ++l ) {
586  ++nonzeros[l->index()];
587  }
588  }
589 
590  // Resizing the left-hand side sparse matrix
591  for( size_t i=0UL; i<m; ++i ) {
592  (~lhs).reserve( i, nonzeros[i] );
593  }
594 
595  // Performing the Schur product
596  for( size_t j=0UL; j<(~lhs).columns(); ++j ) {
597  for( auto element=A.begin(j); element!=A.end(j); ++element )
598  (~lhs).append( element->index(), j, element->value() * B(element->index(),j) );
599  }
600  }
602  //**********************************************************************************************
603 
604  //**Assignment to column-major sparse matrices**************************************************
617  template< typename MT > // Type of the target sparse matrix
618  friend inline auto assign( SparseMatrix<MT,true>& lhs, const TSMatDMatSchurExpr& rhs )
619  -> EnableIf_t< UseAssign_v<MT> >
620  {
622 
623  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
624  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
625 
626  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
627  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side dense matrix operand
628 
629  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
630  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
631  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
632  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
633  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
634  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
635 
636  // Final memory allocation (based on the evaluated operands)
637  (~lhs).reserve( A.nonZeros() );
638 
639  // Performing the Schur product
640  for( size_t j=0UL; j<(~lhs).columns(); ++j ) {
641  for( auto element=A.begin(j); element!=A.end(j); ++element )
642  (~lhs).append( element->index(), j, element->value() * B(element->index(),j) );
643  (~lhs).finalize( j );
644  }
645  }
647  //**********************************************************************************************
648 
649  //**Addition assignment to dense matrices*******************************************************
662  template< typename MT // Type of the target dense matrix
663  , bool SO2 > // Storage order of the target dense matrix
664  friend inline auto addAssign( DenseMatrix<MT,SO2>& lhs, const TSMatDMatSchurExpr& rhs )
665  -> EnableIf_t< UseAssign_v<MT> >
666  {
668 
669  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
670  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
671 
672  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
673  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side dense matrix operand
674 
675  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
676  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
677  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
678  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
679  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
680  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
681 
682  for( size_t j=0UL; j<(~lhs).columns(); ++j ) {
683  for( auto element=A.begin(j); element!=A.end(j); ++element )
684  (~lhs)(element->index(),j) += element->value() * B(element->index(),j);
685  }
686  }
688  //**********************************************************************************************
689 
690  //**Addition assignment to sparse matrices******************************************************
691  // No special implementation for the addition assignment to sparse matrices.
692  //**********************************************************************************************
693 
694  //**Subtraction assignment to dense matrices****************************************************
707  template< typename MT // Type of the target dense matrix
708  , bool SO2 > // Storage order of the target dense matrix
709  friend inline auto subAssign( DenseMatrix<MT,SO2>& lhs, const TSMatDMatSchurExpr& rhs )
710  -> EnableIf_t< UseAssign_v<MT> >
711  {
713 
714  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
715  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
716 
717  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
718  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side dense matrix operand
719 
720  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
721  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
722  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
723  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
724  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
725  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
726 
727  for( size_t j=0UL; j<(~lhs).columns(); ++j ) {
728  for( auto element=A.begin(j); element!=A.end(j); ++element )
729  (~lhs)(element->index(),j) -= element->value() * B(element->index(),j);
730  }
731  }
733  //**********************************************************************************************
734 
735  //**Subtraction assignment to sparse matrices***************************************************
736  // No special implementation for the subtraction assignment to sparse matrices.
737  //**********************************************************************************************
738 
739  //**Schur product assignment to dense matrices**************************************************
752  template< typename MT // Type of the target dense matrix
753  , bool SO2 > // Storage order of the target dense matrix
754  friend inline void schurAssign( DenseMatrix<MT,SO2>& lhs, const TSMatDMatSchurExpr& rhs )
755  {
757 
758  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
759  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
760 
761  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
762  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side dense matrix operand
763 
764  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
765  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
766  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
767  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
768  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
769  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
770 
771  for( size_t j=0UL; j<(~lhs).columns(); ++j )
772  {
773  const auto end( A.end(j) );
774  auto begin( A.begin(j) );
775  size_t i( 0UL );
776 
777  for( ; begin!=end; ++begin ) {
778  const size_t index( begin->index() );
779  for( ; i<index; ++i )
780  reset( (~lhs)(i,j) );
781  (~lhs)(index,j) *= begin->value() * B(index,j);
782  ++i;
783  }
784 
785  for( ; i<(~lhs).rows(); ++i )
786  reset( (~lhs)(i,j) );
787  }
788  }
790  //**********************************************************************************************
791 
792  //**Schur product assignment to sparse matrices*************************************************
793  // No special implementation for the Schur product assignment to sparse matrices.
