SMatSMatSchurExpr.h
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1 //=================================================================================================
33 //=================================================================================================
34 
35 #ifndef _BLAZE_MATH_EXPRESSIONS_SMATSMATSCHUREXPR_H_
36 #define _BLAZE_MATH_EXPRESSIONS_SMATSMATSCHUREXPR_H_
37 
38 
39 //*************************************************************************************************
40 // Includes
41 //*************************************************************************************************
42 
43 #include <blaze/math/Aliases.h>
48 #include <blaze/math/Exception.h>
73 #include <blaze/util/Assert.h>
74 #include <blaze/util/DisableIf.h>
75 #include <blaze/util/EnableIf.h>
78 #include <blaze/util/mpl/And.h>
79 #include <blaze/util/mpl/If.h>
80 #include <blaze/util/mpl/Maximum.h>
81 #include <blaze/util/mpl/Or.h>
82 #include <blaze/util/Types.h>
84 #include <blaze/util/Unused.h>
85 
86 
87 namespace blaze {
88 
89 //=================================================================================================
90 //
91 // CLASS SMATSMATSCHUREXPR
92 //
93 //=================================================================================================
94 
95 //*************************************************************************************************
102 template< typename MT1 // Type of the left-hand side sparse matrix
103  , typename MT2 > // Type of the right-hand side sparse matrix
104 class SMatSMatSchurExpr
105  : public SchurExpr< SparseMatrix< SMatSMatSchurExpr<MT1,MT2>, false > >
106  , private Computation
107 {
108  private:
109  //**Type definitions****************************************************************************
116  //**********************************************************************************************
117 
118  //**Return type evaluation**********************************************************************
120 
125  enum : bool { returnExpr = !IsTemporary<RN1>::value && !IsTemporary<RN2>::value };
126 
129  //**********************************************************************************************
130 
131  //**Serial evaluation strategy******************************************************************
133 
138  template< typename T1, typename T2, typename T3 >
139  struct UseSymmetricKernel {
140  enum : bool { value = IsColumnMajorMatrix<T1>::value &&
142  };
144  //**********************************************************************************************
145 
146  public:
147  //**Type definitions****************************************************************************
153 
156 
158  using CompositeType = const ResultType;
159 
161  using LeftOperand = If_< IsExpression<MT1>, const MT1, const MT1& >;
162 
164  using RightOperand = If_< IsExpression<MT2>, const MT2, const MT2& >;
165  //**********************************************************************************************
166 
167  //**Compilation flags***************************************************************************
169  enum : bool { smpAssignable = false };
170  //**********************************************************************************************
171 
172  //**Constructor*********************************************************************************
178  explicit inline SMatSMatSchurExpr( const MT1& lhs, const MT2& rhs ) noexcept
179  : lhs_( lhs ) // Left-hand side sparse matrix of the Schur product expression
180  , rhs_( rhs ) // Right-hand side sparse matrix of the Schur product expression
181  {
182  BLAZE_INTERNAL_ASSERT( lhs.rows() == rhs.rows() , "Invalid number of rows" );
183  BLAZE_INTERNAL_ASSERT( lhs.columns() == rhs.columns(), "Invalid number of columns" );
184  }
185  //**********************************************************************************************
186 
187  //**Access operator*****************************************************************************
194  inline ReturnType operator()( size_t i, size_t j ) const {
195  BLAZE_INTERNAL_ASSERT( i < lhs_.rows() , "Invalid row access index" );
196  BLAZE_INTERNAL_ASSERT( j < lhs_.columns(), "Invalid column access index" );
197  return lhs_(i,j) * rhs_(i,j);
198  }
199  //**********************************************************************************************
200 
201  //**At function*********************************************************************************
209  inline ReturnType at( size_t i, size_t j ) const {
210  if( i >= lhs_.rows() ) {
211  BLAZE_THROW_OUT_OF_RANGE( "Invalid row access index" );
212  }
213  if( j >= lhs_.columns() ) {
214  BLAZE_THROW_OUT_OF_RANGE( "Invalid column access index" );
215  }
216  return (*this)(i,j);
217  }
218  //**********************************************************************************************
219 
220  //**Rows function*******************************************************************************
225  inline size_t rows() const noexcept {
226  return lhs_.rows();
227  }
228  //**********************************************************************************************
229 
230  //**Columns function****************************************************************************
235  inline size_t columns() const noexcept {
236  return lhs_.columns();
237  }
238  //**********************************************************************************************
