DMatSMatSchurExpr.h
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1 //=================================================================================================
33 //=================================================================================================
34 
35 #ifndef _BLAZE_MATH_EXPRESSIONS_DMATSMATSCHUREXPR_H_
36 #define _BLAZE_MATH_EXPRESSIONS_DMATSMATSCHUREXPR_H_
37 
38 
39 //*************************************************************************************************
40 // Includes
41 //*************************************************************************************************
42 
43 #include <iterator>
44 #include <blaze/math/Aliases.h>
50 #include <blaze/math/Exception.h>
72 #include <blaze/util/Assert.h>
73 #include <blaze/util/DisableIf.h>
74 #include <blaze/util/EnableIf.h>
76 #include <blaze/util/mpl/And.h>
77 #include <blaze/util/mpl/If.h>
78 #include <blaze/util/mpl/Maximum.h>
79 #include <blaze/util/mpl/Or.h>
80 #include <blaze/util/Types.h>
81 #include <blaze/util/Unused.h>
82 
83 
84 namespace blaze {
85 
86 //=================================================================================================
87 //
88 // CLASS DMATSMATSCHUREXPR
89 //
90 //=================================================================================================
91 
92 //*************************************************************************************************
99 template< typename MT1 // Type of the left-hand side dense matrix
100  , typename MT2 > // Type of the right-hand side sparse matrix
102  : public SchurExpr< SparseMatrix< DMatSMatSchurExpr<MT1,MT2>, false > >
103  , private Computation
104 {
105  private:
106  //**Type definitions****************************************************************************
113  //**********************************************************************************************
114 
115  //**Return type evaluation**********************************************************************
117 
122  enum : bool { returnExpr = !IsTemporary<RN1>::value && !IsTemporary<RN2>::value };
123 
126  //**********************************************************************************************
127 
128  //**Evaluation strategy*************************************************************************
130 
136  enum : bool { useAssign = ( RequiresEvaluation<MT1>::value || RequiresEvaluation<MT2>::value ) };
137 
139  template< typename VT >
141  struct UseAssign {
142  enum : bool { value = useAssign };
143  };
145  //**********************************************************************************************
146 
147  public:
148  //**Type definitions****************************************************************************
154 
157 
160 
162  using LeftOperand = If_< IsExpression<MT1>, const MT1, const MT1& >;
163 
165  using RightOperand = If_< IsExpression<MT2>, const MT2, const MT2& >;
166  //**********************************************************************************************
167 
168  //**ConstIterator class definition**************************************************************
172  {
173  public:
174  //**Type definitions*************************************************************************
177 
180 
181  using IteratorCategory = std::forward_iterator_tag;
182  using ValueType = Element;
186 
187  // STL iterator requirements
193  //*******************************************************************************************
194 
195  //**Constructor******************************************************************************
202  inline ConstIterator( LeftOperand left, RightIterator right, size_t row )
203  : left_ ( left ) // Left-hand side dense matrix expression
204  , right_( right ) // Iterator over the elements of the right-hand side sparse matrix expression
205  , row_ ( row ) // The row index of the iterator
206  {}
207  //*******************************************************************************************
208 
209  //**Prefix increment operator****************************************************************
215  ++right_;
216  return *this;
217  }
218  //*******************************************************************************************
219 
220  //**Element access operator******************************************************************
225  inline const Element operator*() const {
226  return Element( left_(row_,right_->index()) * right_->value(), right_->index() );
227  }
228  //*******************************************************************************************
229 
230  //**Element access operator******************************************************************
235  inline const ConstIterator* operator->() const {
236  return this;
237  }
238  //*******************************************************************************************
239 
240  //**Value function***************************************************************************
245  inline ReturnType value() const {
246  return left_(row_,right_->index()) * right_->value();
247  }
248  //*******************************************************************************************
249 
250  //**Index function***************************************************************************
255  inline size_t index() const {
256  return right_->index();
257  }
258  //*******************************************************************************************
259 
260  //**Equality operator************************************************************************
266  inline bool operator==( const ConstIterator& rhs ) const {
267  return right_ == rhs.right_;
268  }
269  //*******************************************************************************************
270 
271  //**Inequality operator**********************************************************************
277  inline bool operator!=( const ConstIterator& rhs ) const {
278  return right_ != rhs.right_;
279  }
280  //*******************************************************************************************
281 
282  //**Subtraction operator*********************************************************************
288  inline DifferenceType operator-( const ConstIterator& rhs ) const {
289  return right_ - rhs.right_;
290  }
291  //*******************************************************************************************
292 
293  private:
294  //**Member variables*************************************************************************
297  size_t row_;
298  //*******************************************************************************************
299  };
300  //**********************************************************************************************
301 
302  //**Compilation flags***************************************************************************
304  enum : bool { smpAssignable = false };
