SMatSMatMultExpr.h
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1 //=================================================================================================
33 //=================================================================================================
34 
35 #ifndef _BLAZE_MATH_EXPRESSIONS_SMATSMATMULTEXPR_H_
36 #define _BLAZE_MATH_EXPRESSIONS_SMATSMATMULTEXPR_H_
37 
38 
39 //*************************************************************************************************
40 // Includes
41 //*************************************************************************************************
42 
43 #include <algorithm>
44 #include <vector>
45 #include <blaze/math/Aliases.h>
51 #include <blaze/math/Exception.h>
56 #include <blaze/math/Infinity.h>
58 #include <blaze/math/shims/Reset.h>
79 #include <blaze/util/Assert.h>
80 #include <blaze/util/DisableIf.h>
81 #include <blaze/util/EnableIf.h>
84 #include <blaze/util/InvalidType.h>
85 #include <blaze/util/mpl/And.h>
86 #include <blaze/util/mpl/If.h>
87 #include <blaze/util/mpl/Or.h>
88 #include <blaze/util/Types.h>
90 #include <blaze/util/Unused.h>
91 
92 
93 namespace blaze {
94 
95 //=================================================================================================
96 //
97 // CLASS SMATSMATMULTEXPR
98 //
99 //=================================================================================================
100 
101 //*************************************************************************************************
108 template< typename MT1 // Type of the left-hand side sparse matrix
109  , typename MT2 > // Type of the right-hand side sparse matrix
110 class SMatSMatMultExpr
111  : public MatMatMultExpr< SparseMatrix< SMatSMatMultExpr<MT1,MT2>, false > >
112  , private Computation
113 {
114  private:
115  //**Type definitions****************************************************************************
120  //**********************************************************************************************
121 
122  //**********************************************************************************************
124  enum : bool { evaluateLeft = RequiresEvaluation<MT1>::value };
125  //**********************************************************************************************
126 
127  //**********************************************************************************************
129  enum : bool { evaluateRight = RequiresEvaluation<MT2>::value };
130  //**********************************************************************************************
131 
132  //**********************************************************************************************
134 
139  template< typename T1, typename T2, typename T3 >
140  struct CanExploitSymmetry {
141  enum : bool { value = IsColumnMajorMatrix<T1>::value &&
143  };
145  //**********************************************************************************************
146 
147  //**********************************************************************************************
149 
154  template< typename T1, typename T2, typename T3 >
155  struct IsEvaluationRequired {
156  enum : bool { value = ( evaluateLeft || evaluateRight ) &&
157  !CanExploitSymmetry<T1,T2,T3>::value };
158  };
160  //**********************************************************************************************
161 
162  public:
163  //**Type definitions****************************************************************************
169  using ReturnType = const ElementType;
170  using CompositeType = const ResultType;
171 
173  using LeftOperand = If_< IsExpression<MT1>, const MT1, const MT1& >;
174 
176  using RightOperand = If_< IsExpression<MT2>, const MT2, const MT2& >;
177  //**********************************************************************************************
178 
179  //**Compilation flags***************************************************************************
181  enum : bool { smpAssignable = !evaluateLeft && MT1::smpAssignable &&
182  !evaluateRight && MT2::smpAssignable };
183  //**********************************************************************************************
184 
185  //**Constructor*********************************************************************************
191  explicit inline SMatSMatMultExpr( const MT1& lhs, const MT2& rhs ) noexcept
192  : lhs_( lhs ) // Left-hand side sparse matrix of the multiplication expression
193  , rhs_( rhs ) // Right-hand side sparse matrix of the multiplication expression
194  {
195  BLAZE_INTERNAL_ASSERT( lhs.columns() == rhs.rows(), "Invalid matrix sizes" );
196  }
197  //**********************************************************************************************
198 
199  //**Access operator*****************************************************************************
206  inline ReturnType operator()( size_t i, size_t j ) const {
207  BLAZE_INTERNAL_ASSERT( i < lhs_.rows() , "Invalid row access index" );
208  BLAZE_INTERNAL_ASSERT( j < rhs_.columns(), "Invalid column access index" );
209 
210  if( IsDiagonal<MT1>::value ) {
211  return lhs_(i,i) * rhs_(i,j);
212  }
213  else if( IsDiagonal<MT2>::value ) {
214  return lhs_(i,j) * rhs_(j,j);
215  }
217  const size_t begin( ( IsUpper<MT1>::value )
218  ?( ( IsLower<MT2>::value )
219  ?( max( ( IsStrictlyUpper<MT1>::value ? i+1UL : i )
220  , ( IsStrictlyLower<MT2>::value ? j+1UL : j ) ) )
221  :( IsStrictlyUpper<MT1>::value ? i+1UL : i ) )
222  :( ( IsLower<MT2>::value )
223  ?( IsStrictlyLower<MT2>::value ? j+1UL : j )
224  :( 0UL ) ) );
225  const size_t end( ( IsLower<MT1>::value )
226  ?( ( IsUpper<MT2>::value )
227  ?( min( ( IsStrictlyLower<MT1>::value ? i : i+1UL )
228  , ( IsStrictlyUpper<MT2>::value ? j : j+1UL ) ) )
229  :( IsStrictlyLower<MT1>::value ? i : i+1UL ) )
230  :( ( IsUpper<MT2>::value )