239 
240  //**NonZeros function***************************************************************************
245  inline size_t nonZeros() const {
246  return min( lhs_.nonZeros(), rhs_.nonZeros() );
247  }
248  //**********************************************************************************************
249 
250  //**NonZeros function***************************************************************************
256  inline size_t nonZeros( size_t i ) const {
257  return min( lhs_.nonZeros(i), rhs_.nonZeros(i) );
258  }
259  //**********************************************************************************************
260 
261  //**Left operand access*************************************************************************
266  inline LeftOperand leftOperand() const noexcept {
267  return lhs_;
268  }
269  //**********************************************************************************************
270 
271  //**Right operand access************************************************************************
276  inline RightOperand rightOperand() const noexcept {
277  return rhs_;
278  }
279  //**********************************************************************************************
280 
281  //**********************************************************************************************
287  template< typename T >
288  inline bool canAlias( const T* alias ) const noexcept {
289  return ( lhs_.canAlias( alias ) || rhs_.canAlias( alias ) );
290  }
291  //**********************************************************************************************
292 
293  //**********************************************************************************************
299  template< typename T >
300  inline bool isAliased( const T* alias ) const noexcept {
301  return ( lhs_.isAliased( alias ) || rhs_.isAliased( alias ) );
302  }
303  //**********************************************************************************************
304 
305  private:
306  //**Member variables****************************************************************************
309  //**********************************************************************************************
310 
311  //**Assignment to dense matrices****************************************************************
323  template< typename MT // Type of the target dense matrix
324  , bool SO > // Storage order of the target dense matrix
326  assign( DenseMatrix<MT,SO>& lhs, const SMatSMatSchurExpr& rhs )
327  {
329 
330  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
331  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
332 
333  using LeftIterator = ConstIterator_< RemoveReference_<CT1> >;
334  using RightIterator = ConstIterator_< RemoveReference_<CT2> >;
335 
336  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
337  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
338 
339  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
340  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
341  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
342  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
343  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
344  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
345 
346  for( size_t i=0UL; i<(~lhs).rows(); ++i )
347  {
348  const LeftIterator lend( A.end(i) );
349  const RightIterator rend( B.end(i) );
350 
351  LeftIterator l( A.begin(i) );
352  RightIterator r( B.begin(i) );
353 
354  for( ; l!=lend; ++l ) {
355  while( r!=rend && r->index() < l->index() ) ++r;
356  if( r==rend ) break;
357  if( l->index() == r->index() ) {
358  (~lhs)(i,l->index()) = l->value() * r->value();
359  ++r;
360  }
361  }
362  }
363  }
365  //**********************************************************************************************
366 
367  //**Assignment to row-major sparse matrices*****************************************************
379  template< typename MT > // Type of the target sparse matrix
380  friend inline void assign( SparseMatrix<MT,false>& lhs, const SMatSMatSchurExpr& rhs )
381  {
383 
384  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
385  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
386 
387  using LeftIterator = ConstIterator_< RemoveReference_<CT1> >;
388  using RightIterator = ConstIterator_< RemoveReference_<CT2> >;
389 
390  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
391  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
392 
393  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
394  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
395  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
396  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
397  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
398  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
399 
400  // Final memory allocation (based on the evaluated operands)
401  (~lhs).reserve( min( A.nonZeros(), B.nonZeros() ) );
402 
403  // Performing the Schur product
404  for( size_t i=0UL; i<(~lhs).rows(); ++i )
405  {
406  const LeftIterator lend( A.end(i) );
407  const RightIterator rend( B.end(i) );
408 
409  LeftIterator l( A.begin(i) );
410  RightIterator r( B.begin(i) );
411 
412  for( ; l!=lend; ++l ) {
413  while( r!=rend && r->index() < l->index() ) ++r;
414  if( r==rend ) break;
415  if( l->index() == r->index() ) {
416  (~lhs).append( i, l->index(), l->value() * r->value() );