794  //**********************************************************************************************
795 
796  //**Multiplication assignment to dense matrices*************************************************
797  // No special implementation for the multiplication assignment to dense matrices.
798  //**********************************************************************************************
799 
800  //**Multiplication assignment to sparse matrices************************************************
801  // No special implementation for the multiplication assignment to sparse matrices.
802  //**********************************************************************************************
803 
804  //**SMP assignment to dense matrices************************************************************
805  // No special implementation for the SMP assignment to dense matrices.
806  //**********************************************************************************************
807 
808  //**SMP assignment to sparse matrices***********************************************************
809  // No special implementation for the SMP assignment to sparse matrices.
810  //**********************************************************************************************
811 
812  //**SMP addition assignment to dense matrices***************************************************
813  // No special implementation for the SMP addition assignment to dense matrices.
814  //**********************************************************************************************
815 
816  //**SMP addition assignment to sparse matrices**************************************************
817  // No special implementation for the SMP addition assignment to sparse matrices.
818  //**********************************************************************************************
819 
820  //**SMP subtraction assignment to dense matrices************************************************
821  // No special implementation for the SMP subtraction assignment to dense matrices.
822  //**********************************************************************************************
823 
824  //**SMP subtraction assignment to sparse matrices***********************************************
825  // No special implementation for the SMP subtraction assignment to sparse matrices.
826  //**********************************************************************************************
827 
828  //**SMP Schur product assignment to dense matrices**********************************************
841  template< typename MT // Type of the target dense matrix
842  , bool SO > // Storage order of the target dense matrix
843  friend inline void smpSchurAssign( DenseMatrix<MT,SO>& lhs, const TSMatDMatSchurExpr& rhs )
844  {
846 
847  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
848  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
849 
850  smpSchurAssign( ~lhs, rhs.lhs_ );
851  smpSchurAssign( ~lhs, rhs.rhs_ );
852  }
854  //**********************************************************************************************
855 
856  //**SMP Schur product assignment to sparse matrices*********************************************
857  // No special implementation for the SMP Schur product assignment to sparse matrices.
858  //**********************************************************************************************
859 
860  //**SMP multiplication assignment to dense matrices*********************************************
861  // No special implementation for the SMP multiplication assignment to dense matrices.
862  //**********************************************************************************************
863 
864  //**SMP multiplication assignment to sparse matrices********************************************
865  // No special implementation for the SMP multiplication assignment to sparse matrices.