231  ?( IsStrictlyUpper<MT2>::value ? j : j+1UL )
232  :( lhs_.columns() ) ) );
233 
234  if( begin >= end ) return ElementType();
235 
236  const size_t n( end - begin );
237 
238  return subvector( row( lhs_, i ), begin, n ) * subvector( column( rhs_, j ), begin, n );
239  }
240  else {
241  return row( lhs_, i ) * column( rhs_, j );
242  }
243  }
244  //**********************************************************************************************
245 
246  //**At function*********************************************************************************
254  inline ReturnType at( size_t i, size_t j ) const {
255  if( i >= lhs_.rows() ) {
256  BLAZE_THROW_OUT_OF_RANGE( "Invalid row access index" );
257  }
258  if( j >= rhs_.columns() ) {
259  BLAZE_THROW_OUT_OF_RANGE( "Invalid column access index" );
260  }
261  return (*this)(i,j);
262  }
263  //**********************************************************************************************
264 
265  //**Rows function*******************************************************************************
270  inline size_t rows() const noexcept {
271  return lhs_.rows();
272  }
273  //**********************************************************************************************
274 
275  //**Columns function****************************************************************************
280  inline size_t columns() const noexcept {
281  return rhs_.columns();
282  }
283  //**********************************************************************************************
284 
285  //**NonZeros function***************************************************************************
290  inline constexpr size_t nonZeros() const noexcept {
291  return 0UL;
292  }
293  //**********************************************************************************************
294 
295  //**NonZeros function***************************************************************************
301  inline size_t nonZeros( size_t i ) const noexcept {
302  UNUSED_PARAMETER( i );
303  return 0UL;
304  }
305  //**********************************************************************************************
306 
307  //**Left operand access*************************************************************************
312  inline LeftOperand leftOperand() const noexcept {
313  return lhs_;
314  }
315  //**********************************************************************************************
316 
317  //**Right operand access************************************************************************
322  inline RightOperand rightOperand() const noexcept {
323  return rhs_;
324  }
325  //**********************************************************************************************
326 
327  //**********************************************************************************************
333  template< typename T >
334  inline bool canAlias( const T* alias ) const noexcept {
335  return ( lhs_.isAliased( alias ) || rhs_.isAliased( alias ) );
336  }
337  //**********************************************************************************************
338 
339  //**********************************************************************************************
345  template< typename T >
346  inline bool isAliased( const T* alias ) const noexcept {
347  return ( lhs_.isAliased( alias ) || rhs_.isAliased( alias ) );
348  }
349  //**********************************************************************************************
350 
351  //**********************************************************************************************
356  inline bool canSMPAssign() const noexcept {
357  return ( rows() * columns() >= SMP_SMATSMATMULT_THRESHOLD );
358  }
359  //**********************************************************************************************
360 
361  private:
362  //**Member variables****************************************************************************
365  //**********************************************************************************************
366 
367  //**Assignment to dense matrices****************************************************************
380  template< typename MT // Type of the target dense matrix
381  , bool SO > // Storage order of the target dense matrix
383  assign( DenseMatrix<MT,SO>& lhs, const SMatSMatMultExpr& rhs )
384  {
386 
387  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
388  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
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( B.columns() == (~lhs).columns() , "Invalid number of columns" );
399 
400  SMatSMatMultExpr::selectAssignKernel( ~lhs, A, B );
401  }
403  //**********************************************************************************************
404 
405  //**Default assignment to dense matrices********************************************************
418  template< typename MT3 // Type of the left-hand side target matrix
419  , typename MT4 // Type of the left-hand side matrix operand
420  , typename MT5 > // Type of the right-hand side matrix operand
421  static inline void selectAssignKernel( MT3& C, const MT4& A, const MT5& B )
422  {
423  using LeftIterator = ConstIterator_<MT4>;
424  using RightIterator = ConstIterator_<MT5>;
425 
426  for( size_t i=0UL; i<C.rows(); ++i ) {
427  const LeftIterator lend( A.end(i) );
428  for( LeftIterator lelem=A.begin(i); lelem!=lend; ++lelem ) {
429  const RightIterator rend( B.end( lelem->index() ) );
430  for( RightIterator relem=B.begin( lelem->index() ); relem!=rend; ++relem )
431  {
432  if( IsResizable< ElementType_<MT3> >::value &&
433  isDefault( C(i,relem->index()) ) ) {
434  C(i,relem->index()) = lelem->value() * relem->value();
435  }
436  else {
437  C(i,relem->index()) += lelem->value() * relem->value();
438  }
439  }
440  }
441  }
442  }
