TSMatTSMatSchurExpr.h
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1 //=================================================================================================
33 //=================================================================================================
34 
35 #ifndef _BLAZE_MATH_EXPRESSIONS_TSMATTSMATSCHUREXPR_H_
36 #define _BLAZE_MATH_EXPRESSIONS_TSMATTSMATSCHUREXPR_H_
37 
38 
39 //*************************************************************************************************
40 // Includes
41 //*************************************************************************************************
42 
43 #include <blaze/math/Aliases.h>
48 #include <blaze/math/Exception.h>
72 #include <blaze/util/Assert.h>
73 #include <blaze/util/DisableIf.h>
74 #include <blaze/util/EnableIf.h>
77 #include <blaze/util/mpl/And.h>
78 #include <blaze/util/mpl/If.h>
79 #include <blaze/util/mpl/Maximum.h>
80 #include <blaze/util/mpl/Or.h>
81 #include <blaze/util/Types.h>
83 #include <blaze/util/Unused.h>
84 
85 
86 namespace blaze {
87 
88 //=================================================================================================
89 //
90 // CLASS TSMATTSMATSCHUREXPR
91 //
92 //=================================================================================================
93 
94 //*************************************************************************************************
101 template< typename MT1 // Type of the left-hand side sparse matrix
102  , typename MT2 > // Type of the right-hand side sparse matrix
103 class TSMatTSMatSchurExpr
104  : public SchurExpr< SparseMatrix< TSMatTSMatSchurExpr<MT1,MT2>, true > >
105  , private Computation
106 {
107  private:
108  //**Type definitions****************************************************************************
115  //**********************************************************************************************
116 
117  //**Return type evaluation**********************************************************************
119 
124  enum : bool { returnExpr = !IsTemporary<RN1>::value && !IsTemporary<RN2>::value };
125 
128  //**********************************************************************************************
129 
130  //**Serial evaluation strategy******************************************************************
132 
137  template< typename T1, typename T2, typename T3 >
138  struct UseSymmetricKernel {
139  enum : bool { value = IsRowMajorMatrix<T1>::value &&
141  };
143  //**********************************************************************************************
144 
145  //**Parallel evaluation strategy****************************************************************
147 
152  template< typename MT >
153  struct UseSMPAssign {
154  enum : bool { value = MT::smpAssignable };
155  };
157  //**********************************************************************************************
158 
159  public:
160  //**Type definitions****************************************************************************
166 
169 
171  using CompositeType = const ResultType;
172 
174  using LeftOperand = If_< IsExpression<MT1>, const MT1, const MT1& >;
175 
177  using RightOperand = If_< IsExpression<MT2>, const MT2, const MT2& >;
178  //**********************************************************************************************
179 
180  //**Compilation flags***************************************************************************
182  enum : bool { smpAssignable = false };
183  //**********************************************************************************************
184 
185  //**Constructor*********************************************************************************
191  explicit inline TSMatTSMatSchurExpr( const MT1& lhs, const MT2& rhs ) noexcept
192  : lhs_( lhs ) // Left-hand side sparse matrix of the Schur product expression
193  , rhs_( rhs ) // Right-hand side sparse matrix of the Schur product expression
194  {
195  BLAZE_INTERNAL_ASSERT( lhs.rows() == rhs.rows() , "Invalid number of rows" );
196  BLAZE_INTERNAL_ASSERT( lhs.columns() == rhs.columns(), "Invalid number of columns" );
197  }
198  //**********************************************************************************************
199 
200  //**Access operator*****************************************************************************
207  inline ReturnType operator()( size_t i, size_t j ) const {
208  BLAZE_INTERNAL_ASSERT( i < lhs_.rows() , "Invalid row access index" );
209  BLAZE_INTERNAL_ASSERT( j < lhs_.columns(), "Invalid column access index" );
210  return lhs_(i,j) * rhs_(i,j);
211  }
212  //**********************************************************************************************
213 
214  //**At function*********************************************************************************
222  inline ReturnType at( size_t i, size_t j ) const {
223  if( i >= lhs_.rows() ) {
224  BLAZE_THROW_OUT_OF_RANGE( "Invalid row access index" );
225  }
226  if( j >= lhs_.columns() ) {
227  BLAZE_THROW_OUT_OF_RANGE( "Invalid column access index" );
228  }
229  return (*this)(i,j);
230  }
231  //**********************************************************************************************
232 
233  //**Rows function*******************************************************************************
238  inline size_t rows() const noexcept {
239  return lhs_.rows();
240  }
241  //**********************************************************************************************
242 
243  //**Columns function****************************************************************************
248  inline size_t columns() const noexcept {
249  return lhs_.columns();
250  }
251  //**********************************************************************************************
252 
253  //**NonZeros function***************************************************************************
258  inline size_t nonZeros() const {
259  return min( lhs_.nonZeros(), rhs_.nonZeros() );
260  }
261  //**********************************************************************************************
262 
263  //**NonZeros function***************************************************************************
269  inline size_t nonZeros( size_t i ) const {
270  return min( lhs_.nonZeros(i), rhs_.nonZeros(i) );
271  }