417  ++r;
418  }
419  }
420 
421  (~lhs).finalize( i );
422  }
423  }
425  //**********************************************************************************************
426 
427  //**Assignment to column-major sparse matrices**************************************************
440  template< typename MT > // Type of the target sparse matrix
442  assign( SparseMatrix<MT,true>& lhs, const SMatSMatSchurExpr& rhs )
443  {
445 
447 
448  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
449  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
450 
451  using LeftIterator = ConstIterator_< RemoveReference_<CT1> >;
452  using RightIterator = ConstIterator_< RemoveReference_<CT2> >;
453 
454  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
455  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
456 
457  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
458  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
459  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
460  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
461  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
462  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
463 
464  const size_t m( rhs.rows() );
465  const size_t n( rhs.columns() );
466 
467  // Counting the number of elements per column
468  std::vector<size_t> nonzeros( n, 0UL );
469  for( size_t i=0UL; i<m; ++i )
470  {
471  const LeftIterator lend( A.end(i) );
472  const RightIterator rend( B.end(i) );
473 
474  LeftIterator l( A.begin(i) );
475  RightIterator r( B.begin(i) );
476 
477  for( ; l!=lend; ++l ) {
478  while( r!=rend && r->index() < l->index() ) ++r;
479  if( r==rend ) break;
480  if( l->index() == r->index() ) {
481  ++nonzeros[l->index()];
482  ++r;
483  }
484  }
485  }
486 
487  // Resizing the left-hand side sparse matrix
488  for( size_t j=0UL; j<n; ++j ) {
489  (~lhs).reserve( j, nonzeros[j] );
490  }
491 
492  // Performing the Schur product
493  for( size_t i=0UL; i<m; ++i )
494  {
495  const LeftIterator lend( A.end(i) );
496  const RightIterator rend( B.end(i) );
497 
498  LeftIterator l( A.begin(i) );
499  RightIterator r( B.begin(i) );
500 
501  for( ; l!=lend; ++l ) {
502  while( r!=rend && r->index() < l->index() ) ++r;
503  if( r==rend ) break;
504  if( l->index() == r->index() ) {
505  (~lhs).append( i, l->index(), l->value() * r->value() );
506  ++r;
507  }
508  }
509  }
510  }
512  //**********************************************************************************************
513 
514  //**Restructuring assignment to column-major matrices*******************************************
527  template< typename MT > // Type of the target matrix
529  assign( Matrix<MT,true>& lhs, const SMatSMatSchurExpr& rhs )
530  {
532 
534 
535  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
536  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
537 
538  assign( ~lhs, trans( rhs.lhs_ ) % trans( rhs.rhs_ ) );
539  }
541  //**********************************************************************************************
542 
543  //**Addition assignment to dense matrices*******************************************************
555  template< typename MT // Type of the target dense matrix
556  , bool SO > // Storage order of the target dense matrix
558  addAssign( DenseMatrix<MT,SO>& lhs, const SMatSMatSchurExpr& rhs )
559  {
561 
562  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
563  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
564 
565  using LeftIterator = ConstIterator_< RemoveReference_<CT1> >;
566  using RightIterator = ConstIterator_< RemoveReference_<CT2> >;
567 
568  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
569  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
570 
571  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
572  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
573  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
574  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
575  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
576  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
577 
578  for( size_t i=0UL; i<(~lhs).rows(); ++i )
579  {
580  const LeftIterator lend( A.end(i) );
581  const RightIterator rend( B.end(i) );
582 
583  LeftIterator l( A.begin(i) );
584  RightIterator r( B.begin(i) );
585 
586  for( ; l!=lend; ++l ) {
587  while( r!=rend && r->index() < l->index() ) ++r;
588  if( r==rend ) break;
589  if( l->index() == r->index() ) {
590  (~lhs)(i,l->index()) += l->value() * r->value();
591  ++r;
592  }
593  }
594  }
595  }
597  //**********************************************************************************************
598 
599  //**Restructuring addition assignment to column-major matrices**********************************
612  template< typename MT > // Type of the target matrix
614  addAssign( Matrix<MT,true>& lhs, const SMatSMatSchurExpr& rhs )
615  {
617 
619 
620  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
621  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
622 
623  addAssign( ~lhs, trans( rhs.lhs_ ) % trans( rhs.rhs_ ) );
624  }
626  //**********************************************************************************************
627 
628  //**Addition assignment to sparse matrices******************************************************
629  // No special implementation for the addition assignment to sparse matrices.