444  //**********************************************************************************************
445 
446  //**Assignment to row-major sparse matrices*****************************************************
459  template< typename MT > // Type of the target sparse matrix
460  friend inline void assign( SparseMatrix<MT,false>& lhs, const SMatSMatMultExpr& rhs )
461  {
463 
464  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
465  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
466 
467  using LeftIterator = ConstIterator_< RemoveReference_<CT1> >;
468  using RightIterator = ConstIterator_< RemoveReference_<CT2> >;
469 
470  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
471  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
472 
473  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
474  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
475  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
476  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
477  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
478  BLAZE_INTERNAL_ASSERT( B.columns() == (~lhs).columns() , "Invalid number of columns" );
479 
480  // (Over-)Estimating the number of non-zero entries in the resulting matrix
481  size_t nonzeros( 0UL );
482 
483  for( size_t i=0UL; i<(~lhs).rows(); ++i ) {
484  const LeftIterator lend( A.end(i) );
485  for( LeftIterator lelem=A.begin(i); lelem!=lend; ++lelem ) {
486  nonzeros += B.nonZeros( lelem->index() );
487  }
488  }
489 
490  if( nonzeros > (~lhs).rows() * (~lhs).columns() ) {
491  nonzeros = (~lhs).rows() * (~lhs).columns();
492  }
493 
494  (~lhs).reserve( nonzeros );
495  nonzeros = 0UL;
496 
497  // Performing the matrix-matrix multiplication
498  std::vector<ElementType> values ( (~lhs).columns(), ElementType() );
499  std::vector<byte_t> valid ( (~lhs).columns(), 0 );
500  std::vector<size_t> indices( (~lhs).columns(), 0UL );
501  size_t minIndex( inf ), maxIndex( 0UL );
502 
503  for( size_t i=0UL; i<(~lhs).rows(); ++i )
504  {
505  const LeftIterator lend( A.end(i) );
506  for( LeftIterator lelem=A.begin(i); lelem!=lend; ++lelem )
507  {
508  const RightIterator rend( B.end( lelem->index() ) );
509  for( RightIterator relem=B.begin( lelem->index() ); relem!=rend; ++relem )
510  {
511  if( !valid[relem->index()] ) {
512  values[relem->index()] = lelem->value() * relem->value();
513  valid [relem->index()] = 1;
514  indices[nonzeros] = relem->index();
515  ++nonzeros;
516  if( relem->index() < minIndex ) minIndex = relem->index();
517  if( relem->index() > maxIndex ) maxIndex = relem->index();
518  }
519  else {
520  values[relem->index()] += lelem->value() * relem->value();
521  }
522  }
523  }
524 
525  BLAZE_INTERNAL_ASSERT( nonzeros <= (~lhs).columns(), "Invalid number of non-zero elements" );
526 
527  if( nonzeros > 0UL )
528  {
529  BLAZE_INTERNAL_ASSERT( minIndex <= maxIndex, "Invalid index detected" );
530 
531  if( ( nonzeros + nonzeros ) < ( maxIndex - minIndex ) )
532  {
533  std::sort( indices.begin(), indices.begin() + nonzeros );
534 
535  for( size_t j=0UL; j<nonzeros; ++j )
536  {
537  const size_t index( indices[j] );
538  if( !isDefault( values[index] ) ) {
539  (~lhs).append( i, index, values[index] );
540  reset( values[index] );
541  }
542 
543  reset( valid [index] );
544  }
545  }
546  else {
547  for( size_t j=minIndex; j<=maxIndex; ++j )
548  {
549  if( !isDefault( values[j] ) ) {
550  (~lhs).append( i, j, values[j] );
551  reset( values[j] );
552  }
553 
554  reset( valid [j] );
555  }
556  }
557 
558  nonzeros = 0UL;
559  minIndex = inf;
560  maxIndex = 0UL;
561  }
562 
563  (~lhs).finalize( i );
564  }
565  }
567  //**********************************************************************************************
568 
569  //**Assignment to column-major sparse matrices**************************************************
582  template< typename MT > // Type of the target sparse matrix
584  assign( SparseMatrix<MT,true>& lhs, const SMatSMatMultExpr& rhs )
585  {
587 
589 
590  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
591  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
592 
595 
596  const ResultType tmp( serial( rhs ) );
597  (~lhs).reserve( tmp.nonZeros() );
598  assign( ~lhs, tmp );
599  }
601  //**********************************************************************************************
602 
603  //**Restructuring assignment to column-major matrices*******************************************
618  template< typename MT > // Type of the target matrix
620  assign( Matrix<MT,true>& lhs, const SMatSMatMultExpr& rhs )
621  {
623 
625 
626  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
627  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
628 
629  assign( ~lhs, trans( rhs.lhs_ ) * trans( rhs.rhs_ ) );
630  }
632  //**********************************************************************************************
633 
634  //**Addition assignment to dense matrices*******************************************************
647  template< typename MT // Type of the target dense matrix
648  , bool SO > // Storage order of the target dense matarix
650  addAssign( DenseMatrix<MT,SO>& lhs, const SMatSMatMultExpr& rhs )
651  {
653 
654  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
655  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
656 
657  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
658  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
659 
660  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
661  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
662  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
663  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
664  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
665  BLAZE_INTERNAL_ASSERT( B.columns() == (~lhs).columns() , "Invalid number of columns" );