272  //**********************************************************************************************
273 
274  //**Left operand access*************************************************************************
279  inline LeftOperand leftOperand() const noexcept {
280  return lhs_;
281  }
282  //**********************************************************************************************
283 
284  //**Right operand access************************************************************************
289  inline RightOperand rightOperand() const noexcept {
290  return rhs_;
291  }
292  //**********************************************************************************************
293 
294  //**********************************************************************************************
300  template< typename T >
301  inline bool canAlias( const T* alias ) const noexcept {
302  return ( lhs_.canAlias( alias ) || rhs_.canAlias( alias ) );
303  }
304  //**********************************************************************************************
305 
306  //**********************************************************************************************
312  template< typename T >
313  inline bool isAliased( const T* alias ) const noexcept {
314  return ( lhs_.isAliased( alias ) || rhs_.isAliased( alias ) );
315  }
316  //**********************************************************************************************
317 
318  private:
319  //**Member variables****************************************************************************
322  //**********************************************************************************************
323 
324  //**Assignment to dense matrices****************************************************************
337  template< typename MT // Type of the target dense matrix
338  , bool SO > // Storage order of the target dense matrix
340  assign( DenseMatrix<MT,SO>& lhs, const TSMatTSMatSchurExpr& rhs )
341  {
343 
344  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
345  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
346 
347  using LeftIterator = ConstIterator_< RemoveReference_<CT1> >;
348  using RightIterator = ConstIterator_< RemoveReference_<CT2> >;
349 
350  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
351  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
352 
353  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
354  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
355  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
356  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
357  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
358  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
359 
360  for( size_t j=0UL; j<(~lhs).columns(); ++j )
361  {
362  const LeftIterator lend( A.end(j) );
363  const RightIterator rend( B.end(j) );
364 
365  LeftIterator l( A.begin(j) );
366  RightIterator r( B.begin(j) );
367 
368  for( ; l!=lend; ++l ) {
369  while( r!=rend && r->index() < l->index() ) ++r;
370  if( r==rend ) break;
371  if( l->index() == r->index() ) {
372  (~lhs)(l->index(),j) = l->value() * r->value();
373  ++r;
374  }
375  }
376  }
377  }
379  //**********************************************************************************************
380 
381  //**Assignment to row-major sparse matrices*****************************************************
394  template< typename MT > // Type of the target sparse matrix
396  assign( SparseMatrix<MT,false>& lhs, const TSMatTSMatSchurExpr& rhs )
397  {
399 
401 
402  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
403  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
404 
405  using LeftIterator = ConstIterator_< RemoveReference_<CT1> >;
406  using RightIterator = ConstIterator_< RemoveReference_<CT2> >;
407 
408  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
409  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
410 
411  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
412  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
413  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
414  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
415  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
416  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
417 
418  const size_t m( rhs.rows() );
419  const size_t n( rhs.columns() );
420 
421  // Counting the number of elements per column
422  std::vector<size_t> nonzeros( m, 0UL );
423  for( size_t j=0UL; j<n; ++j )
424  {
425  const LeftIterator lend( A.end(j) );
426  const RightIterator rend( B.end(j) );
427 
428  LeftIterator l( A.begin(j) );
429  RightIterator r( B.begin(j) );
430 
431  for( ; l!=lend; ++l ) {
432  while( r!=rend && r->index() < l->index() ) ++r;
433  if( r==rend ) break;
434  if( l->index() == r->index() ) {
435  ++nonzeros[l->index()];
436  ++r;
437  }
438  }
439  }
440 
441  // Resizing the left-hand side sparse matrix
442  for( size_t i=0UL; i<m; ++i ) {
443  (~lhs).reserve( i, nonzeros[i] );
444  }
445 
446  // Performing the Schur product
447  for( size_t j=0UL; j<n; ++j )
448  {
449  const LeftIterator lend( A.end(j) );
450  const RightIterator rend( B.end(j) );
451 
452  LeftIterator l( A.begin(j) );
453  RightIterator r( B.begin(j) );
454 
455  for( ; l!=lend; ++l ) {
456  while( r!=rend && r->index() < l->index() ) ++r;
457  if( r==rend ) break;
458  if( l->index() == r->index() ) {
459  (~lhs).append( l->index(), j, l->value() * r->value() );
460  ++r;
461  }
462  }
463  }
464  }
466  //**********************************************************************************************
467 
468  //**Assignment to column-major sparse matrices**************************************************
481  template< typename MT > // Type of the target sparse matrix
482  friend inline void assign( SparseMatrix<MT,true>& lhs, const TSMatTSMatSchurExpr& rhs )
483  {
485 
486  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
487  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
488 
489  using LeftIterator = ConstIterator_< RemoveReference_<CT1> >;
490  using RightIterator = ConstIterator_< RemoveReference_<CT2> >;
491 
492  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
493  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
494 
495  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
496  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