630  //**********************************************************************************************
631 
632  //**Subtraction assignment to dense matrices****************************************************
645  template< typename MT // Type of the target dense matrix
646  , bool SO > // Storage order of the target dense matrix
648  subAssign( DenseMatrix<MT,SO>& lhs, const SMatSMatSchurExpr& rhs )
649  {
651 
652  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
653  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
654 
655  using LeftIterator = ConstIterator_< RemoveReference_<CT1> >;
656  using RightIterator = ConstIterator_< RemoveReference_<CT2> >;
657 
658  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
659  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
660 
661  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
662  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
663  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
664  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
665  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
666  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
667 
668  for( size_t i=0UL; i<(~lhs).rows(); ++i )
669  {
670  const LeftIterator lend( A.end(i) );
671  const RightIterator rend( B.end(i) );
672 
673  LeftIterator l( A.begin(i) );
674  RightIterator r( B.begin(i) );
675 
676  for( ; l!=lend; ++l ) {
677  while( r!=rend && r->index() < l->index() ) ++r;
678  if( r==rend ) break;
679  if( l->index() == r->index() ) {
680  (~lhs)(i,l->index()) -= l->value() * r->value();
681  ++r;
682  }
683  }
684  }
685  }
687  //**********************************************************************************************
688 
689  //**Restructuring subtraction assignment to column-major matrices*******************************
702  template< typename MT > // Type of the target matrix
704  subAssign( Matrix<MT,true>& lhs, const SMatSMatSchurExpr& rhs )
705  {
707 
709 
710  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
711  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
712 
713  subAssign( ~lhs, trans( rhs.lhs_ ) % trans( rhs.rhs_ ) );
714  }
716  //**********************************************************************************************
717 
718  //**Subtraction assignment to sparse matrices***************************************************
719  // No special implementation for the subtraction assignment to sparse matrices.
720  //**********************************************************************************************
721 
722  //**Schur product assignment to dense matrices**************************************************
735  template< typename MT // Type of the target dense matrix
736  , bool SO > // Storage order of the target dense matrix
738  schurAssign( DenseMatrix<MT,SO>& lhs, const SMatSMatSchurExpr& rhs )
739  {
741 
742  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
743  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
744 
745  using LeftIterator = ConstIterator_< RemoveReference_<CT1> >;
746  using RightIterator = ConstIterator_< RemoveReference_<CT2> >;
747 
748  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
749  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
750 
751  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
752  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
753  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
754  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
755  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
756  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
757 
758  for( size_t i=0UL; i<(~lhs).rows(); ++i )
759  {
760  const LeftIterator lend( A.end(i) );
761  const RightIterator rend( B.end(i) );
762 
763  LeftIterator l( A.begin(i) );
764  RightIterator r( B.begin(i) );
765 
766  size_t j( 0 );
767 
768  for( ; l!=lend; ++l ) {
769  while( r!=rend && r->index() < l->index() ) ++r;
770  if( r==rend ) break;
771  if( l->index() == r->index() ) {
772  for( ; j<l->index(); ++j )
773  reset( (~lhs)(i,j) );
774  (~lhs)(i,l->index()) *= l->value() * r->value();
775  ++r;
776  ++j;
777  }
778  }
779 
780  for( ; j<(~lhs).columns(); ++j )
781  reset( (~lhs)(i,j) );
782  }
783  }
785  //**********************************************************************************************
786 
787  //**Restructuring Schur product assignment to column-major matrices*****************************
800  template< typename MT > // Type of the target matrix
802  schurAssign( Matrix<MT,true>& lhs, const SMatSMatSchurExpr& rhs )
803  {
805 
807 
808  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
809  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
810 
811  schurAssign( ~lhs, trans( rhs.lhs_ ) % trans( rhs.rhs_ ) );
812  }
814  //**********************************************************************************************
815 
816  //**Schur product assignment to sparse matrices*************************************************
817  // No special implementation for the Schur product assignment to sparse matrices.