666 
667  SMatSMatMultExpr::selectAddAssignKernel( ~lhs, A, B );
668  }
670  //**********************************************************************************************
671 
672  //**Default addition assignment to dense matrices***********************************************
686  template< typename MT3 // Type of the left-hand side target matrix
687  , typename MT4 // Type of the left-hand side matrix operand
688  , typename MT5 > // Type of the right-hand side matrix operand
689  static inline void selectAddAssignKernel( MT3& C, const MT4& A, const MT5& B )
690  {
691  using LeftIterator = ConstIterator_<MT4>;
692  using RightIterator = ConstIterator_<MT5>;
693 
694  for( size_t i=0UL; i<C.rows(); ++i ) {
695  const LeftIterator lend( A.end(i) );
696  for( LeftIterator lelem=A.begin(i); lelem!=lend; ++lelem ) {
697  const RightIterator rend( B.end( lelem->index() ) );
698  for( RightIterator relem=B.begin( lelem->index() ); relem!=rend; ++relem ) {
699  C(i,relem->index()) += lelem->value() * relem->value();
700  }
701  }
702  }
703  }
705  //**********************************************************************************************
706 
707  //**Restructuring addition assignment to column-major matrices**********************************
722  template< typename MT > // Type of the target matrix
724  addAssign( Matrix<MT,true>& lhs, const SMatSMatMultExpr& rhs )
725  {
727 
729 
730  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
731  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
732 
733  addAssign( ~lhs, trans( rhs.lhs_ ) * trans( rhs.rhs_ ) );
734  }
736  //**********************************************************************************************
737 
738  //**Addition assignment to sparse matrices******************************************************
739  // No special implementation for the addition assignment to sparse matrices.
740  //**********************************************************************************************
741 
742  //**Subtraction assignment to dense matrices****************************************************
755  template< typename MT // Type of the target dense matrix
756  , bool SO > // Storage order of the target dense matrix
758  subAssign( DenseMatrix<MT,SO>& lhs, const SMatSMatMultExpr& rhs )
759  {
761 
762  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
763  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
764 
765  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
766  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
767 
768  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
769  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
770  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
771  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
772  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
773  BLAZE_INTERNAL_ASSERT( B.columns() == (~lhs).columns() , "Invalid number of columns" );
774 
775  SMatSMatMultExpr::selectSubAssignKernel( ~lhs, A, B );
776  }
778  //**********************************************************************************************
779 
780  //**Default subtraction assignment to dense matrices********************************************
794  template< typename MT3 // Type of the left-hand side target matrix
795  , typename MT4 // Type of the left-hand side matrix operand
796  , typename MT5 > // Type of the right-hand side matrix operand
797  static inline void selectSubAssignKernel( MT3& C, const MT4& A, const MT5& B )
798  {
799  using LeftIterator = ConstIterator_<MT4>;
800  using RightIterator = ConstIterator_<MT5>;
801 
802  for( size_t i=0UL; i<C.rows(); ++i ) {
803  const LeftIterator lend( A.end(i) );
804  for( LeftIterator lelem=A.begin(i); lelem!=lend; ++lelem ) {
805  const RightIterator rend( B.end( lelem->index() ) );
806  for( RightIterator relem=B.begin( lelem->index() ); relem!=rend; ++relem ) {
807  C(i,relem->index()) -= lelem->value() * relem->value();
808  }
809  }
810  }
811  }
813  //**********************************************************************************************
814 
815  //**Restructuring subtraction assignment to column-major matrices*******************************
830  template< typename MT > // Type of the target matrix
832  subAssign( Matrix<MT,true>& lhs, const SMatSMatMultExpr& rhs )
833  {
835 
837 
838  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
839  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
840 
841  subAssign( ~lhs, trans( rhs.lhs_ ) * trans( rhs.rhs_ ) );
842  }
844  //**********************************************************************************************
845 
846  //**Subtraction assignment to sparse matrices***************************************************
847  // No special implementation for the subtraction assignment to sparse matrices.
848  //**********************************************************************************************
849 
850  //**Schur product assignment to dense matrices**************************************************
863  template< typename MT // Type of the target dense matrix
864  , bool SO > // Storage order of the target dense matrix
865  friend inline void schurAssign( DenseMatrix<MT,SO>& lhs, const SMatSMatMultExpr& rhs )
866  {
868 
872 
873  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
874  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
875 
876  const ResultType tmp( serial( rhs ) );
877  schurAssign( ~lhs, tmp );
878  }
880  //**********************************************************************************************
881 
882  //**Schur product assignment to sparse matrices*************************************************
883  // No special implementation for the Schur product assignment to sparse matrices.