497  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
498  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
499  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
500  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
501 
502  // Final memory allocation (based on the evaluated operands)
503  (~lhs).reserve( min( A.nonZeros(), B.nonZeros() ) );
504 
505  // Performing the Schur product
506  for( size_t j=0UL; j<(~lhs).columns(); ++j )
507  {
508  const LeftIterator lend( A.end(j) );
509  const RightIterator rend( B.end(j) );
510 
511  LeftIterator l( A.begin(j) );
512  RightIterator r( B.begin(j) );
513 
514  for( ; l!=lend; ++l ) {
515  while( r!=rend && r->index() < l->index() ) ++r;
516  if( r==rend ) break;
517  if( l->index() == r->index() ) {
518  (~lhs).append( l->index(), j, l->value() * r->value() );
519  ++r;
520  }
521  }
522 
523  (~lhs).finalize( j );
524  }
525  }
527  //**********************************************************************************************
528 
529  //**Restructuring assignment to row-major matrices**********************************************
542  template< typename MT > // Type of the target matrix
544  assign( Matrix<MT,false>& lhs, const TSMatTSMatSchurExpr& rhs )
545  {
547 
549 
550  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
551  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
552 
553  assign( ~lhs, trans( rhs.lhs_ ) % trans( rhs.rhs_ ) );
554  }
556  //**********************************************************************************************
557 
558  //**Addition assignment to dense matrices*******************************************************
571  template< typename MT // Type of the target dense matrix
572  , bool SO > // Storage order of the target dense matrix
574  addAssign( DenseMatrix<MT,SO>& lhs, const TSMatTSMatSchurExpr& rhs )
575  {
577 
578  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
579  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
580 
581  using LeftIterator = ConstIterator_< RemoveReference_<CT1> >;
582  using RightIterator = ConstIterator_< RemoveReference_<CT2> >;
583 
584  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
585  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
586 
587  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
588  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
589  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
590  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
591  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
592  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
593 
594  for( size_t j=0UL; j<(~lhs).columns(); ++j )
595  {
596  const LeftIterator lend( A.end(j) );
597  const RightIterator rend( B.end(j) );
598 
599  LeftIterator l( A.begin(j) );
600  RightIterator r( B.begin(j) );
601 
602  for( ; l!=lend; ++l ) {
603  while( r!=rend && r->index() < l->index() ) ++r;
604  if( r==rend ) break;
605  if( l->index() == r->index() ) {
606  (~lhs)(l->index(),j) += l->value() * r->value();
607  ++r;
608  }
609  }
610  }
611  }
613  //**********************************************************************************************
614 
615  //**Restructuring addition assignment to row-major matrices*************************************
628  template< typename MT > // Type of the target matrix
630  addAssign( Matrix<MT,false>& lhs, const TSMatTSMatSchurExpr& rhs )
631  {
633 
635 
636  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
637  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
638 
639  addAssign( ~lhs, trans( rhs.lhs_ ) % trans( rhs.rhs_ ) );
640  }
642  //**********************************************************************************************
643 
644  //**Addition assignment to sparse matrices******************************************************
645  // No special implementation for the addition assignment to sparse matrices.
646  //**********************************************************************************************
647 
648  //**Subtraction assignment to dense matrices****************************************************
661  template< typename MT // Type of the target dense matrix
662  , bool SO > // Storage order of the target dense matrix
664  subAssign( DenseMatrix<MT,SO>& lhs, const TSMatTSMatSchurExpr& rhs )
665  {
667 
668  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
669  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
670 
671  using LeftIterator = ConstIterator_< RemoveReference_<CT1> >;
672  using RightIterator = ConstIterator_< RemoveReference_<CT2> >;
673 
674  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
675  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
676 
677  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
678  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
679  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
680  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
681  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
682  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
683 
684  for( size_t j=0UL; j<(~lhs).columns(); ++j )
685  {
686  const LeftIterator lend( A.end(j) );
687  const RightIterator rend( B.end(j) );
688 
689  LeftIterator l( A.begin(j) );
690  RightIterator r( B.begin(j) );
691 
692  for( ; l!=lend; ++l ) {
693  while( r!=rend && r->index() < l->index() ) ++r;
694  if( r==rend ) break;
695  if( l->index() == r->index() ) {
696  (~lhs)(l->index(),j) -= l->value() * r->value();
697  ++r;
698  }
699  }
700  }
701  }
703  //**********************************************************************************************
704 
705  //**Restructuring subtraction assignment to row-major matrices**********************************
718  template< typename MT > // Type of the target matrix
720  subAssign( Matrix<MT,false>& lhs, const TSMatTSMatSchurExpr& rhs )
721  {
723 
725 
726  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
727  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
728 
729  subAssign( ~lhs, trans( rhs.lhs_ ) % trans( rhs.rhs_ ) );
730  }
732  //**********************************************************************************************
733 
734  //**Subtraction assignment to sparse matrices***************************************************
735  // No special implementation for the subtraction assignment to sparse matrices.