305  //**********************************************************************************************
306 
307  //**Constructor*********************************************************************************
313  explicit inline DMatSMatSchurExpr( const MT1& lhs, const MT2& rhs ) noexcept
314  : lhs_( lhs ) // Left-hand side dense matrix of the Schur product expression
315  , rhs_( rhs ) // Right-hand side sparse matrix of the Schur product expression
316  {
317  BLAZE_INTERNAL_ASSERT( lhs.rows() == rhs.rows() , "Invalid number of rows" );
318  BLAZE_INTERNAL_ASSERT( lhs.columns() == rhs.columns(), "Invalid number of columns" );
319  }
320  //**********************************************************************************************
321 
322  //**Access operator*****************************************************************************
329  inline ReturnType operator()( size_t i, size_t j ) const {
330  BLAZE_INTERNAL_ASSERT( i < lhs_.rows() , "Invalid row access index" );
331  BLAZE_INTERNAL_ASSERT( j < lhs_.columns(), "Invalid column access index" );
332  return lhs_(i,j) * rhs_(i,j);
333  }
334  //**********************************************************************************************
335 
336  //**At function*********************************************************************************
344  inline ReturnType at( size_t i, size_t j ) const {
345  if( i >= lhs_.rows() ) {
346  BLAZE_THROW_OUT_OF_RANGE( "Invalid row access index" );
347  }
348  if( j >= lhs_.columns() ) {
349  BLAZE_THROW_OUT_OF_RANGE( "Invalid column access index" );
350  }
351  return (*this)(i,j);
352  }
353  //**********************************************************************************************
354 
355  //**Begin function******************************************************************************
361  inline ConstIterator begin( size_t i ) const {
362  return ConstIterator( lhs_, rhs_.begin(i), i );
363  }
364  //**********************************************************************************************
365 
366  //**End function********************************************************************************
372  inline ConstIterator end( size_t i ) const {
373  return ConstIterator( lhs_, rhs_.end(i), i );
374  }
375  //**********************************************************************************************
376 
377  //**Rows function*******************************************************************************
382  inline size_t rows() const noexcept {
383  return lhs_.rows();
384  }
385  //**********************************************************************************************
386 
387  //**Columns function****************************************************************************
392  inline size_t columns() const noexcept {
393  return lhs_.columns();
394  }
395  //**********************************************************************************************
396 
397  //**NonZeros function***************************************************************************
402  inline size_t nonZeros() const {
403  return rhs_.nonZeros();
404  }
405  //**********************************************************************************************
406 
407  //**NonZeros function***************************************************************************
413  inline size_t nonZeros( size_t i ) const {
414  return rhs_.nonZeros(i);
415  }
416  //**********************************************************************************************
417 
418  //**Find function*******************************************************************************
425  inline ConstIterator find( size_t i, size_t j ) const {
427  return ConstIterator( lhs_, rhs_.find( i, j ), i );
428  }
429  //**********************************************************************************************
430 
431  //**LowerBound function*************************************************************************
438  inline ConstIterator lowerBound( size_t i, size_t j ) const {
440  return ConstIterator( lhs_, rhs_.lowerBound( i, j ), i );
441  }
442  //**********************************************************************************************
443 
444  //**UpperBound function*************************************************************************
451  inline ConstIterator upperBound( size_t i, size_t j ) const {
453  return ConstIterator( lhs_, rhs_.upperBound( i, j ), i );
454  }
455  //**********************************************************************************************
456 
457  //**Left operand access*************************************************************************
462  inline LeftOperand leftOperand() const noexcept {
463  return lhs_;
464  }
465  //**********************************************************************************************
466 
467  //**Right operand access************************************************************************
472  inline RightOperand rightOperand() const noexcept {
473  return rhs_;
474  }
475  //**********************************************************************************************
476 
477  //**********************************************************************************************
483  template< typename T >
484  inline bool canAlias( const T* alias ) const noexcept {
485  return ( lhs_.canAlias( alias ) || rhs_.canAlias( alias ) );
486  }
487  //**********************************************************************************************
488 
489  //**********************************************************************************************
495  template< typename T >
496  inline bool isAliased( const T* alias ) const noexcept {
497  return ( lhs_.isAliased( alias ) || rhs_.isAliased( alias ) );
498  }
499  //**********************************************************************************************
500 
501  private:
502  //**Member variables****************************************************************************
505  //**********************************************************************************************
506 
507  //**Assignment to dense matrices****************************************************************
519  template< typename MT // Type of the target dense matrix
520  , bool SO2 > // Storage order of the target dense matrix
521  friend inline EnableIf_< UseAssign<MT> >
522  assign( DenseMatrix<MT,SO2>& lhs, const DMatSMatSchurExpr& rhs )
523  {
525 
526  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
527  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
528 
530 
531  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side dense matrix operand
532  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
533 
534  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
535  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
536  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