818  //**********************************************************************************************
819 
820  //**Multiplication assignment to dense matrices*************************************************
821  // No special implementation for the multiplication assignment to dense matrices.
822  //**********************************************************************************************
823 
824  //**Multiplication assignment to sparse matrices************************************************
825  // No special implementation for the multiplication assignment to sparse matrices.
826  //**********************************************************************************************
827 
828  //**SMP assignment to dense matrices************************************************************
829  // No special implementation for the SMP assignment to dense matrices.
830  //**********************************************************************************************
831 
832  //**SMP assignment to sparse matrices***********************************************************
833  // No special implementation for the SMP assignment to sparse matrices.
834  //**********************************************************************************************
835 
836  //**SMP addition assignment to dense matrices***************************************************
837  // No special implementation for the SMP addition assignment to dense matrices.
838  //**********************************************************************************************
839 
840  //**SMP addition assignment to sparse matrices**************************************************
841  // No special implementation for the SMP addition assignment to sparse matrices.
842  //**********************************************************************************************
843 
844  //**SMP subtraction assignment to dense matrices************************************************
845  // No special implementation for the SMP subtraction assignment to dense matrices.
846  //**********************************************************************************************
847 
848  //**SMP subtraction assignment to sparse matrices***********************************************
849  // No special implementation for the SMP subtraction assignment to sparse matrices.
850  //**********************************************************************************************
851 
852  //**SMP Schur product assignment to dense matrices**********************************************
865  template< typename MT // Type of the target dense matrix
866  , bool SO > // Storage order of the target dense matrix
867  friend inline void smpSchurAssign( DenseMatrix<MT,SO>& lhs, const SMatSMatSchurExpr& rhs )
868  {
870 
871  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
872  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
873 
874  smpSchurAssign( ~lhs, rhs.lhs_ );
875  smpSchurAssign( ~lhs, rhs.rhs_ );
876  }
878  //**********************************************************************************************
879 
880  //**SMP Schur product assignment to sparse matrices*********************************************
881  // No special implementation for the SMP Schur product assignment to sparse matrices.
882  //**********************************************************************************************
883 
884  //**SMP multiplication assignment to dense matrices*********************************************
885  // No special implementation for the SMP multiplication assignment to dense matrices.
886  //**********************************************************************************************
887 
888  //**SMP multiplication assignment to sparse matrices********************************************
889  // No special implementation for the SMP multiplication assignment to sparse matrices.
890  //**********************************************************************************************
891 
892  //**Compile time checks*************************************************************************
900  //**********************************************************************************************
901 };
902 //*************************************************************************************************
903 
904 
905 
906 
907 //=================================================================================================
908 //
909 // GLOBAL BINARY ARITHMETIC OPERATORS
910 //
911 //=================================================================================================
912 
913 //*************************************************************************************************
926 template< typename MT1 // Type of the left-hand side sparse matrix
927  , typename MT2 // Type of the right-hand side sparse matrix
930 inline const SMatSMatSchurExpr<MT1,MT2>
931  smatsmatschur( const SparseMatrix<MT1,false>& lhs, const SparseMatrix<MT2,false>& rhs )
932 {
934 
935  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
936  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
937 
938  return SMatSMatSchurExpr<MT1,MT2>( ~lhs, ~rhs );
939 }
941 //*************************************************************************************************
942 
943 
944 //*************************************************************************************************