736  //**********************************************************************************************
737 
738  //**Schur product assignment to dense matrices**************************************************
751  template< typename MT // Type of the target dense matrix
752  , bool SO > // Storage order of the target dense matrix
754  schurAssign( DenseMatrix<MT,SO>& lhs, const TSMatTSMatSchurExpr& 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  using LeftIterator = ConstIterator_< RemoveReference_<CT1> >;
762  using RightIterator = ConstIterator_< RemoveReference_<CT2> >;
763 
764  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
765  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
766 
767  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
768  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
769  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
770  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
771  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
772  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
773 
774  for( size_t j=0UL; j<(~lhs).columns(); ++j )
775  {
776  const LeftIterator lend( A.end(j) );
777  const RightIterator rend( B.end(j) );
778 
779  LeftIterator l( A.begin(j) );
780  RightIterator r( B.begin(j) );
781 
782  size_t i( 0UL );
783 
784  for( ; l!=lend; ++l ) {
785  while( r!=rend && r->index() < l->index() ) ++r;
786  if( r==rend ) break;
787  if( l->index() == r->index() ) {
788  for( ; i<l->index(); ++i )
789  reset( (~lhs)(i,j) );
790  (~lhs)(l->index(),j) *= l->value() * r->value();
791  ++r;
792  ++i;
793  }
794  }
795 
796  for( ; i<(~lhs).rows(); ++i )
797  reset( (~lhs)(i,j) );
798  }
799  }
801  //**********************************************************************************************
802 
803  //**Restructuring Schur product assignment to row-major matrices********************************
816  template< typename MT > // Type of the target matrix
818  schurAssign( Matrix<MT,false>& lhs, const TSMatTSMatSchurExpr& rhs )
819  {
821 
823 
824  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
825  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
826 
827  schurAssign( ~lhs, trans( rhs.lhs_ ) % trans( rhs.rhs_ ) );
828  }
830  //**********************************************************************************************
831 
832  //**Schur product assignment to sparse matrices*************************************************
833  // No special implementation for the Schur product assignment to sparse matrices.
834  //**********************************************************************************************
835 
836  //**Multiplication assignment to dense matrices*************************************************
837  // No special implementation for the multiplication assignment to dense matrices.
838  //**********************************************************************************************
839 
840  //**Multiplication assignment to sparse matrices************************************************
841  // No special implementation for the multiplication assignment to sparse matrices.
842  //**********************************************************************************************
843 
844  //**SMP assignment to dense matrices************************************************************
845  // No special implementation for the SMP assignment to dense matrices.
846  //**********************************************************************************************
847 
848  //**SMP assignment to sparse matrices***********************************************************
849  // No special implementation for the SMP assignment to sparse matrices.
850  //**********************************************************************************************
851 
852  //**SMP addition assignment to dense matrices***************************************************
853  // No special implementation for the SMP addition assignment to dense matrices.
854  //**********************************************************************************************
855 
856  //**SMP addition assignment to sparse matrices**************************************************
857  // No special implementation for the SMP addition assignment to sparse matrices.
858  //**********************************************************************************************
859 
860  //**SMP subtraction assignment to dense matrices************************************************
861  // No special implementation for the SMP subtraction assignment to dense matrices.
862  //**********************************************************************************************
863 
864  //**SMP subtraction assignment to sparse matrices***********************************************
865  // No special implementation for the SMP subtraction assignment to sparse matrices.
866  //**********************************************************************************************
867 
868  //**SMP Schur product assignment to dense matrices**********************************************
881  template< typename MT // Type of the target dense matrix
882  , bool SO > // Storage order of the target dense matrix
883  friend inline void smpSchurAssign( DenseMatrix<MT,SO>& lhs, const TSMatTSMatSchurExpr& rhs )
884  {
886 
887  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
888  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
889 
890  smpSchurAssign( ~lhs, rhs.lhs_ );
891  smpSchurAssign( ~lhs, rhs.rhs_ );
892  }
894  //**********************************************************************************************
895 
896  //**SMP Schur product assignment to sparse matrices*********************************************
897  // No special implementation for the SMP Schur product assignment to sparse matrices.