537  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
538  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
539  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
540 
541  for( size_t i=0UL; i<(~lhs).rows(); ++i ) {
542  for( ConstIterator element=B.begin(i); element!=B.end(i); ++element )
543  (~lhs)(i,element->index()) = A(i,element->index()) * element->value();
544  }
545  }
547  //**********************************************************************************************
548 
549  //**Assignment to row-major sparse matrices*****************************************************
561  template< typename MT > // Type of the target sparse matrix
562  friend inline EnableIf_< UseAssign<MT> >
563  assign( SparseMatrix<MT,false>& lhs, const DMatSMatSchurExpr& rhs )
564  {
566 
567  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
568  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
569 
571 
572  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side dense matrix operand
573  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
574 
575  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
576  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
577  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
578  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
579  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
580  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
581 
582  // Final memory allocation (based on the evaluated operands)
583  (~lhs).reserve( B.nonZeros() );
584 
585  // Performing the Schur product
586  for( size_t i=0UL; i<(~lhs).rows(); ++i ) {
587  for( ConstIterator element=B.begin(i); element!=B.end(i); ++element )
588  (~lhs).append( i, element->index(), A(i,element->index()) * element->value() );
589  (~lhs).finalize( i );
590  }
591  }
593  //**********************************************************************************************
594 
595  //**Assignment to column-major sparse matrices**************************************************
608  template< typename MT > // Type of the target sparse matrix
609  friend inline EnableIf_< UseAssign<MT> >
610  assign( SparseMatrix<MT,true>& lhs, const DMatSMatSchurExpr& rhs )
611  {
613 
614  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
615  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
616 
618 
619  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side dense matrix operand
620  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
621 
622  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
623  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
624  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
625  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
626  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
627  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
628 
629  const size_t m( rhs.rows() );
630  const size_t n( rhs.columns() );
631 
632  // Counting the number of elements per column
633  std::vector<size_t> nonzeros( n, 0UL );
634  for( size_t i=0UL; i<m; ++i ) {
635  const ConstIterator lend( B.end(i) );
636  for( ConstIterator l=B.begin(i); l!=lend; ++l ) {
637  ++nonzeros[l->index()];
638  }
639  }
640 
641  // Resizing the left-hand side sparse matrix
642  for( size_t j=0UL; j<n; ++j ) {
643  (~lhs).reserve( j, nonzeros[j] );
644  }
645 
646  // Performing the Schur product
647  for( size_t i=0UL; i<(~lhs).rows(); ++i ) {
648  for( ConstIterator element=B.begin(i); element!=B.end(i); ++element )
649  (~lhs).append( i, element->index(), A(i,element->index()) * element->value() );
650  }
651  }
653  //**********************************************************************************************
654 
655  //**Addition assignment to dense matrices*******************************************************
667  template< typename MT // Type of the target dense matrix
668  , bool SO2 > // Storage order of the target dense matrix
669  friend inline EnableIf_< UseAssign<MT> >
670  addAssign( DenseMatrix<MT,SO2>& lhs, const DMatSMatSchurExpr& rhs )
671  {
673 
674  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
675  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
676 
678 
679  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side dense matrix operand
680  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
681 
682  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
683  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
684  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
685  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
686  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
687  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
688 
689  for( size_t i=0UL; i<(~lhs).rows(); ++i ) {
690  for( ConstIterator element=B.begin(i); element!=B.end(i); ++element )
691  (~lhs)(i,element->index()) += A(i,element->index()) * element->value();
692  }
693  }
695  //**********************************************************************************************
696 
697  //**Addition assignment to sparse matrices******************************************************
698  // No special implementation for the addition assignment to sparse matrices.
699  //**********************************************************************************************
700 
701  //**Subtraction assignment to dense matrices****************************************************
713  template< typename MT // Type of the target dense matrix
714  , bool SO2 > // Storage order of the target dense matrix
715  friend inline EnableIf_< UseAssign<MT> >
716  subAssign( DenseMatrix<MT,SO2>& lhs, const DMatSMatSchurExpr& rhs )
717  {
719 
720  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
721  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
722 
724 
725  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side dense matrix operand
726  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
727 
728  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
729  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
730  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
731  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
732  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
733  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
734 
735  for( size_t i=0UL; i<(~lhs).rows(); ++i ) {
736  for( ConstIterator element=B.begin(i); element!=B.end(i); ++element )
737  (~lhs)(i,element->index()) -= A(i,element->index()) * element->value();
738  }
739  }
741  //**********************************************************************************************
742 
743  //**Subtraction assignment to sparse matrices***************************************************
744  // No special implementation for the subtraction assignment to sparse matrices.
