TSMatTSMatMultExpr.h
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1 //=================================================================================================
33 //=================================================================================================
34 
35 #ifndef _BLAZE_MATH_EXPRESSIONS_TSMATTSMATMULTEXPR_H_
36 #define _BLAZE_MATH_EXPRESSIONS_TSMATTSMATMULTEXPR_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>
91 #include <blaze/util/Unused.h>
92 
93 
94 namespace blaze {
95 
96 //=================================================================================================
97 //
98 // CLASS TSMATTSMATMULTEXPR
99 //
100 //=================================================================================================
101 
102 //*************************************************************************************************
109 template< typename MT1 // Type of the left-hand side sparse matrix
110  , typename MT2 > // Type of the right-hand side sparse matrix
111 class TSMatTSMatMultExpr
112  : public MatMatMultExpr< SparseMatrix< TSMatTSMatMultExpr<MT1,MT2>, true > >
113  , private Computation
114 {
115  private:
116  //**Type definitions****************************************************************************
121  //**********************************************************************************************
122 
123  //**********************************************************************************************
125  enum : bool { evaluateLeft = RequiresEvaluation<MT1>::value };
126  //**********************************************************************************************
127 
128  //**********************************************************************************************
130  enum : bool { evaluateRight = RequiresEvaluation<MT2>::value };
131  //**********************************************************************************************
132 
133  //**********************************************************************************************
135 
140  template< typename T1, typename T2, typename T3 >
141  struct CanExploitSymmetry {
142  enum : bool { value = IsRowMajorMatrix<T1>::value &&
144  };
146  //**********************************************************************************************
147 
148  //**********************************************************************************************
150 
155  template< typename T1, typename T2, typename T3 >
156  struct IsEvaluationRequired {
157  enum : bool { value = ( evaluateLeft || evaluateRight ) &&
158  !CanExploitSymmetry<T1,T2,T3>::value };
159  };
161  //**********************************************************************************************
162 
163  public:
164  //**Type definitions****************************************************************************
170  using ReturnType = const ElementType;
171  using CompositeType = const ResultType;
172 
174  using LeftOperand = If_< IsExpression<MT1>, const MT1, const MT1& >;
175 
177  using RightOperand = If_< IsExpression<MT2>, const MT2, const MT2& >;
178  //**********************************************************************************************
179 
180  //**Compilation flags***************************************************************************
182  enum : bool { smpAssignable = !evaluateLeft && MT1::smpAssignable &&
183  !evaluateRight && MT2::smpAssignable };
184  //**********************************************************************************************
185 
186  //**Constructor*********************************************************************************
192  explicit inline TSMatTSMatMultExpr( const MT1& lhs, const MT2& rhs ) noexcept
193  : lhs_( lhs ) // Left-hand side sparse matrix of the multiplication expression
194  , rhs_( rhs ) // Right-hand side sparse matrix of the multiplication expression
195  {
196  BLAZE_INTERNAL_ASSERT( lhs.columns() == rhs.rows(), "Invalid matrix sizes" );
197  }
198  //**********************************************************************************************
199 
200  //**Access operator*****************************************************************************
207  inline ReturnType operator()( size_t i, size_t j ) const {
208  BLAZE_INTERNAL_ASSERT( i < lhs_.rows() , "Invalid row access index" );
209  BLAZE_INTERNAL_ASSERT( j < rhs_.columns(), "Invalid column access index" );
210 
211  if( IsDiagonal<MT1>::value ) {
212  return lhs_(i,i) * rhs_(i,j);
213  }
214  else if( IsDiagonal<MT2>::value ) {
215  return lhs_(i,j) * rhs_(j,j);
216  }
218  const size_t begin( ( IsUpper<MT1>::value )
219  ?( ( IsLower<MT2>::value )
220  ?( max( ( IsStrictlyUpper<MT1>::value ? i+1UL : i )
221  , ( IsStrictlyLower<MT2>::value ? j+1UL : j ) ) )
222  :( IsStrictlyUpper<MT1>::value ? i+1UL : i ) )
223  :( ( IsLower<MT2>::value )
224  ?( IsStrictlyLower<MT2>::value ? j+1UL : j )
225  :( 0UL ) ) );
226  const size_t end( ( IsLower<MT1>::value )
227  ?( ( IsUpper<MT2>::value )
228  ?( min( ( IsStrictlyLower<MT1>::value ? i : i+1UL )
229  , ( IsStrictlyUpper<MT2>::value ? j : j+1UL ) ) )
230  :( IsStrictlyLower<MT1>::value ? i : i+1UL ) )
231  :( ( IsUpper<MT2>::value )
232  ?( IsStrictlyUpper<MT2>::value ? j : j+1UL )
233  :( lhs_.columns() ) ) );
234 
235  if( begin >= end ) return ElementType();
236 
237  const size_t n( end - begin );
238 
239  return subvector( row( lhs_, i ), begin, n ) * subvector( column( rhs_, j ), begin, n );
240  }
241  else {
242  return row( lhs_, i ) * column( rhs_, j );