898  //**********************************************************************************************
899 
900  //**SMP multiplication assignment to dense matrices*********************************************
901  // No special implementation for the SMP multiplication assignment to dense matrices.
902  //**********************************************************************************************
903 
904  //**SMP multiplication assignment to sparse matrices********************************************
905  // No special implementation for the SMP multiplication assignment to sparse matrices.
906  //**********************************************************************************************
907 
908  //**Compile time checks*************************************************************************
916  //**********************************************************************************************
917 };
918 //*************************************************************************************************
919 
920 
921 
922 
923 //=================================================================================================
924 //
925 // GLOBAL BINARY ARITHMETIC OPERATORS
926 //
927 //=================================================================================================
928 
929 //*************************************************************************************************
941 template< typename MT1 // Type of the left-hand side sparse matrix
942  , typename MT2 // Type of the right-hand side sparse matrix
945 inline const TSMatTSMatSchurExpr<MT1,MT2>
947 {
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  return TSMatTSMatSchurExpr<MT1,MT2>( ~lhs, ~rhs );
954 }
955 //*************************************************************************************************
956 
957 
958 //*************************************************************************************************
971 template< typename MT1 // Type of the left-hand side sparse matrix
972  , typename MT2 // Type of the right-hand side sparse matrix
973  , typename = EnableIf_< Or< And< IsUniLower<MT1>, IsUniUpper<MT2> >
974  , And< IsUniUpper<MT1>, IsUniLower<MT2> > > > >
977 {
979 
980  UNUSED_PARAMETER( rhs );
981 
982  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
983  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
984 
985  return IdentityMatrix< MultTrait_< ElementType_<MT1>, ElementType_<MT2> >, true >( (~lhs).rows() );
986 }
988 //*************************************************************************************************
989 
990 
991 //*************************************************************************************************
1017 template< typename MT1 // Type of the left-hand side sparse matrix
1018  , typename MT2 > // Type of the right-hand side sparse matrix
1019 inline decltype(auto)
1020  operator%( const SparseMatrix<MT1,true>& lhs, const SparseMatrix<MT2,true>& rhs )
1021 {
1023 
1024  if( (~lhs).rows() != (~rhs).rows() || (~lhs).columns() != (~rhs).columns() ) {
1025  BLAZE_THROW_INVALID_ARGUMENT( "Matrix sizes do not match" );
1026  }
1027 
1028  return tsmattsmatschur( ~lhs, ~rhs );
1029 }
1030 //*************************************************************************************************
1031 
1032 
1033 
1034 
1035 //=================================================================================================
1036 //
1037 // ROWS SPECIALIZATIONS
1038 //
1039 //=================================================================================================
1040 
1041 //*************************************************************************************************
1043 template< typename MT1, typename MT2 >
1044 struct Rows< TSMatTSMatSchurExpr<MT1,MT2> >
1045  : public Maximum< Rows<MT1>, Rows<MT2> >
1046 {};
1048 //*************************************************************************************************
1049 
1050 
1051 
1052 
1053 //=================================================================================================
1054 //
1055 // COLUMNS SPECIALIZATIONS
1056 //
1057 //=================================================================================================
1058 
1059 //*************************************************************************************************
1061 template< typename MT1, typename MT2 >
1062 struct Columns< TSMatTSMatSchurExpr<MT1,MT2> >
1063  : public Maximum< Columns<MT1>, Columns<MT2> >
1064 {};
1066 //*************************************************************************************************
1067 
1068 
1069 
1070 
1071 //=================================================================================================
1072 //
1073 // ISSYMMETRIC SPECIALIZATIONS
1074 //
1075 //=================================================================================================
1076 
1077 //*************************************************************************************************
1079 template< typename MT1, typename MT2 >
1080 struct IsSymmetric< TSMatTSMatSchurExpr<MT1,MT2> >
1081  : public BoolConstant< IsSymmetric<MT1>::value && IsSymmetric<MT2>::value >
1082 {};
1084 //*************************************************************************************************
1085 
1086 
1087 
1088 
1089 //=================================================================================================
1090 //
1091 // ISHERMITIAN SPECIALIZATIONS
1092 //
1093 //=================================================================================================
1094 
1095 //*************************************************************************************************
1097 template< typename MT1, typename MT2 >
1098 struct IsHermitian< TSMatTSMatSchurExpr<MT1,MT2> >
1099  : public BoolConstant< IsHermitian<MT1>::value && IsHermitian<MT2>::value >
1100 {};