745  //**********************************************************************************************
746 
747  //**Schur product assignment to dense matrices**************************************************
760  template< typename MT // Type of the target dense matrix
761  , bool SO2 > // Storage order of the target dense matrix
762  friend inline void schurAssign( DenseMatrix<MT,SO2>& lhs, const DMatSMatSchurExpr& rhs )
763  {
765 
766  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
767  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
768 
770 
771  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side dense matrix operand
772  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
773 
774  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
775  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
776  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
777  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
778  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
779  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
780 
781  for( size_t i=0UL; i<(~lhs).rows(); ++i )
782  {
783  const ConstIterator end( B.end(i) );
784  ConstIterator begin( B.begin(i) );
785  size_t j( 0UL );
786 
787  for( ; begin!=end; ++begin ) {
788  const size_t index( begin->index() );
789  for( ; j<index; ++j )
790  reset( (~lhs)(i,j) );
791  (~lhs)(i,index) *= A(i,index) * begin->value();
792  ++j;
793  }
794 
795  for( ; j<(~lhs).columns(); ++j )
796  reset( (~lhs)(i,j) );
797  }
798  }
800  //**********************************************************************************************
801 
802  //**Schur product assignment to sparse matrices*************************************************
803  // No special implementation for the Schur product assignment to sparse matrices.
804  //**********************************************************************************************
805 
806  //**Multiplication assignment to dense matrices*************************************************
807  // No special implementation for the multiplication assignment to dense matrices.
808  //**********************************************************************************************
809 
810  //**Multiplication assignment to sparse matrices************************************************
811  // No special implementation for the multiplication assignment to sparse matrices.
812  //**********************************************************************************************
813 
814  //**SMP assignment to dense matrices************************************************************
815  // No special implementation for the SMP assignment to dense matrices.
816  //**********************************************************************************************
817 
818  //**SMP assignment to sparse matrices***********************************************************
819  // No special implementation for the SMP assignment to sparse matrices.
820  //**********************************************************************************************
821 
822  //**SMP addition assignment to dense matrices***************************************************
823  // No special implementation for the SMP addition assignment to dense matrices.
824  //**********************************************************************************************
825 
826  //**SMP addition assignment to sparse matrices**************************************************
827  // No special implementation for the SMP addition assignment to sparse matrices.
828  //**********************************************************************************************
829 
830  //**SMP subtraction assignment to dense matrices************************************************
831  // No special implementation for the SMP subtraction assignment to dense matrices.
832  //**********************************************************************************************
833 
834  //**SMP subtraction assignment to sparse matrices***********************************************
835  // No special implementation for the SMP subtraction assignment to sparse matrices.
836  //**********************************************************************************************
837 
838  //**SMP Schur product assignment to dense matrices**********************************************
851  template< typename MT // Type of the target dense matrix
852  , bool SO > // Storage order of the target dense matrix
853  friend inline void smpSchurAssign( DenseMatrix<MT,SO>& lhs, const DMatSMatSchurExpr& rhs )
854  {
856 
857  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
858  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
859 
860  smpSchurAssign( ~lhs, rhs.lhs_ );
861  smpSchurAssign( ~lhs, rhs.rhs_ );
862  }
864  //**********************************************************************************************
865 
866  //**SMP Schur product assignment to sparse matrices*********************************************
867  // No special implementation for the SMP Schur product assignment to sparse matrices.
868  //**********************************************************************************************
869 
870  //**SMP multiplication assignment to dense matrices*********************************************
871  // No special implementation for the SMP multiplication assignment to dense matrices.
872  //**********************************************************************************************
873 
874  //**SMP multiplication assignment to sparse matrices********************************************
875  // No special implementation for the SMP multiplication assignment to sparse matrices.
876  //**********************************************************************************************
877 
878  //**Compile time checks*************************************************************************
885  //**********************************************************************************************
886 };
887 //*************************************************************************************************
888 
889 
890 
891 
892 //=================================================================================================
893 //
894 // GLOBAL BINARY ARITHMETIC OPERATORS
895 //
896 //=================================================================================================
897 