884  //**********************************************************************************************
885 
886  //**Multiplication assignment to dense matrices*************************************************
887  // No special implementation for the multiplication assignment to dense matrices.
888  //**********************************************************************************************
889 
890  //**Multiplication assignment to sparse matrices************************************************
891  // No special implementation for the multiplication assignment to sparse matrices.
892  //**********************************************************************************************
893 
894  //**SMP assignment to matrices******************************************************************
909  template< typename MT // Type of the target matrix
910  , bool SO > // Storage order of the target matrix
912  smpAssign( Matrix<MT,SO>& lhs, const SMatSMatMultExpr& rhs )
913  {
915 
916  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
917  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
918 
919  CT1 A( rhs.lhs_ ); // Evaluation of the left-hand side sparse matrix operand
920  CT2 B( rhs.rhs_ ); // Evaluation of the right-hand side sparse matrix operand
921 
922  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
923  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
924  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
925  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
926  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
927  BLAZE_INTERNAL_ASSERT( B.columns() == (~lhs).columns() , "Invalid number of columns" );
928 
929  smpAssign( ~lhs, A * B );
930  }
932  //**********************************************************************************************
933 
934  //**Restructuring SMP assignment to column-major matrices***************************************
949  template< typename MT > // Type of the target matrix
951  smpAssign( Matrix<MT,true>& lhs, const SMatSMatMultExpr& rhs )
952  {
954 
956 
957  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
958  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
959 
960  smpAssign( ~lhs, trans( rhs.lhs_ ) * trans( rhs.rhs_ ) );
961  }
963  //**********************************************************************************************
964 
965  //**SMP addition assignment to dense matrices***************************************************
981  template< typename MT // Type of the target dense matrix
982  , bool SO > // Storage order of the target dense matarix
985  {
987 
988  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
989  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
990 
991  CT1 A( rhs.lhs_ ); // Evaluation of the left-hand side sparse matrix operand
992  CT2 B( rhs.rhs_ ); // Evaluation of the right-hand side sparse matrix operand
993 
994  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
995  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
996  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
997  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
998  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
999  BLAZE_INTERNAL_ASSERT( B.columns() == (~lhs).columns() , "Invalid number of columns" );
1000 
1001  smpAddAssign( ~lhs, A * B );
1002  }
1004  //**********************************************************************************************
1005 
1006  //**Restructuring SMP addition assignment to column-major matrices******************************
1021  template< typename MT > // Type of the target matrix
1023  smpAddAssign( Matrix<MT,true>& lhs, const SMatSMatMultExpr& rhs )
1024  {
1026 
1028 
1029  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
1030  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
1031 
1032  smpAddAssign( ~lhs, trans( rhs.lhs_ ) * trans( rhs.rhs_ ) );
1033  }
1035  //**********************************************************************************************
1036 
1037  //**SMP addition assignment to sparse matrices**************************************************
1038  // No special implementation for the SMP addition assignment to sparse matrices.
1039  //**********************************************************************************************
1040 
1041  //**SMP subtraction assignment to dense matrices************************************************
1057  template< typename MT // Type of the target dense matrix
1058  , bool SO > // Storage order of the target dense matrix
1061  {
1063 
1064  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
1065  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
1066 
1067  CT1 A( rhs.lhs_ ); // Evaluation of the left-hand side sparse matrix operand
1068  CT2 B( rhs.rhs_ ); // Evaluation of the right-hand side sparse matrix operand
1069 
1070  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
1071  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
1072  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
1073  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
1074  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
1075  BLAZE_INTERNAL_ASSERT( B.columns() == (~lhs).columns() , "Invalid number of columns" );
1076 
1077  smpSubAssign( ~lhs, A * B );
1078  }
1080  //**********************************************************************************************
1081 
1082  //**Restructuring SMP subtraction assignment to column-major matrices***************************
1097  template< typename MT > // Type of the target matrix
1099  smpSubAssign( Matrix<MT,true>& lhs, const SMatSMatMultExpr& rhs )
1100  {
1102 
1104 
1105  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
1106  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
1107 
1108  smpSubAssign( ~lhs, trans( rhs.lhs_ ) * trans( rhs.rhs_ ) );
1109  }
1111  //**********************************************************************************************
1112 
1113  //**SMP subtraction assignment to sparse matrices***********************************************
1114  // No special implementation for the SMP subtraction assignment to sparse matrices.
1115  //**********************************************************************************************
1116 
1117  //**SMP Schur product assignment to dense matrices**********************************************
1130  template< typename MT // Type of the target dense matrix
1131  , bool SO > // Storage order of the target dense matrix
1132  friend inline void
1134  {
1136 
1140 
1141  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
1142  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
1143 
1144  const ResultType tmp( rhs );
1145  smpSchurAssign( ~lhs, tmp );
1146  }
1148  //**********************************************************************************************
1149 
1150  //**SMP Schur product assignment to sparse matrices*********************************************
1151  // No special implementation for the SMP Schur product assignment to sparse matrices.