1102 //*************************************************************************************************
1103 
1104 
1105 
1106 
1107 //=================================================================================================
1108 //
1109 // ISLOWER SPECIALIZATIONS
1110 //
1111 //=================================================================================================
1112 
1113 //*************************************************************************************************
1115 template< typename MT1, typename MT2 >
1116 struct IsLower< TSMatTSMatSchurExpr<MT1,MT2> >
1117  : public BoolConstant< Or< IsLower<MT1>, IsLower<MT2> >::value >
1118 {};
1120 //*************************************************************************************************
1121 
1122 
1123 
1124 
1125 //=================================================================================================
1126 //
1127 // ISUNILOWER SPECIALIZATIONS
1128 //
1129 //=================================================================================================
1130 
1131 //*************************************************************************************************
1133 template< typename MT1, typename MT2 >
1134 struct IsUniLower< TSMatTSMatSchurExpr<MT1,MT2> >
1135  : public BoolConstant< And< IsUniLower<MT1>, IsUniLower<MT2> >::value >
1136 {};
1138 //*************************************************************************************************
1139 
1140 
1141 
1142 
1143 //=================================================================================================
1144 //
1145 // ISSTRICTLYLOWER SPECIALIZATIONS
1146 //
1147 //=================================================================================================
1148 
1149 //*************************************************************************************************
1151 template< typename MT1, typename MT2 >
1152 struct IsStrictlyLower< TSMatTSMatSchurExpr<MT1,MT2> >
1153  : public BoolConstant< Or< IsStrictlyLower<MT1>, IsStrictlyLower<MT2> >::value >
1154 {};
1156 //*************************************************************************************************
1157 
1158 
1159 
1160 
1161 //=================================================================================================
1162 //
1163 // ISUPPER SPECIALIZATIONS
1164 //
1165 //=================================================================================================
1166 
1167 //*************************************************************************************************
1169 template< typename MT1, typename MT2 >
1170 struct IsUpper< TSMatTSMatSchurExpr<MT1,MT2> >
1171  : public BoolConstant< Or< IsUpper<MT1>, IsUpper<MT2> >::value >
1172 {};
1174 //*************************************************************************************************
1175 
1176 
1177 
1178 
1179 //=================================================================================================
1180 //
1181 // ISUNIUPPER SPECIALIZATIONS
1182 //
1183 //=================================================================================================
1184 
1185 //*************************************************************************************************
1187 template< typename MT1, typename MT2 >
1188 struct IsUniUpper< TSMatTSMatSchurExpr<MT1,MT2> >
1189  : public BoolConstant< Or< IsUniUpper<MT1>, IsUniUpper<MT2> >::value >
1190 {};
1192 //*************************************************************************************************
1193 
1194 
1195 
1196 
1197 //=================================================================================================
1198 //
1199 // ISSTRICTLYUPPER SPECIALIZATIONS
1200 //
1201 //=================================================================================================
1202 
1203 //*************************************************************************************************
1205 template< typename MT1, typename MT2 >
1206 struct IsStrictlyUpper< TSMatTSMatSchurExpr<MT1,MT2> >
1207  : public BoolConstant< Or< IsStrictlyUpper<MT1>, IsStrictlyUpper<MT2> >::value >
1208 {};
1210 //*************************************************************************************************
1211 
1212 } // namespace blaze
1213 
1214 #endif
#define BLAZE_THROW_INVALID_ARGUMENT(MESSAGE)
Macro for the emission of a std::invalid_argument exception.This macro encapsulates the default way o...
Definition: Exception.h:235
const ResultType CompositeType
Data type for composite expression templates.
Definition: TSMatTSMatSchurExpr.h:171
Header file for auxiliary alias declarations.
Headerfile for the generic min algorithm.
Header file for the Schur product trait.
Compile time check whether the given type is a temporary vector or matrix type.This type trait class ...
Definition: IsTemporary.h:70
Header file for the Rows type trait.
Header file for the UNUSED_PARAMETER function template.
Header file for the IsUniUpper type trait.
EnableIf_< IsDenseMatrix< MT1 > > smpSchurAssign(Matrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs)
Default implementation of the SMP Schur product assignment of a matrix to dense matrix.
Definition: DenseMatrix.h:196
Header file for basic type definitions.
size_t nonZeros() const
Returns the number of non-zero elements in the sparse matrix.
Definition: TSMatTSMatSchurExpr.h:258
ElementType_< ResultType > ElementType
Resulting element type.
Definition: TSMatTSMatSchurExpr.h:165
Header file for the serial shim.
Generic wrapper for a compile time constant integral value.The IntegralConstant class template repres...
Definition: IntegralConstant.h:71
void reset(const DiagonalProxy< MT > &proxy)
Resetting the represented element to the default initial values.
Definition: DiagonalProxy.h:560
size_t rows() const noexcept
Returns the current number of rows of the matrix.