898 //*************************************************************************************************
911 template< typename MT1 // Type of the left-hand side dense matrix
912  , typename MT2 // Type of the right-hand side sparse matrix
915 inline const DMatSMatSchurExpr<MT1,MT2>
916  dmatsmatschur( const DenseMatrix<MT1,false>& lhs, const SparseMatrix<MT2,false>& rhs )
917 {
919 
920  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
921  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
922 
923  return DMatSMatSchurExpr<MT1,MT2>( ~lhs, ~rhs );
924 }
926 //*************************************************************************************************
927 
928 
929 //*************************************************************************************************
942 template< typename MT1 // Type of the left-hand side dense matrix
943  , typename MT2 // Type of the right-hand side sparse matrix
944  , typename = EnableIf_< Or< And< IsUniLower<MT1>, IsUniUpper<MT2> >
945  , And< IsUniUpper<MT1>, IsUniLower<MT2> > > > >
947  dmatsmatschur( const DenseMatrix<MT1,false>& lhs, const SparseMatrix<MT2,false>& rhs )
948 {
950 
951  UNUSED_PARAMETER( rhs );
952 
953  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
954  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
955 
956  return IdentityMatrix< MultTrait_< ElementType_<MT1>, ElementType_<MT2> >, false >( (~lhs).rows() );
957 }
959 //*************************************************************************************************
960 
961 
962 //*************************************************************************************************
991 template< typename MT1 // Type of the left-hand side dense matrix
992  , typename MT2 > // Type of the right-hand side sparse matrix
993 inline decltype(auto)
994  operator%( const DenseMatrix<MT1,false>& lhs, const SparseMatrix<MT2,false>& rhs )
995 {
997 
998  if( (~lhs).rows() != (~rhs).rows() || (~lhs).columns() != (~rhs).columns() ) {
999  BLAZE_THROW_INVALID_ARGUMENT( "Matrix sizes do not match" );
1000  }
1001 
1002  return dmatsmatschur( ~lhs, ~rhs );
1003 }
1004 //*************************************************************************************************
1005 
1006 
1007 //*************************************************************************************************
1020 template< typename MT1 // Type of the left-hand side dense matrix
1021  , typename MT2 // Type of the right-hand side sparse matrix
1024 inline const DMatSMatSchurExpr<MT1,MT2>
1025  tdmatsmatschur( const DenseMatrix<MT1,true>& lhs, const SparseMatrix<MT2,false>& rhs )
1026 {
1028 
1029  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
1030  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
1031 
1032  return DMatSMatSchurExpr<MT1,MT2>( ~lhs, ~rhs );
1033 }
1034 //*************************************************************************************************
1035 
1036 
1037 //*************************************************************************************************
1050 template< typename MT1 // Type of the left-hand side dense matrix
1051  , typename MT2 // Type of the right-hand side sparse matrix
1055  tdmatsmatschur( const DenseMatrix<MT1,true>& lhs, const SparseMatrix<MT2,false>& rhs )
1056 {
1058 
1059  UNUSED_PARAMETER( rhs );
1060 
1061  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
1062  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
1063 
1065 }
1067 //*************************************************************************************************
1068 
1069 
1070 //*************************************************************************************************
1100 template< typename MT1 // Type of the left-hand side dense matrix
1101  , typename MT2 > // Type of the right-hand side sparse matrix
1102 inline decltype(auto)
1103  operator%( const DenseMatrix<MT1,true>& lhs, const SparseMatrix<MT2,false>& rhs )
1104 {
1106 
1107  if( (~lhs).rows() != (~rhs).rows() || (~lhs).columns() != (~rhs).columns() ) {
1108  BLAZE_THROW_INVALID_ARGUMENT( "Matrix sizes do not match" );
1109  }
1110 
1111  return tdmatsmatschur( ~lhs, ~rhs );
1112 }
1113 //*************************************************************************************************
1114 
1115 
1116 
1117 
1118 //=================================================================================================
1119 //
1120 // SIZE SPECIALIZATIONS
1121 //
1122 //=================================================================================================
1123 
1124 //*************************************************************************************************
1126 template< typename MT1, typename MT2 >
1127 struct Size< DMatSMatSchurExpr<MT1,MT2>, 0UL >
1128  : public Maximum< Size<MT1,0UL>, Size<MT2,0UL> >
1129 {};
1130 
1131 template< typename MT1, typename MT2 >
1132 struct Size< DMatSMatSchurExpr<MT1,MT2>, 1UL >
1133  : public Maximum< Size<MT1,1UL>, Size<MT2,1UL> >
1134 {};
1136 //*************************************************************************************************
1137 
1138 
1139 
1140 
1141 //=================================================================================================
1142 //
1143 // ISSYMMETRIC SPECIALIZATIONS
1144 //
1145 //=================================================================================================
1146 
1147 //*************************************************************************************************
1149 template< typename MT1, typename MT2 >
1150 struct IsSymmetric< DMatSMatSchurExpr<MT1,MT2> >
1151  : public And< IsSymmetric<MT1>, IsSymmetric<MT2> >
1152 {};
1154 //*************************************************************************************************
1155 
1156 
1157 
1158 
1159 //=================================================================================================
1160 //
1161 // ISHERMITIAN SPECIALIZATIONS
1162 //
1163 //=================================================================================================
1164 
1165 //*************************************************************************************************
1167 template< typename MT1, typename MT2 >
1168 struct IsHermitian< DMatSMatSchurExpr<MT1,MT2> >
1169  : public And< IsHermitian<MT1>, IsHermitian<MT2> >
1170 {};
1172 //*************************************************************************************************
1173 
1174 