1152  //**********************************************************************************************
1153 
1154  //**SMP multiplication assignment to dense matrices*********************************************
1155  // No special implementation for the SMP multiplication assignment to dense matrices.
1156  //**********************************************************************************************
1157 
1158  //**SMP multiplication assignment to sparse matrices********************************************
1159  // No special implementation for the SMP multiplication assignment to sparse matrices.
1160  //**********************************************************************************************
1161 
1162  //**Compile time checks*************************************************************************
1170  //**********************************************************************************************
1171 };
1172 //*************************************************************************************************
1173 
1174 
1175 
1176 
1177 //=================================================================================================
1178 //
1179 // GLOBAL BINARY ARITHMETIC OPERATORS
1180 //
1181 //=================================================================================================
1182 
1183 //*************************************************************************************************
1210 template< typename MT1 // Type of the left-hand side sparse matrix
1211  , typename MT2 > // Type of the right-hand side sparse matrix
1212 inline decltype(auto)
1213  operator*( const SparseMatrix<MT1,false>& lhs, const SparseMatrix<MT2,false>& rhs )
1214 {
1216 
1217  if( (~lhs).columns() != (~rhs).rows() ) {
1218  BLAZE_THROW_INVALID_ARGUMENT( "Matrix sizes do not match" );
1219  }
1220 
1221  using ReturnType = const SMatSMatMultExpr<MT1,MT2>;
1222  return ReturnType( ~lhs, ~rhs );
1223 }
1224 //*************************************************************************************************
1225 
1226 
1227 
1228 
1229 //=================================================================================================
1230 //
1231 // ROWS SPECIALIZATIONS
1232 //
1233 //=================================================================================================
1234 
1235 //*************************************************************************************************
1237 template< typename MT1, typename MT2 >
1238 struct Rows< SMatSMatMultExpr<MT1,MT2> >
1239  : public Rows<MT1>
1240 {};
1242 //*************************************************************************************************
1243 
1244 
1245 
1246 
1247 //=================================================================================================
1248 //
1249 // COLUMNS SPECIALIZATIONS
1250 //
1251 //=================================================================================================
1252 
1253 //*************************************************************************************************
1255 template< typename MT1, typename MT2 >
1256 struct Columns< SMatSMatMultExpr<MT1,MT2> >
1257  : public Columns<MT2>
1258 {};
1260 //*************************************************************************************************
1261 
1262 
1263 
1264 
1265 //=================================================================================================
1266 //
1267 // ISLOWER SPECIALIZATIONS
1268 //
1269 //=================================================================================================
1270 
1271 //*************************************************************************************************
1273 template< typename MT1, typename MT2 >
1274 struct IsLower< SMatSMatMultExpr<MT1,MT2> >
1275  : public BoolConstant< And< IsLower<MT1>, IsLower<MT2> >::value >
1276 {};
1278 //*************************************************************************************************
1279 
1280 
1281 
1282 
1283 //=================================================================================================
1284 //
1285 // ISUNILOWER SPECIALIZATIONS
1286 //
1287 //=================================================================================================
1288 
1289 //*************************************************************************************************
1291 template< typename MT1, typename MT2 >
1292 struct IsUniLower< SMatSMatMultExpr<MT1,MT2> >
1293  : public BoolConstant< And< IsUniLower<MT1>, IsUniLower<MT2> >::value >
1294 {};
1296 //*************************************************************************************************
1297 
1298 
1299 
1300 
1301 //=================================================================================================
1302 //
1303 // ISSTRICTLYLOWER SPECIALIZATIONS
1304 //
1305 //=================================================================================================
1306 
1307 //*************************************************************************************************
1309 template< typename MT1, typename MT2 >
1310 struct IsStrictlyLower< SMatSMatMultExpr<MT1,MT2> >
1311  : public BoolConstant< Or< And< IsStrictlyLower<MT1>, IsLower<MT2> >
1312  , And< IsStrictlyLower<MT2>, IsLower<MT1> > >::value >
1313 {};
1315 //*************************************************************************************************
1316 
1317 
1318 
1319 
1320 //=================================================================================================
1321 //
1322 // ISUPPER SPECIALIZATIONS
1323 //
1324 //=================================================================================================
1325 
1326 //*************************************************************************************************
1328 template< typename MT1, typename MT2 >
1329 struct IsUpper< SMatSMatMultExpr<MT1,MT2> >
1330  : public BoolConstant< And< IsUpper<MT1>, IsUpper<MT2> >::value >
1331 {};
1333 //*************************************************************************************************
1334 
1335 
1336 
1337 
1338 //=================================================================================================
1339 //
1340 // ISUNIUPPER SPECIALIZATIONS
1341 //
1342 //=================================================================================================
1343 
1344 //*************************************************************************************************
1346 template< typename MT1, typename MT2 >
1347 struct IsUniUpper< SMatSMatMultExpr<MT1,MT2> >
1348  : public BoolConstant< And< IsUniUpper<MT1>, IsUniUpper<MT2> >::value >
1349 {};
1351 //*************************************************************************************************
1352 
1353 
1354 
1355 
1356 //=================================================================================================
1357 //
1358 // ISSTRICTLYUPPER SPECIALIZATIONS
1359 //
1360 //=================================================================================================
1361 
1362 //*************************************************************************************************
1364 template< typename MT1, typename MT2 >
1365 struct IsStrictlyUpper< SMatSMatMultExpr<MT1,MT2> >
1366  : public BoolConstant< Or< And< IsStrictlyUpper<MT1>, IsUpper<MT2> >
1367  , And< IsStrictlyUpper<MT2>, IsUpper<MT1> > >::value >
1368 {};
1370 //*************************************************************************************************
1371 
1372 } // namespace blaze
1373 
1374 #endif
ReturnType operator()(size_t i, size_t j) const
2D-access to the matrix elements.