866  //**********************************************************************************************
867 
868  //**Compile time checks*************************************************************************
876  //**********************************************************************************************
877 };
878 //*************************************************************************************************
879 
880 
881 
882 
883 //=================================================================================================
884 //
885 // GLOBAL BINARY ARITHMETIC OPERATORS
886 //
887 //=================================================================================================
888 
889 //*************************************************************************************************
902 template< typename MT1 // Type of the left-hand side sparse matrix
903  , typename MT2 // Type of the right-hand side dense matrix
904  , DisableIf_t< ( IsUniLower_v<MT1> && IsUniUpper_v<MT2> ) ||
905  ( IsUniUpper_v<MT1> && IsUniLower_v<MT2> ) ||
906  ( IsStrictlyLower_v<MT1> && IsUpper_v<MT2> ) ||
907  ( IsStrictlyUpper_v<MT1> && IsLower_v<MT2> ) ||
908  ( IsLower_v<MT1> && IsStrictlyUpper_v<MT2> ) ||
909  ( IsUpper_v<MT1> && IsStrictlyLower_v<MT2> ) ||
910  IsZero_v<MT1> >* = nullptr >
911 inline const TSMatDMatSchurExpr<MT1,MT2>
912  tsmatdmatschur( const SparseMatrix<MT1,true>& lhs, const DenseMatrix<MT2,false>& rhs )
913 {
915 
916  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
917  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
918 
919  return TSMatDMatSchurExpr<MT1,MT2>( ~lhs, ~rhs );
920 }
922 //*************************************************************************************************
923 
924 
925 //*************************************************************************************************
939 template< typename MT1 // Type of the left-hand side sparse matrix
940  , typename MT2 // Type of the right-hand side dense matrix
941  , EnableIf_t< ( IsUniLower_v<MT1> && IsUniUpper_v<MT2> ) ||
942  ( IsUniUpper_v<MT1> && IsUniLower_v<MT2> ) >* = nullptr >
943 inline decltype(auto)
944  tsmatdmatschur( const SparseMatrix<MT1,true>& lhs, const DenseMatrix<MT2,false>& rhs )
945 {
947 
948  MAYBE_UNUSED( rhs );
949 
950  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
951  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
952 
953  using ReturnType = const SchurTrait_t< ResultType_t<MT1>, ResultType_t<MT2> >;
954 
957 
958  return ReturnType( (~lhs).rows() );
959 }
961 //*************************************************************************************************
962 
963 
964 //*************************************************************************************************
978 template< typename MT1 // Type of the left-hand side sparse matrix
979  , typename MT2 // Type of the right-hand side dense matrix
980  , EnableIf_t< ( IsStrictlyLower_v<MT1> && IsUpper_v<MT2> ) ||
981  ( IsStrictlyUpper_v<MT1> && IsLower_v<MT2> ) ||
982  ( IsLower_v<MT1> && IsStrictlyUpper_v<MT2> ) ||
983  ( IsUpper_v<MT1> && IsStrictlyLower_v<MT2> ) ||
984  IsZero_v<MT1> >* = nullptr >
985 inline decltype(auto)
986  tsmatdmatschur( const SparseMatrix<MT1,true>& lhs, const DenseMatrix<MT2,false>& rhs )
987 {
989 
990  MAYBE_UNUSED( rhs );
991 
992  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
993  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
994 
995  using ReturnType = const SchurTrait_t< ResultType_t<MT1>, ResultType_t<MT2> >;
996 
999 
1000  return ReturnType( (~lhs).rows(), (~lhs).columns() );
1001 }
1003 //*************************************************************************************************
1004 
1005 
1006 //*************************************************************************************************
1036 template< typename MT1 // Type of the left-hand side sparse matrix
1037  , typename MT2 > // Type of the right-hand side dense matrix
1038 inline decltype(auto)
1039  operator%( const SparseMatrix<MT1,true>& lhs, const DenseMatrix<MT2,false>& rhs )
1040 {
1042 
1043  if( (~lhs).rows() != (~rhs).rows() || (~lhs).columns() != (~rhs).columns() ) {
1044  BLAZE_THROW_INVALID_ARGUMENT( "Matrix sizes do not match" );
1045  }
1046 
1047  return tsmatdmatschur( ~lhs, ~rhs );
1048 }
1049 //*************************************************************************************************
1050 
1051 
1052 //*************************************************************************************************
1065 template< typename MT1 // Type of the left-hand side sparse matrix
1066  , typename MT2 // Type of the right-hand side dense matrix
1067  , DisableIf_t< ( IsUniLower_v<MT1> && IsUniUpper_v<MT2> ) ||