Definition: TSMatTSMatSchurExpr.h:238
typename DisableIf< Condition, T >::Type DisableIf_
Auxiliary type for the DisableIf class template.The DisableIf_ alias declaration provides a convenien...
Definition: DisableIf.h:224
Header file for the And class template.
const ElementType_< MT > min(const DenseMatrix< MT, SO > &dm)
Returns the smallest element of the dense matrix.
Definition: DenseMatrix.h:1762
Compile time value evaluation.The Maximum alias declaration selects the larger of the two given templ...
Definition: Maximum.h:73
Compile time check for lower triangular matrices.This type trait tests whether or not the given templ...
Definition: IsLower.h:88
Header file for the Computation base class.
Compile time check for upper triangular matrices.This type trait tests whether or not the given templ...
Definition: IsUpper.h:88
Expression object for transpose sparse matrix-transpose sparse matrix Schur product.The TSMatTSMatSchurExpr class represents the compile time expression for Schur products between two column-major sparse matrices.
Definition: Forward.h:171
const TSMatTSMatSchurExpr< MT1, MT2 > tsmattsmatschur(const SparseMatrix< MT1, true > &lhs, const SparseMatrix< MT2, true > &rhs)
Backend implementation of the Schur product between two column-major sparse matrices ( )...
Definition: TSMatTSMatSchurExpr.h:946
ResultType_< MT1 > RT1
Result type of the left-hand side sparse matrix expression.
Definition: TSMatTSMatSchurExpr.h:109
Header file for the IsUniLower type trait.
typename T::ResultType ResultType_
Alias declaration for nested ResultType type definitions.The ResultType_ alias declaration provides a...
Definition: Aliases.h:343
#define BLAZE_CONSTRAINT_MUST_FORM_VALID_SCHUREXPR(T1, T2)
Constraint on the data type.In case the given data types T1 and T2 do not form a valid matrix/matrix ...
Definition: SchurExpr.h:108
Base class for dense matrices.The DenseMatrix class is a base class for all dense matrix classes...
Definition: DenseMatrix.h:78
Base class for sparse matrices.The SparseMatrix class is a base class for all sparse matrix classes...
Definition: Forward.h:129
Header file for all forward declarations for sparse vectors and matrices.
CompositeType_< MT2 > CT2
Composite type of the right-hand side sparse matrix expression.
Definition: TSMatTSMatSchurExpr.h:114
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
SchurTrait_< RT1, RT2 > ResultType
Result type for expression template evaluations.
Definition: TSMatTSMatSchurExpr.h:162
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.
Constraint on the data type.
Header file for the Maximum class template.
ResultType_< MT2 > RT2
Result type of the right-hand side sparse matrix expression.
Definition: TSMatTSMatSchurExpr.h:110
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.
typename T::CompositeType CompositeType_
Alias declaration for nested CompositeType type definitions.The CompositeType_ alias declaration prov...
Definition: Aliases.h:83
Compile time check for upper unitriangular matrices.This type trait tests whether or not the given te...
Definition: IsUniUpper.h:86
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 IsStrictlyUpper type trait.
Header file for the IsSymmetric type trait.
Namespace of the Blaze C++ math library.
Definition: Blaze.h:57
Header file for the If class template.
Compile time check for row-major matrix types.This type trait tests whether or not the given template...
Definition: IsRowMajorMatrix.h:110
#define BLAZE_CONSTRAINT_MUST_BE_COLUMN_MAJOR_MATRIX_TYPE(T)
Constraint on the data type.In case the given data type T is not a column-major dense or sparse matri...
Definition: ColumnMajorMatrix.h:61
Header file for the Or class template.
#define BLAZE_THROW_OUT_OF_RANGE(MESSAGE)
Macro for the emission of a std::out_of_range exception.This macro encapsulates the default way of Bl...
Definition: Exception.h:331
Header file for the Columns type trait.
typename T::ElementType ElementType_
Alias declaration for nested ElementType type definitions.The ElementType_ alias declaration provides...
Definition: Aliases.h:163
If_< IsExpression< MT1 >, const MT1, const MT1 &> LeftOperand
Composite type of the left-hand side sparse matrix expression.
Definition: TSMatTSMatSchurExpr.h:174
LeftOperand leftOperand() const noexcept
Returns the left-hand side transpose sparse matrix operand.
Definition: TSMatTSMatSchurExpr.h:279
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:167
MultExprTrait_< RN1, RN2 > ExprReturnType
Expression return type for the subscript operator.
Definition: TSMatTSMatSchurExpr.h:127
size_t columns() const noexcept
Returns the current number of columns of the matrix.
Definition: TSMatTSMatSchurExpr.h:248
Compile time check for symmetric matrices.This type trait tests whether or not the given template par...