Definition: SMatSMatMultExpr.h:206
#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
Header file for auxiliary alias declarations.
Headerfile for the generic min algorithm.
bool canAlias(const T *alias) const noexcept
Returns whether the expression can alias with the given address alias.
Definition: SMatSMatMultExpr.h:334
RightOperand rhs_
Right-hand side sparse matrix of the multiplication expression.
Definition: SMatSMatMultExpr.h:364
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
Compile time check for triangular matrix types.This type trait tests whether or not the given templat...
Definition: IsTriangular.h:87
Header file for basic type definitions.
Subvector< VT, AF > subvector(Vector< VT, TF > &vector, size_t index, size_t size)
Creating a view on a specific subvector of the given vector.
Definition: Subvector.h:322
If_< IsExpression< MT2 >, const MT2, const MT2 &> RightOperand
Composite type of the right-hand side sparse matrix expression.
Definition: SMatSMatMultExpr.h:176
EnableIf_< IsDenseMatrix< MT1 > > smpSubAssign(Matrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs)
Default implementation of the SMP subtraction assignment of a matrix to dense matrix.
Definition: DenseMatrix.h:164
Header file for the serial shim.
Generic wrapper for a compile time constant integral value.The IntegralConstant class template repres...
Definition: IntegralConstant.h:71
BLAZE_ALWAYS_INLINE MT::Iterator begin(Matrix< MT, SO > &matrix, size_t i)
Returns an iterator to the first element of row/column i.
Definition: Matrix.h:198
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
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 check for lower triangular matrices.This type trait tests whether or not the given templ...
Definition: IsLower.h:88
CompositeType_< MT2 > CT2
Composite type of the right-hand side sparse matrix expression.
Definition: SMatSMatMultExpr.h:119
OppositeType_< ResultType > OppositeType
Result type with opposite storage order for expression template evaluations.
Definition: SMatSMatMultExpr.h:166
typename MultTrait< T1, T2 >::Type MultTrait_
Auxiliary alias declaration for the MultTrait class template.The MultTrait_ alias declaration provide...
Definition: MultTrait.h:250
Column< MT > column(Matrix< MT, SO > &matrix, size_t index)
Creating a view on a specific column of the given matrix.
Definition: Column.h:124
Header file for the Computation base class.
Header file for the MatMatMultExpr base class.
Compile time check for upper triangular matrices.This type trait tests whether or not the given templ...
Definition: IsUpper.h:88
bool isAliased(const T *alias) const noexcept
Returns whether the expression is aliased with the given address alias.
Definition: SMatSMatMultExpr.h:346
Constraints on the storage order of matrix types.
Header file for the RequiresEvaluation type trait.
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
const ElementType_< MT > max(const DenseMatrix< MT, SO > &dm)
Returns the largest element of the dense matrix.
Definition: DenseMatrix.h:1809
EnableIf_< IsDenseMatrix< MT1 > > smpAddAssign(Matrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs)
Default implementation of the SMP addition assignment of a matrix to a dense matrix.
Definition: DenseMatrix.h:133
size_t rows() const noexcept
Returns the current number of rows of the matrix.
Definition: SMatSMatMultExpr.h:270
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
RightOperand rightOperand() const noexcept
Returns the right-hand side sparse matrix operand.
Definition: SMatSMatMultExpr.h:322
Header file for the SparseMatrix base class.
Row< MT > row(Matrix< MT, SO > &matrix, size_t index)
Creating a view on a specific row of the given matrix.
Definition: Row.h:124
Constraint on the data type.
Compile time check to query the requirement to evaluate an expression.Via this type trait it is possi...
Definition: RequiresEvaluation.h:72
typename T::CompositeType CompositeType_
Alias declaration for nested CompositeType type definitions.The CompositeType_ alias declaration prov...
Definition: Aliases.h:83
Compile time check for upper unitriangular matrices.This type trait tests whether or not the given te...
Definition: IsUniUpper.h:86
Headerfile for the generic max algorithm.
Header file for the DisableIf class template.
LeftOperand lhs_
Left-hand side sparse matrix of the multiplication expression.
Definition: SMatSMatMultExpr.h:363
Header file for the multiplication trait.
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.