1175 
1176 
1177 //=================================================================================================
1178 //
1179 // ISLOWER SPECIALIZATIONS
1180 //
1181 //=================================================================================================
1182 
1183 //*************************************************************************************************
1185 template< typename MT1, typename MT2 >
1186 struct IsLower< DMatSMatSchurExpr<MT1,MT2> >
1187  : public Or< IsLower<MT1>, IsLower<MT2> >
1188 {};
1190 //*************************************************************************************************
1191 
1192 
1193 
1194 
1195 //=================================================================================================
1196 //
1197 // ISUNILOWER SPECIALIZATIONS
1198 //
1199 //=================================================================================================
1200 
1201 //*************************************************************************************************
1203 template< typename MT1, typename MT2 >
1204 struct IsUniLower< DMatSMatSchurExpr<MT1,MT2> >
1205  : public And< IsUniLower<MT1>, IsUniLower<MT2> >
1206 {};
1208 //*************************************************************************************************
1209 
1210 
1211 
1212 
1213 //=================================================================================================
1214 //
1215 // ISSTRICTLYLOWER SPECIALIZATIONS
1216 //
1217 //=================================================================================================
1218 
1219 //*************************************************************************************************
1221 template< typename MT1, typename MT2 >
1222 struct IsStrictlyLower< DMatSMatSchurExpr<MT1,MT2> >
1223  : public Or< IsStrictlyLower<MT1>, IsStrictlyLower<MT2> >
1224 {};
1226 //*************************************************************************************************
1227 
1228 
1229 
1230 
1231 //=================================================================================================
1232 //
1233 // ISUPPER SPECIALIZATIONS
1234 //
1235 //=================================================================================================
1236 
1237 //*************************************************************************************************
1239 template< typename MT1, typename MT2 >
1240 struct IsUpper< DMatSMatSchurExpr<MT1,MT2> >
1241  : public Or< IsUpper<MT1>, IsUpper<MT2> >
1242 {};
1244 //*************************************************************************************************
1245 
1246 
1247 
1248 
1249 //=================================================================================================
1250 //
1251 // ISUNIUPPER SPECIALIZATIONS
1252 //
1253 //=================================================================================================
1254 
1255 //*************************************************************************************************
1257 template< typename MT1, typename MT2 >
1258 struct IsUniUpper< DMatSMatSchurExpr<MT1,MT2> >
1259  : public And< IsUniUpper<MT1>, IsUniUpper<MT2> >
1260 {};
1262 //*************************************************************************************************
1263 
1264 
1265 
1266 
1267 //=================================================================================================
1268 //
1269 // ISSTRICTLYUPPER SPECIALIZATIONS
1270 //
1271 //=================================================================================================
1272 
1273 //*************************************************************************************************
1275 template< typename MT1, typename MT2 >
1276 struct IsStrictlyUpper< DMatSMatSchurExpr<MT1,MT2> >
1277  : public Or< IsStrictlyUpper<MT1>, IsStrictlyUpper<MT2> >
1278 {};
1280 //*************************************************************************************************
1281 
1282 } // namespace blaze
1283 
1284 #endif
RightOperand rightOperand() const noexcept
Returns the right-hand side sparse matrix operand.
Definition: DMatSMatSchurExpr.h:472
#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.
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:69
OppositeType_< ResultType > OppositeType
Result type with opposite storage order for expression template evaluations.
Definition: DMatSMatSchurExpr.h:151
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
LeftOperand left_
Left-hand side dense matrix expression.
Definition: DMatSMatSchurExpr.h:295
Header file for basic type definitions.
ConstIterator & operator++()
Pre-increment operator.
Definition: DMatSMatSchurExpr.h:214
SchurTrait_< RT1, RT2 > ResultType
Result type for expression template evaluations.
Definition: DMatSMatSchurExpr.h:150
ConstIterator upperBound(size_t i, size_t j) const
Returns an iterator to the first index greater then the given index.
Definition: DMatSMatSchurExpr.h:451
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
ConstIterator find(size_t i, size_t j) const
Searches for a specific matrix element.
Definition: DMatSMatSchurExpr.h:425
TransposeType_< ResultType > TransposeType
Transpose type for expression template evaluations.
Definition: DMatSMatSchurExpr.h:152
void reset(const DiagonalProxy< MT > &proxy)
Resetting the represented element to the default initial values.
Definition: DiagonalProxy.h:588
RightIterator right_
Iterator over the elements of the right-hand side sparse matrix expression.
Definition: DMatSMatSchurExpr.h:296
typename DisableIf< Condition, T >::Type DisableIf_
Auxiliary type for the DisableIf class template.The DisableIf_ alias declaration provides a convenien...
Definition: DisableIf.h:224
Expression object for dense matrix-sparse matrix Schur product.The DMatSMatSchurExpr class represents...
Definition: DMatSMatSchurExpr.h:101
Header file for the And class template.
Compile time value evaluation.The Maximum alias declaration selects the larger of the two given templ...
Definition: Maximum.h:73
Compile time check for lower triangular matrices.This type trait tests whether or not the given templ...
Definition: IsLower.h:87
size_t nonZeros(size_t i) const
Returns the number of non-zero elements in the specified row.
Definition: DMatSMatSchurExpr.h:413
const ConstIterator * operator->() const
Direct access to the sparse matrix element at the current iterator position.