1068  ( IsUniUpper_v<MT1> && IsUniLower_v<MT2> ) ||
1069  ( IsStrictlyLower_v<MT1> && IsUpper_v<MT2> ) ||
1070  ( IsStrictlyUpper_v<MT1> && IsLower_v<MT2> ) ||
1071  ( IsLower_v<MT1> && IsStrictlyUpper_v<MT2> ) ||
1072  ( IsUpper_v<MT1> && IsStrictlyLower_v<MT2> ) ||
1073  IsZero_v<MT1> >* = nullptr >
1074 inline const TSMatDMatSchurExpr<MT1,MT2>
1075  tsmattdmatschur( const SparseMatrix<MT1,true>& lhs, const DenseMatrix<MT2,true>& rhs )
1076 {
1078 
1079  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
1080  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
1081 
1082  return TSMatDMatSchurExpr<MT1,MT2>( ~lhs, ~rhs );
1083 }
1085 //*************************************************************************************************
1086 
1087 
1088 //*************************************************************************************************
1102 template< typename MT1 // Type of the left-hand side sparse matrix
1103  , typename MT2 // Type of the right-hand side dense matrix
1104  , EnableIf_t< ( IsUniLower_v<MT1> && IsUniUpper_v<MT2> ) ||
1105  ( IsUniUpper_v<MT1> && IsUniLower_v<MT2> ) >* = nullptr >
1106 inline decltype(auto)
1107  tsmattdmatschur( const SparseMatrix<MT1,true>& lhs, const DenseMatrix<MT2,true>& rhs )
1108 {
1110 
1111  MAYBE_UNUSED( rhs );
1112 
1113  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
1114  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
1115 
1116  using ReturnType = const SchurTrait_t< ResultType_t<MT1>, ResultType_t<MT2> >;
1117 
1120 
1121  return ReturnType( (~lhs).rows() );
1122 }
1124 //*************************************************************************************************
1125 
1126 
1127 //*************************************************************************************************
1141 template< typename MT1 // Type of the left-hand side sparse matrix
1142  , typename MT2 // Type of the right-hand side dense matrix
1143  , EnableIf_t< ( IsStrictlyLower_v<MT1> && IsUpper_v<MT2> ) ||
1144  ( IsStrictlyUpper_v<MT1> && IsLower_v<MT2> ) ||
1145  ( IsLower_v<MT1> && IsStrictlyUpper_v<MT2> ) ||
1146  ( IsUpper_v<MT1> && IsStrictlyLower_v<MT2> ) ||
1147  IsZero_v<MT1> >* = nullptr >
1148 inline decltype(auto)
1149  tsmattdmatschur( const SparseMatrix<MT1,true>& lhs, const DenseMatrix<MT2,true>& rhs )
1150 {
1152 
1153  MAYBE_UNUSED( rhs );
1154 
1155  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
1156  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
1157 
1158  using ReturnType = const SchurTrait_t< ResultType_t<MT1>, ResultType_t<MT2> >;
1159 
1161  BLAZE_CONSTRAINT_MUST_BE_ZERO_TYPE( ReturnType );
1162 
1163  return ReturnType( (~lhs).rows(), (~lhs).columns() );
1164 }
1166 //*************************************************************************************************
1167 
1168 
1169 //*************************************************************************************************
1198 template< typename MT1 // Type of the left-hand side sparse matrix
1199  , typename MT2 > // Type of the right-hand side dense matrix
1200 inline decltype(auto)
1201  operator%( const SparseMatrix<MT1,true>& lhs, const DenseMatrix<MT2,true>& rhs )
1202 {
1204 
1205  if( (~lhs).rows() != (~rhs).rows() || (~lhs).columns() != (~rhs).columns() ) {
1206  BLAZE_THROW_INVALID_ARGUMENT( "Matrix sizes do not match" );
1207  }
1208 
1209  return tsmattdmatschur( ~lhs, ~rhs );
1210 }
1211 //*************************************************************************************************
1212 
1213 
1214 
1215 
1216 //=================================================================================================
1217 //
1218 // SIZE SPECIALIZATIONS
1219 //
1220 //=================================================================================================
1221 
1222 //*************************************************************************************************
1224 template< typename MT1, typename MT2 >
1225 struct Size< TSMatDMatSchurExpr<MT1,MT2>, 0UL >
1226  : public Max_t< Size<MT1,0UL>, Size<MT2,0UL> >
1227 {};
1228 
1229 template< typename MT1, typename MT2 >
1230 struct Size< TSMatDMatSchurExpr<MT1,MT2>, 1UL >
1231  : public Max_t< Size<MT1,1UL>, Size<MT2,1UL> >
1232 {};
1234 //*************************************************************************************************
1235 
1236 } // namespace blaze
1237 
1238 #endif
Constraint on the data type.
#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.
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:133
#define BLAZE_CONSTRAINT_MUST_BE_IDENTITY_MATRIX_TYPE(T)
Constraint on the data type.In case the given data type T is not an identity matrix type,...