957 template< typename MT1 // Type of the left-hand side sparse matrix
958  , typename MT2 // Type of the right-hand side sparse matrix
959  , typename = EnableIf_< Or< And< IsUniLower<MT1>, IsUniUpper<MT2> >
960  , And< IsUniUpper<MT1>, IsUniLower<MT2> > > > >
962  smatsmatschur( const SparseMatrix<MT1,false>& lhs, const SparseMatrix<MT2,false>& rhs )
963 {
965 
966  UNUSED_PARAMETER( rhs );
967 
968  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
969  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
970 
971  return IdentityMatrix< MultTrait_< ElementType_<MT1>, ElementType_<MT2> >, false >( (~lhs).rows() );
972 }
974 //*************************************************************************************************
975 
976 
977 //*************************************************************************************************
1003 template< typename MT1 // Type of the left-hand side sparse matrix
1004  , typename MT2 > // Type of the right-hand side sparse matrix
1005 inline decltype(auto)
1006  operator%( const SparseMatrix<MT1,false>& lhs, const SparseMatrix<MT2,false>& rhs )
1007 {
1009 
1010  if( (~lhs).rows() != (~rhs).rows() || (~lhs).columns() != (~rhs).columns() ) {
1011  BLAZE_THROW_INVALID_ARGUMENT( "Matrix sizes do not match" );
1012  }
1013 
1014  return smatsmatschur( ~lhs, ~rhs );
1015 }
1016 //*************************************************************************************************
1017 
1018 
1019 
1020 
1021 //=================================================================================================
1022 //
1023 // ROWS SPECIALIZATIONS
1024 //
1025 //=================================================================================================
1026 
1027 //*************************************************************************************************
1029 template< typename MT1, typename MT2 >
1030 struct Rows< SMatSMatSchurExpr<MT1,MT2> >
1031  : public Maximum< Rows<MT1>, Rows<MT2> >
1032 {};
1034 //*************************************************************************************************
1035 
1036 
1037 
1038 
1039 //=================================================================================================
1040 //
1041 // COLUMNS SPECIALIZATIONS
1042 //
1043 //=================================================================================================
1044 
1045 //*************************************************************************************************
1047 template< typename MT1, typename MT2 >
1048 struct Columns< SMatSMatSchurExpr<MT1,MT2> >
1049  : public Maximum< Columns<MT1>, Columns<MT2> >
1050 {};
1052 //*************************************************************************************************
1053 
1054 
1055 
1056 
1057 //=================================================================================================
1058 //
1059 // ISSYMMETRIC SPECIALIZATIONS
1060 //
1061 //=================================================================================================
1062 
1063 //*************************************************************************************************
1065 template< typename MT1, typename MT2 >
1066 struct IsSymmetric< SMatSMatSchurExpr<MT1,MT2> >
1067  : public BoolConstant< IsSymmetric<MT1>::value && IsSymmetric<MT2>::value >
1068 {};
1070 //*************************************************************************************************
1071 
1072 
1073 
1074 
1075 //=================================================================================================
1076 //
1077 // ISHERMITIAN SPECIALIZATIONS
1078 //
1079 //=================================================================================================
1080 
1081 //*************************************************************************************************
1083 template< typename MT1, typename MT2 >
1084 struct IsHermitian< SMatSMatSchurExpr<MT1,MT2> >
1085  : public BoolConstant< IsHermitian<MT1>::value && IsHermitian<MT2>::value >
1086 {};
1088 //*************************************************************************************************
1089 
1090 
1091 
1092 
1093 //=================================================================================================
1094 //
1095 // ISLOWER SPECIALIZATIONS
1096 //
1097 //=================================================================================================
1098 
1099 //*************************************************************************************************
1101 template< typename MT1, typename MT2 >
1102 struct IsLower< SMatSMatSchurExpr<MT1,MT2> >
1103  : public BoolConstant< Or< IsLower<MT1>, IsLower<MT2> >::value >
1104 {};
1106 //*************************************************************************************************
1107 
1108 
1109 
1110 
1111 //=================================================================================================
1112 //
1113 // ISUNILOWER SPECIALIZATIONS
1114 //
1115 //=================================================================================================
1116 
1117 //*************************************************************************************************
1119 template< typename MT1, typename MT2 >
1120 struct IsUniLower< SMatSMatSchurExpr<MT1,MT2> >
1121  : public BoolConstant< And< IsUniLower<MT1>, IsUniLower<MT2> >::value >
1122 {};