Definition: DMatSMatSchurExpr.h:235
size_t index() const
Access to the current index of the sparse element.
Definition: DMatSMatSchurExpr.h:255
std::forward_iterator_tag IteratorCategory
The iterator category.
Definition: DMatSMatSchurExpr.h:181
Header file for the Computation base class.
Compile time check for upper triangular matrices.This type trait tests whether or not the given templ...
Definition: IsUpper.h:87
Constraints on the storage order of matrix types.
bool isAliased(const T *alias) const noexcept
Returns whether the expression is aliased with the given address alias.
Definition: DMatSMatSchurExpr.h:496
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
#define BLAZE_CONSTRAINT_MUST_FORM_VALID_SCHUREXPR(T1, T2)
Constraint on the data type.In case the given data types T1 and T2 do not form a valid matrix/matrix ...
Definition: SchurExpr.h:107
Base class for dense matrices.The DenseMatrix class is a base class for all dense matrix classes...
Definition: DenseMatrix.h:80
Base class for sparse matrices.The SparseMatrix class is a base class for all sparse matrix classes...
Definition: Forward.h:129
Header file for all forward declarations for sparse vectors and matrices.
const IfTrue_< returnExpr, ExprReturnType, ElementType > ReturnType
Return type for expression template evaluations.
Definition: DMatSMatSchurExpr.h:156
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
MultExprTrait_< RN1, RN2 > ExprReturnType
Expression return type for the subscript operator.
Definition: DMatSMatSchurExpr.h:125
ReturnType_< MT2 > RN2
Return type of the right-hand side sparse matrix expression.
Definition: DMatSMatSchurExpr.h:110
typename T::ReturnType ReturnType_
Alias declaration for nested ReturnType type definitions.The ReturnType_ alias declaration provides a...
Definition: Aliases.h:363
Header file for the SparseMatrix base class.
ConstIterator end(size_t i) const
Returns an iterator just past the last non-zero element of row i.
Definition: DMatSMatSchurExpr.h:372
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:71
typename T::CompositeType CompositeType_
Alias declaration for nested CompositeType type definitions.The CompositeType_ alias declaration prov...
Definition: Aliases.h:83
Iterator over the elements of the dense matrix/sparse matrix Schur product expression.
Definition: DMatSMatSchurExpr.h:171
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.
CompositeType_< MT1 > CT1
Composite type of the left-hand side dense matrix expression.
Definition: DMatSMatSchurExpr.h:111
Efficient implementation of an identity matrix.The IdentityMatrix class template is the representati...
Definition: Forward.h:49
Header file for the DisableIf class template.
Header file for the IsTemporary type trait class.
Header file for the multiplication trait.
Header file for the IsStrictlyUpper type trait.
Header file for the IsSymmetric type trait.
If_< IsExpression< MT1 >, const MT1, const MT1 &> LeftOperand
Composite type of the left-hand side dense matrix expression.
Definition: DMatSMatSchurExpr.h:162
Namespace of the Blaze C++ math library.
Definition: Blaze.h:58
Header file for the If class template.
IfTrue_< useAssign, const ResultType, const DMatSMatSchurExpr &> CompositeType
Data type for composite expression templates.
Definition: DMatSMatSchurExpr.h:159
ReturnType at(size_t i, size_t j) const
Checked access to the matrix elements.
Definition: DMatSMatSchurExpr.h:344
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
const Element * ConstIterator
Iterator over constant elements.
Definition: CompressedMatrix.h:3085
typename T::ElementType ElementType_
Alias declaration for nested ElementType type definitions.The ElementType_ alias declaration provides...
Definition: Aliases.h:163
bool canAlias(const T *alias) const noexcept
Returns whether the expression can alias with the given address alias.
Definition: DMatSMatSchurExpr.h:484
bool operator==(const ConstIterator &rhs) const
Equality comparison between two ConstIterator objects.
Definition: DMatSMatSchurExpr.h:266
CompositeType_< MT2 > CT2
Composite type of the right-hand side sparse matrix expression.
Definition: DMatSMatSchurExpr.h:112
Header file for the IsLower type trait.
typename SchurTrait< T1, T2 >::Type SchurTrait_
Auxiliary alias declaration for the SchurTrait class template.The SchurTrait_ alias declaration provi...
Definition: SchurTrait.h:208
LeftOperand leftOperand() const noexcept
Returns the left-hand side dense matrix operand.
Definition: DMatSMatSchurExpr.h:462
ResultType_< MT2 > RT2
Result type of the right-hand side sparse matrix expression.
Definition: DMatSMatSchurExpr.h:108
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
LeftOperand lhs_
Left-hand side dense matrix of the Schur product expression.
Definition: DMatSMatSchurExpr.h:503
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
size_t row_
The row index of the iterator.
Definition: DMatSMatSchurExpr.h:297
IteratorCategory iterator_category
The iterator category.