Definition: Identity.h:60
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:412
ValueIndexPair< ElementType > Element
Element type of the sparse matrix expression.
Definition: TSMatDMatSchurExpr.h:175
Header file for the IsUniUpper type trait.
Expression object for transpose sparse matrix-dense matrix Schur product.The TSMatDMatSchurExpr class...
Definition: Forward.h:180
Header file for basic type definitions.
LeftOperand lhs_
Left-hand side sparse matrix of the Schur product expression.
Definition: TSMatDMatSchurExpr.h:502
OppositeType_t< ResultType > OppositeType
Result type with opposite storage order for expression template evaluations.
Definition: TSMatDMatSchurExpr.h:150
Header file for all forward declarations for sparse vectors and matrices.
typename If< Condition, T1, T2 >::Type If_t
Auxiliary alias template for the If class template.The If_t alias template provides a convenient shor...
Definition: If.h:109
ReturnType at(size_t i, size_t j) const
Checked access to the matrix elements.
Definition: TSMatDMatSchurExpr.h:343
typename T::ResultType ResultType_t
Alias declaration for nested ResultType type definitions.The ResultType_t alias declaration provides ...
Definition: Aliases.h:390
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
ElementType_t< ResultType > ElementType
Resulting element type.
Definition: TSMatDMatSchurExpr.h:152
void reset(const DiagonalProxy< MT > &proxy)
Resetting the represented element to the default initial values.
Definition: DiagonalProxy.h:595
ConstIterator upperBound(size_t i, size_t j) const
Returns an iterator to the first index greater then the given index.
Definition: TSMatDMatSchurExpr.h:450
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: TSMatDMatSchurExpr.h:437
Header file for the MAYBE_UNUSED function template.
Header file for the Computation base class.
ResultType_t< MT1 > RT1
Result type of the left-hand side sparse matrix expression.
Definition: TSMatDMatSchurExpr.h:107
ValueType * PointerType
Pointer return type.
Definition: TSMatDMatSchurExpr.h:182
ReturnType value() const
Access to the current value of the sparse element.
Definition: TSMatDMatSchurExpr.h:244
typename T::ReturnType ReturnType_t
Alias declaration for nested ReturnType type definitions.The ReturnType_t alias declaration provides ...
Definition: Aliases.h:410
Header file for the IsUniLower type trait.
ConstIterator(LeftIterator left, RightOperand right, size_t column)
Constructor for the ConstIterator class.
Definition: TSMatDMatSchurExpr.h:201
#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 Schur product,...
Definition: SchurExpr.h:103
constexpr size_t columns(const Matrix< MT, SO > &matrix) noexcept
Returns the current number of columns of the matrix.
Definition: Matrix.h:514
Base class for dense matrices.The DenseMatrix class is a base class for all dense matrix classes....
Definition: DenseMatrix.h:81
Base class for sparse matrices.The SparseMatrix class is a base class for all sparse matrix classes....
Definition: Forward.h:145
typename T::ElementType ElementType_t
Alias declaration for nested ElementType type definitions.The ElementType_t alias declaration provide...
Definition: Aliases.h:170
DifferenceType operator-(const ConstIterator &rhs) const
Calculating the number of elements between two expression iterators.
Definition: TSMatDMatSchurExpr.h:287
Header file for the SparseMatrix base class.
const ConstIterator * operator->() const
Direct access to the sparse matrix element at the current iterator position.
Definition: TSMatDMatSchurExpr.h:234
bool operator==(const ConstIterator &rhs) const
Equality comparison between two ConstIterator objects.
Definition: TSMatDMatSchurExpr.h:265
ConstIterator_t< RemoveReference_t< LeftOperand > > LeftIterator
Iterator type of the sparse matrix expression.
Definition: TSMatDMatSchurExpr.h:178
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:391
typename EnableIf< Condition, T >::Type EnableIf_t
Auxiliary type for the EnableIf class template.The EnableIf_t alias declaration provides a convenient...
Definition: EnableIf.h:138
size_t rows() const noexcept
Returns the current number of rows of the matrix.
Definition: TSMatDMatSchurExpr.h:381
Element ValueType
Type of the underlying pointers.