EnableIf_< IsDenseMatrix< MT1 > > smpAssign(Matrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs)
Default implementation of the SMP assignment of a matrix to a dense matrix.
Definition: DenseMatrix.h:102
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.
ReturnType at(size_t i, size_t j) const
Checked access to the matrix elements.
Definition: SMatSMatMultExpr.h:254
Numerical infinity for built-in data types.
typename T::ElementType ElementType_
Alias declaration for nested ElementType type definitions.The ElementType_ alias declaration provides...
Definition: Aliases.h:163
Header file for the IsLower type trait.
Compile time check for diagonal matrices.This type trait tests whether or not the given template para...
Definition: IsDiagonal.h:90
Header file for the IsTriangular type trait.
LeftOperand leftOperand() const noexcept
Returns the left-hand side sparse matrix operand.
Definition: SMatSMatMultExpr.h:312
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
BLAZE_ALWAYS_INLINE MT::Iterator end(Matrix< MT, SO > &matrix, size_t i)
Returns an iterator just past the last element of row/column i.
Definition: Matrix.h:264
Constraint on the data type.
Header file for all forward declarations for expression class templates.
Header file for the EnableIf class template.
Header file for the IsStrictlyLower type trait.
size_t nonZeros(size_t i) const noexcept
Returns the number of non-zero elements in the specified row.
Definition: SMatSMatMultExpr.h:301
#define BLAZE_CONSTRAINT_MUST_FORM_VALID_MATMATMULTEXPR(T1, T2)
Constraint on the data type.In case the given data types T1 and T2 do not form a valid matrix/matrix ...
Definition: MatMatMultExpr.h:108
MultTrait_< RT1, RT2 > ResultType
Result type for expression template evaluations.
Definition: SMatSMatMultExpr.h:165
Compile time check for lower unitriangular matrices.This type trait tests whether or not the given te...
Definition: IsUniLower.h:86
Compile time check for resizable data types.This type trait tests whether the given data type is a re...
Definition: IsResizable.h:75
size_t columns() const noexcept
Returns the current number of columns of the matrix.
Definition: SMatSMatMultExpr.h:280
#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
Expression object for sparse matrix-sparse matrix multiplications.The SMatSMatMultExpr class represen...
Definition: Forward.h:117
SMatSMatMultExpr(const MT1 &lhs, const MT2 &rhs) noexcept
Constructor for the SMatSMatMultExpr class.
Definition: SMatSMatMultExpr.h:191
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
Utility type for generic codes.
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
Header file for the reset shim.
#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
const ResultType CompositeType
Data type for composite expression templates.
Definition: SMatSMatMultExpr.h:170
Header file for the isDefault shim.
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
#define BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION(T)
Constraint on the data type.In case the given data type T requires an intermediate evaluation within ...
Definition: RequiresEvaluation.h:81
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
Compile time check for strictly lower triangular matrices.This type trait tests whether or not the gi...
Definition: IsStrictlyLower.h:86
const Type & ReturnType
Return type for expression template evaluations.
Definition: CompressedMatrix.h:3082
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
If_< IsExpression< MT1 >, const MT1, const MT1 &> LeftOperand
Composite type of the left-hand side sparse matrix expression.
Definition: SMatSMatMultExpr.h:173
Header file for the IsComputation type trait class.
const ElementType ReturnType
Return type for expression template evaluations.
Definition: SMatSMatMultExpr.h:169
TransposeType_< ResultType > TransposeType
Transpose type for expression template evaluations.
Definition: SMatSMatMultExpr.h:167
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
constexpr Infinity inf
Global Infinity instance.The blaze::inf instance can be used wherever a built-in data type is expecte...
Definition: Infinity.h:1073
Compile time evaluation of the number of rows of a matrix.The Rows type trait evaluates the number of...
Definition: Rows.h:75
CompositeType_< MT1 > CT1
Composite type of the left-hand side sparse matrix expression.
Definition: SMatSMatMultExpr.h:118
bool isDefault(const DiagonalProxy< MT > &proxy)
Returns whether the represented element is in default state.
Definition: DiagonalProxy.h:600
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
constexpr size_t nonZeros() const noexcept
Returns the number of non-zero elements in the sparse matrix.
Definition: SMatSMatMultExpr.h:290
Constraint on the data type.
ElementType_< ResultType > ElementType
Resulting element type.
Definition: SMatSMatMultExpr.h:168
Header file for the IsResizable type trait.
bool canSMPAssign() const noexcept
Returns whether the expression can be used in SMP assignments.
Definition: SMatSMatMultExpr.h:356
ResultType_< MT1 > RT1
Result type of the left-hand side sparse matrix expression.
Definition: SMatSMatMultExpr.h:116
Header file for the thresholds for matrix/vector and matrix/matrix multiplications.
#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
Header file for the IsExpression type trait class.
Header file for the function trace functionality.
ResultType_< MT2 > RT2
Result type of the right-hand side sparse matrix expression.
Definition: SMatSMatMultExpr.h:117