1124 //*************************************************************************************************
1125 
1126 
1127 
1128 
1129 //=================================================================================================
1130 //
1131 // ISSTRICTLYLOWER SPECIALIZATIONS
1132 //
1133 //=================================================================================================
1134 
1135 //*************************************************************************************************
1137 template< typename MT1, typename MT2 >
1138 struct IsStrictlyLower< SMatSMatSchurExpr<MT1,MT2> >
1139  : public BoolConstant< Or< IsStrictlyLower<MT1>, IsStrictlyLower<MT2> >::value >
1140 {};
1142 //*************************************************************************************************
1143 
1144 
1145 
1146 
1147 //=================================================================================================
1148 //
1149 // ISUPPER SPECIALIZATIONS
1150 //
1151 //=================================================================================================
1152 
1153 //*************************************************************************************************
1155 template< typename MT1, typename MT2 >
1156 struct IsUpper< SMatSMatSchurExpr<MT1,MT2> >
1157  : public BoolConstant< Or< IsUpper<MT1>, IsUpper<MT2> >::value >
1158 {};
1160 //*************************************************************************************************
1161 
1162 
1163 
1164 
1165 //=================================================================================================
1166 //
1167 // ISUNIUPPER SPECIALIZATIONS
1168 //
1169 //=================================================================================================
1170 
1171 //*************************************************************************************************
1173 template< typename MT1, typename MT2 >
1174 struct IsUniUpper< SMatSMatSchurExpr<MT1,MT2> >
1175  : public BoolConstant< And< IsUniUpper<MT1>, IsUniUpper<MT2> >::value >
1176 {};
1178 //*************************************************************************************************
1179 
1180 
1181 
1182 
1183 //=================================================================================================
1184 //
1185 // ISSTRICTLYUPPER SPECIALIZATIONS
1186 //
1187 //=================================================================================================
1188 
1189 //*************************************************************************************************
1191 template< typename MT1, typename MT2 >
1192 struct IsStrictlyUpper< SMatSMatSchurExpr<MT1,MT2> >
1193  : public BoolConstant< Or< IsStrictlyUpper<MT1>, IsStrictlyUpper<MT2> >::value >
1194 {};
1196 //*************************************************************************************************
1197 
1198 } // namespace blaze
1199 
1200 #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
OppositeType_< ResultType > OppositeType
Result type with opposite storage order for expression template evaluations.
Definition: SMatSMatSchurExpr.h:150
Header file for auxiliary alias declarations.
Headerfile for the generic min algorithm.
bool isAliased(const T *alias) const noexcept
Returns whether the expression is aliased with the given address alias.
Definition: SMatSMatSchurExpr.h:300
Header file for the Schur product trait.
size_t nonZeros(size_t i) const
Returns the number of non-zero elements in the specified row.
Definition: SMatSMatSchurExpr.h:256
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.
ReturnType operator()(size_t i, size_t j) const
2D-access to the matrix elements.
Definition: SMatSMatSchurExpr.h:194
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.
Header file for the serial shim.
Generic wrapper for a compile time constant integral value.The IntegralConstant class template repres...
Definition: IntegralConstant.h:71
Header file for the IsColumnMajorMatrix type trait.
void reset(const DiagonalProxy< MT > &proxy)
Resetting the represented element to the default initial values.
Definition: DiagonalProxy.h:560
ElementType_< ResultType > ElementType
Resulting element type.
Definition: SMatSMatSchurExpr.h:152
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
CompositeType_< MT1 > CT1
Composite type of the left-hand side sparse matrix expression.
Definition: SMatSMatSchurExpr.h:114
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
Constraints on the storage order of matrix types.
const ResultType CompositeType
Data type for composite expression templates.
Definition: SMatSMatSchurExpr.h:158
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
RightOperand rhs_
Right-hand side sparse matrix of the Schur product expression.
Definition: SMatSMatSchurExpr.h:308
#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.
typename IfTrue< Condition, T1, T2 >::Type IfTrue_
Auxiliary alias declaration for the IfTrue class template.The IfTrue_ alias declaration provides a co...
Definition: If.h:109
typename T::ReturnType ReturnType_
Alias declaration for nested ReturnType type definitions.The ReturnType_ alias declaration provides a...
Definition: Aliases.h:363
Header file for the SparseMatrix base class.
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.
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
Headerfile for the generic max algorithm.
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.