Definition: TSMatDMatSchurExpr.h:181
Header file for the ValueIndexPair class.
Header file for the DisableIf class template.
Header file for the IsTemporary type trait class.
Header file for the IsStrictlyUpper type trait.
ConstIterator & operator++()
Pre-increment operator.
Definition: TSMatDMatSchurExpr.h:213
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
#define BLAZE_CONSTRAINT_MUST_BE_ZERO_TYPE(T)
Constraint on the data type.In case the given data type T is not a zero vector or matrix type,...
Definition: Zero.h:61
#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
RightOperand rightOperand() const noexcept
Returns the right-hand side dense matrix operand.
Definition: TSMatDMatSchurExpr.h:471
Header file for the IsLower type trait.
constexpr void MAYBE_UNUSED(const Args &...)
Suppression of unused parameter warnings.
Definition: MaybeUnused.h:81
If_t< IsExpression_v< MT2 >, const MT2, const MT2 & > RightOperand
Composite type of the right-hand side dense matrix expression.
Definition: TSMatDMatSchurExpr.h:164
static constexpr bool useAssign
Compilation switch for the evaluation strategy of the Schur product expression.
Definition: TSMatDMatSchurExpr.h:136
LeftOperand leftOperand() const noexcept
Returns the left-hand side transpose sparse matrix operand.
Definition: TSMatDMatSchurExpr.h:461
static constexpr bool returnExpr
Compilation switch for the selection of the subscript operator return type.
Definition: TSMatDMatSchurExpr.h:122
bool operator!=(const ConstIterator &rhs) const
Inequality comparison between two ConstIterator objects.
Definition: TSMatDMatSchurExpr.h:276
Header file for the exception macros of the math module.
size_t col_
The column index of the iterator.
Definition: TSMatDMatSchurExpr.h:296
ConstIterator end(size_t j) const
Returns an iterator just past the last non-zero element of column j.
Definition: TSMatDMatSchurExpr.h:371
Constraint on the data type.
ReturnType_t< MT1 > RN1
Return type of the left-hand side sparse matrix expression.
Definition: TSMatDMatSchurExpr.h:109
Header file for the EnableIf class template.
Header file for the IsStrictlyLower type trait.
If_t< useAssign, const ResultType, const TSMatDMatSchurExpr & > CompositeType
Data type for composite expression templates.
Definition: TSMatDMatSchurExpr.h:158
typename T::OppositeType OppositeType_t
Alias declaration for nested OppositeType type definitions.The OppositeType_t alias declaration provi...
Definition: Aliases.h:270
std::forward_iterator_tag IteratorCategory
The iterator category.
Definition: TSMatDMatSchurExpr.h:180
const If_t< returnExpr, ExprReturnType, ElementType > ReturnType
Return type for expression template evaluations.
Definition: TSMatDMatSchurExpr.h:155
TSMatDMatSchurExpr(const MT1 &lhs, const MT2 &rhs) noexcept
Constructor for the TSMatDMatSchurExpr class.
Definition: TSMatDMatSchurExpr.h:312
decltype(std::declval< RN1 >() *std::declval< RN2 >()) ExprReturnType
Expression return type for the subscript operator.
Definition: TSMatDMatSchurExpr.h:125
typename T::TransposeType TransposeType_t
Alias declaration for nested TransposeType type definitions.The TransposeType_t alias declaration pro...
Definition: Aliases.h:470
Header file for run time assertion macros.
ptrdiff_t DifferenceType
Difference between two iterators.
Definition: TSMatDMatSchurExpr.h:184
typename T::CompositeType CompositeType_t
Alias declaration for nested CompositeType type definitions.The CompositeType_t alias declaration pro...
Definition: Aliases.h:90
SchurTrait_t< RT1, RT2 > ResultType
Result type for expression template evaluations.
Definition: TSMatDMatSchurExpr.h:149
ResultType_t< MT2 > RT2
Result type of the right-hand side dense matrix expression.
Definition: TSMatDMatSchurExpr.h:108
size_t nonZeros() const
Returns the number of non-zero elements in the sparse matrix.