Definition: IsSymmetric.h:85
bool canAlias(const T *alias) const noexcept
Returns whether the expression can alias with the given address alias.
Definition: TSMatTSMatSchurExpr.h:301
Header file for the exception macros of the math module.
RightOperand rightOperand() const noexcept
Returns the right-hand side transpose sparse matrix operand.
Definition: TSMatTSMatSchurExpr.h:289
Compile time check for strictly upper triangular matrices.This type trait tests whether or not the gi...
Definition: IsStrictlyUpper.h:86
ReturnType_< MT1 > RN1
Return type of the left-hand side sparse matrix expression.
Definition: TSMatTSMatSchurExpr.h:111
TransposeType_< ResultType > TransposeType
Transpose type for expression template evaluations.
Definition: TSMatTSMatSchurExpr.h:164
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
#define BLAZE_CONSTRAINT_MUST_NOT_BE_SYMMETRIC_MATRIX_TYPE(T)
Constraint on the data type.In case the given data type T is a symmetric matrix type, a compilation error is created.
Definition: Symmetric.h:79
Header file for run time assertion macros.
LeftOperand lhs_
Left-hand side sparse matrix of the Schur product expression.
Definition: TSMatTSMatSchurExpr.h:320
ReturnType_< MT2 > RN2
Return type of the right-hand side sparse matrix expression.
Definition: TSMatTSMatSchurExpr.h:112
TSMatTSMatSchurExpr(const MT1 &lhs, const MT2 &rhs) noexcept
Constructor for the TSMatTSMatSchurExpr class.
Definition: TSMatTSMatSchurExpr.h:191
bool isAliased(const T *alias) const noexcept
Returns whether the expression is aliased with the given address alias.
Definition: TSMatTSMatSchurExpr.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
#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
Compile time check for Hermitian matrices.This type trait tests whether or not the given template par...
Definition: IsHermitian.h:85
Base class for matrices.The Matrix class is a base class for all dense and sparse matrix classes with...
Definition: Forward.h:101
const IfTrue_< returnExpr, ExprReturnType, ElementType > ReturnType
Return type for expression template evaluations.
Definition: TSMatTSMatSchurExpr.h:168
Constraint on the data type.
CompositeType_< MT1 > CT1
Composite type of the left-hand side sparse matrix expression.
Definition: TSMatTSMatSchurExpr.h:113
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:819
Header file for the RemoveReference type trait.
typename EnableIf< Condition, T >::Type EnableIf_
Auxiliary alias declaration for the EnableIf class template.The EnableIf_ alias declaration provides ...
Definition: EnableIf.h:224
typename T::OppositeType OppositeType_
Alias declaration for nested OppositeType type definitions.The OppositeType_ alias declaration provid...
Definition: Aliases.h:263
RightOperand rhs_
Right-hand side sparse matrix of the Schur product expression.
Definition: TSMatTSMatSchurExpr.h:321
Compile time check for strictly lower triangular matrices.This type trait tests whether or not the gi...
Definition: IsStrictlyLower.h:86
typename T::ConstIterator ConstIterator_
Alias declaration for nested ConstIterator type definitions.The ConstIterator_ alias declaration prov...
Definition: Aliases.h:103
decltype(auto) trans(const DenseMatrix< MT, SO > &dm)
Calculation of the transpose of the given dense matrix.
Definition: DMatTransExpr.h:790
Header file for the IsRowMajorMatrix type trait.
Header file for the IsComputation type trait class.
Header file for the IntegralConstant class template.
Compile time evaluation of the number of columns of a matrix.The Columns type trait evaluates the num...
Definition: Columns.h:75
Compile time evaluation of the number of rows of a matrix.The Rows type trait evaluates the number of...
Definition: Rows.h:75
Compile time logical and evaluation.The And alias declaration performs at compile time a logical and ...
Definition: And.h:76
ReturnType operator()(size_t i, size_t j) const
2D-access to the matrix elements.
Definition: TSMatTSMatSchurExpr.h:207
If_< IsExpression< MT2 >, const MT2, const MT2 &> RightOperand
Composite type of the right-hand side sparse matrix expression.
Definition: TSMatTSMatSchurExpr.h:177
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
size_t nonZeros(size_t i) const
Returns the number of non-zero elements in the specified row.
Definition: TSMatTSMatSchurExpr.h:269
Header file for the IsHermitian type trait.
ReturnType at(size_t i, size_t j) const
Checked access to the matrix elements.
Definition: TSMatTSMatSchurExpr.h:222
#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
#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
OppositeType_< ResultType > OppositeType
Result type with opposite storage order for expression template evaluations.
Definition: TSMatTSMatSchurExpr.h:163
Header file for the IsExpression type trait class.
Header file for the function trace functionality.
Constraint on the data type.