ReturnType_< MT1 > RN1
ReturnType type of the left-hand side sparse matrix expression.
Definition: SMatSMatSchurExpr.h:112
Namespace of the Blaze C++ math library.
Definition: Blaze.h:57
Header file for the If class template.
LeftOperand leftOperand() const noexcept
Returns the left-hand side sparse matrix operand.
Definition: SMatSMatSchurExpr.h:266
ResultType_< MT1 > RT1
Result type of the left-hand side sparse matrix expression.
Definition: SMatSMatSchurExpr.h:110
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
If_< IsExpression< MT2 >, const MT2, const MT2 &> RightOperand
Composite type of the right-hand side sparse matrix expression.
Definition: SMatSMatSchurExpr.h:164
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: SMatSMatSchurExpr.h:161
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
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
ReturnType_< MT2 > RN2
ReturnType type of the right-hand side sparse matrix expression.
Definition: SMatSMatSchurExpr.h:113
size_t columns() const noexcept
Returns the current number of columns of the matrix.
Definition: SMatSMatSchurExpr.h:235
Header file for all forward declarations for expression class templates.
SMatSMatSchurExpr(const MT1 &lhs, const MT2 &rhs) noexcept
Constructor for the SMatSMatSchurExpr class.
Definition: SMatSMatSchurExpr.h:178
TransposeType_< ResultType > TransposeType
Transpose type for expression template evaluations.
Definition: SMatSMatSchurExpr.h:151
Header file for the EnableIf class template.
Header file for the IsStrictlyLower type trait.
Expression object for sparse matrix-sparse matrix Schur product.The SMatSMatSchurExpr class represent...
Definition: Forward.h:118
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
#define BLAZE_CONSTRAINT_MUST_BE_ROW_MAJOR_MATRIX_TYPE(T)
Constraint on the data type.In case the given data type T is not a row-major dense or sparse matrix t...
Definition: RowMajorMatrix.h:61
size_t nonZeros() const
Returns the number of non-zero elements in the sparse matrix.
Definition: SMatSMatSchurExpr.h:245
Header file for run time assertion macros.
Compile time check for column-major matrix types.This type trait tests whether or not the given templ...
Definition: IsColumnMajorMatrix.h:110
LeftOperand lhs_
Left-hand side sparse matrix of the Schur product expression.
Definition: SMatSMatSchurExpr.h:307
MultExprTrait_< RN1, RN2 > ExprReturnType
Expression return type for the subscript operator.
Definition: SMatSMatSchurExpr.h:128
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
ReturnType at(size_t i, size_t j) const
Checked access to the matrix elements.
Definition: SMatSMatSchurExpr.h:209
bool canAlias(const T *alias) const noexcept
Returns whether the expression can alias with the given address alias.
Definition: SMatSMatSchurExpr.h:288
Base class for matrices.The Matrix class is a base class for all dense and sparse matrix classes with...
Definition: Forward.h:101
Constraint on the data type.
decltype(auto) serial(const DenseMatrix< MT, SO > &dm)
Forces the serial evaluation of the given dense matrix expression dm.
Definition: DMatSerialExpr.h:819
SchurTrait_< RT1, RT2 > ResultType
Result type for expression template evaluations.
Definition: SMatSMatSchurExpr.h:149
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
ResultType_< MT2 > RT2
Result type of the right-hand side sparse matrix expression.
Definition: SMatSMatSchurExpr.h:111
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 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
size_t rows() const noexcept
Returns the current number of rows of the matrix.
Definition: SMatSMatSchurExpr.h:225
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
const IfTrue_< returnExpr, ExprReturnType, ElementType > ReturnType
Return type for expression template evaluations.
Definition: SMatSMatSchurExpr.h:155
Header file for the IsHermitian type trait.
RightOperand rightOperand() const noexcept
Returns the right-hand side sparse matrix operand.
Definition: SMatSMatSchurExpr.h:276
#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
CompositeType_< MT2 > CT2
Composite type of the right-hand side sparse matrix expression.
Definition: SMatSMatSchurExpr.h:115
Header file for the IsExpression type trait class.
Header file for the function trace functionality.
Constraint on the data type.