Definition: DMatSMatSchurExpr.h:188
DifferenceType operator-(const ConstIterator &rhs) const
Calculating the number of elements between two expression iterators.
Definition: DMatSMatSchurExpr.h:288
#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
const Element operator*() const
Direct access to the sparse matrix element at the current iterator position.
Definition: DMatSMatSchurExpr.h:225
Base class for all Schur product expression templates.The SchurExpr class serves as a tag for all exp...
Definition: SchurExpr.h:66
Header file for run time assertion macros.
DMatSMatSchurExpr(const MT1 &lhs, const MT2 &rhs) noexcept
Constructor for the DMatSMatSchurExpr class.
Definition: DMatSMatSchurExpr.h:313
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
decltype(auto) row(Matrix< MT, SO > &, RRAs...)
Creating a view on a specific row of the given matrix.
Definition: Row.h:131
ReturnType_< MT1 > RN1
Return type of the left-hand side dense matrix expression.
Definition: DMatSMatSchurExpr.h:109
#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
ElementType_< ResultType > ElementType
Resulting element type.
Definition: DMatSMatSchurExpr.h:153
Compile time check for Hermitian matrices.This type trait tests whether or not the given template par...
Definition: IsHermitian.h:85
ConstIterator begin(size_t i) const
Returns an iterator to the first non-zero element of row i.
Definition: DMatSMatSchurExpr.h:361
size_t rows() const noexcept
Returns the current number of rows of the matrix.
Definition: DMatSMatSchurExpr.h:382
ConstIterator(LeftOperand left, RightIterator right, size_t row)
Constructor for the ConstIterator class.
Definition: DMatSMatSchurExpr.h:202
ConstIterator lowerBound(size_t i, size_t j) const
Returns an iterator to the first index not less then the given index.
Definition: DMatSMatSchurExpr.h:438
decltype(auto) serial(const DenseMatrix< MT, SO > &dm)
Forces the serial evaluation of the given dense matrix expression dm.
Definition: DMatSerialExpr.h:816
#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
bool operator!=(const ConstIterator &rhs) const
Inequality comparison between two ConstIterator objects.
Definition: DMatSMatSchurExpr.h:277
typename T::OppositeType OppositeType_
Alias declaration for nested OppositeType type definitions.The OppositeType_ alias declaration provid...
Definition: Aliases.h:263
RightOperand rhs_
Right-hand side sparse matrix of the Schur product expression.
Definition: DMatSMatSchurExpr.h:504
size_t nonZeros() const
Returns the number of non-zero elements in the sparse matrix.
Definition: DMatSMatSchurExpr.h:402
Compile time check for strictly lower triangular matrices.This type trait tests whether or not the gi...
Definition: IsStrictlyLower.h:86
ReturnType operator()(size_t i, size_t j) const
2D-access to the matrix elements.
Definition: DMatSMatSchurExpr.h:329
typename T::ConstIterator ConstIterator_
Alias declaration for nested ConstIterator type definitions.The ConstIterator_ alias declaration prov...
Definition: Aliases.h:103
Index-value-pair for sparse vectors and matrices.The ValueIndexPair class represents a single index-v...
Definition: ValueIndexPair.h:73
Base class for all compute expression templates.The Computation class serves as a tag for all computa...
Definition: Computation.h:66
Compile time logical &#39;or&#39; evaluation.The Or alias declaration performs at compile time a logical &#39;or&#39;...
Definition: Or.h:76
Compile time evaluation of the size of vectors and matrices.The Size type trait evaluates the size of...
Definition: Size.h:80
ResultType_< MT1 > RT1
Result type of the left-hand side dense matrix expression.
Definition: DMatSMatSchurExpr.h:107
ReturnType value() const
Access to the current value of the sparse element.
Definition: DMatSMatSchurExpr.h:245
Compile time logical &#39;and&#39; evaluation.The And alias declaration performs at compile time a logical &#39;a...
Definition: And.h:76
typename T::TransposeType TransposeType_
Alias declaration for nested TransposeType type definitions.The TransposeType_ alias declaration prov...
Definition: Aliases.h:423
Header file for the IsUpper type trait.
void UNUSED_PARAMETER(const Args &...)
Suppression of unused parameter warnings.
Definition: Unused.h:81
Header file for the IsHermitian type trait.
Header file for the Size type trait.
#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
If_< IsExpression< MT2 >, const MT2, const MT2 &> RightOperand
Composite type of the right-hand side sparse matrix expression.
Definition: DMatSMatSchurExpr.h:165
#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
ConstIterator_< RemoveReference_< RightOperand > > RightIterator
Iterator type of the sparse matrix expression.
Definition: DMatSMatSchurExpr.h:179
Header file for the IsExpression type trait class.
size_t columns() const noexcept
Returns the current number of columns of the matrix.
Definition: DMatSMatSchurExpr.h:392
Header file for the function trace functionality.
Constraint on the data type.