Definition: TSMatDMatSchurExpr.h:401
Header file for the SchurExpr base class.
typename SchurTrait< T1, T2 >::Type SchurTrait_t
Auxiliary alias declaration for the SchurTrait class template.The SchurTrait_t alias declaration prov...
Definition: SchurTrait.h:163
RightOperand right_
Right-hand side dense matrix expression.
Definition: TSMatDMatSchurExpr.h:295
Header file for the IsZero type trait.
const Element operator *() const
Direct access to the sparse matrix element at the current iterator position.
Definition: TSMatDMatSchurExpr.h:224
#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:170
Header file for all forward declarations for expression class templates.
RightOperand rhs_
Right-hand side dense matrix of the Schur product expression.
Definition: TSMatDMatSchurExpr.h:503
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:808
ConstIterator begin(size_t j) const
Returns an iterator to the first non-zero element of column j.
Definition: TSMatDMatSchurExpr.h:360
#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
auto smpSchurAssign(Matrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs) -> EnableIf_t< IsDenseMatrix_v< MT1 > >
Default implementation of the SMP Schur product assignment of a matrix to dense matrix.
Definition: DenseMatrix.h:194
constexpr size_t rows(const Matrix< MT, SO > &matrix) noexcept
Returns the current number of rows of the matrix.
Definition: Matrix.h:498
Header file for the RemoveReference type trait.
typename T::ConstIterator ConstIterator_t
Alias declaration for nested ConstIterator type definitions.The ConstIterator_t alias declaration pro...
Definition: Aliases.h:110
ReturnType_t< MT2 > RN2
Return type of the right-hand side dense matrix expression.
Definition: TSMatDMatSchurExpr.h:110
If_t< IsExpression_v< MT1 >, const MT1, const MT1 & > LeftOperand
Composite type of the left-hand side sparse matrix expression.
Definition: TSMatDMatSchurExpr.h:161
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:294
IteratorCategory iterator_category
The iterator category.
Definition: TSMatDMatSchurExpr.h:187
CompositeType_t< MT2 > CT2
Composite type of the right-hand side dense matrix expression.
Definition: TSMatDMatSchurExpr.h:112
bool isAliased(const T *alias) const noexcept
Returns whether the expression is aliased with the given address alias.
Definition: TSMatDMatSchurExpr.h:495
Header file for the IntegralConstant class template.
Header file for the Max_t alias template.
Header file for the IsUpper type trait.
typename DisableIf< Condition, T >::Type DisableIf_t
Auxiliary type for the DisableIf class template.The DisableIf_t alias declaration provides a convenie...
Definition: DisableIf.h:138
CompositeType_t< MT1 > CT1
Composite type of the left-hand side sparse matrix expression.
Definition: TSMatDMatSchurExpr.h:111
ValueType & ReferenceType
Reference return type.
Definition: TSMatDMatSchurExpr.h:183
ReturnType operator()(size_t i, size_t j) const
2D-access to the matrix elements.
Definition: TSMatDMatSchurExpr.h:328
static constexpr bool smpAssignable
Compilation switch for the expression template assignment strategy.
Definition: TSMatDMatSchurExpr.h:303
ConstIterator find(size_t i, size_t j) const
Searches for a specific matrix element.
Definition: TSMatDMatSchurExpr.h:424
Header file for the Size type trait.
#define BLAZE_CONSTRAINT_MUST_NOT_BE_ZERO_TYPE(T)
Constraint on the data type.In case the given data type T is a zero vector or matrix type,...
Definition: Zero.h:81
bool canAlias(const T *alias) const noexcept
Returns whether the expression can alias with the given address alias.
Definition: TSMatDMatSchurExpr.h:483
#define BLAZE_INTERNAL_ASSERT(expr, msg)
Run time assertion macro for internal checks.In case of an invalid run time expression,...
Definition: Assert.h:101
TransposeType_t< ResultType > TransposeType
Transpose type for expression template evaluations.
Definition: TSMatDMatSchurExpr.h:151
size_t index() const
Access to the current index of the sparse element.
Definition: TSMatDMatSchurExpr.h:254
#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.
If_t< Less_t< T1, T2 >::value, T2, T1 > Max_t
Compile time value evaluation.The Max_t alias template selects the larger of the two given template a...
Definition: Max.h:73
Constraint on the data type.