243  }
244  }
245  //**********************************************************************************************
246 
247  //**At function*********************************************************************************
255  inline ReturnType at( size_t i, size_t j ) const {
256  if( i >= lhs_.rows() ) {
257  BLAZE_THROW_OUT_OF_RANGE( "Invalid row access index" );
258  }
259  if( j >= rhs_.columns() ) {
260  BLAZE_THROW_OUT_OF_RANGE( "Invalid column access index" );
261  }
262  return (*this)(i,j);
263  }
264  //**********************************************************************************************
265 
266  //**Rows function*******************************************************************************
271  inline size_t rows() const noexcept {
272  return lhs_.rows();
273  }
274  //**********************************************************************************************
275 
276  //**Columns function****************************************************************************
281  inline size_t columns() const noexcept {
282  return rhs_.columns();
283  }
284  //**********************************************************************************************
285 
286  //**NonZeros function***************************************************************************
291  inline constexpr size_t nonZeros() const noexcept {
292  return 0UL;
293  }
294  //**********************************************************************************************
295 
296  //**NonZeros function***************************************************************************
302  inline size_t nonZeros( size_t i ) const noexcept {
303  UNUSED_PARAMETER( i );
304  return 0UL;
305  }
306  //**********************************************************************************************
307 
308  //**Left operand access*************************************************************************
313  inline LeftOperand leftOperand() const noexcept {
314  return lhs_;
315  }
316  //**********************************************************************************************
317 
318  //**Right operand access************************************************************************
323  inline RightOperand rightOperand() const noexcept {
324  return rhs_;
325  }
326  //**********************************************************************************************
327 
328  //**********************************************************************************************
334  template< typename T >
335  inline bool canAlias( const T* alias ) const noexcept {
336  return ( lhs_.isAliased( alias ) || rhs_.isAliased( alias ) );
337  }
338  //**********************************************************************************************
339 
340  //**********************************************************************************************
346  template< typename T >
347  inline bool isAliased( const T* alias ) const noexcept {
348  return ( lhs_.isAliased( alias ) || rhs_.isAliased( alias ) );
349  }
350  //**********************************************************************************************
351 
352  //**********************************************************************************************
357  inline bool canSMPAssign() const noexcept {
358  return ( rows() * columns() >= SMP_TSMATTSMATMULT_THRESHOLD );
359  }
360  //**********************************************************************************************
361 
362  private:
363  //**Member variables****************************************************************************
366  //**********************************************************************************************
367 
368  //**Assignment to dense matrices****************************************************************
381  template< typename MT // Type of the target dense matrix
382  , bool SO > // Storage order of the target dense matrix
384  assign( DenseMatrix<MT,SO>& lhs, const TSMatTSMatMultExpr& rhs )
385  {
387 
388  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
389  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
390 
391  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
392  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
393 
394  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
395  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
396  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
397  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
398  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
399  BLAZE_INTERNAL_ASSERT( B.columns() == (~lhs).columns() , "Invalid number of columns" );
400 
401  TSMatTSMatMultExpr::selectAssignKernel( ~lhs, A, B );
402  }
404  //**********************************************************************************************
405 
406  //**Default assignment to dense matrices********************************************************
420  template< typename MT3 // Type of the left-hand side target matrix
421  , typename MT4 // Type of the left-hand side matrix operand
422  , typename MT5 > // Type of the right-hand side matrix operand
423  static inline void selectAssignKernel( MT3& C, const MT4& A, const MT5& B )
424  {
425  using LeftIterator = ConstIterator_<MT4>;
426  using RightIterator = ConstIterator_<MT5>;
427 
428  for( size_t j=0UL; j<C.columns(); ++j ) {
429  const RightIterator rend( B.end(j) );
430  for( RightIterator relem=B.begin(j); relem!=rend; ++relem ) {
431  const LeftIterator lend( A.end( relem->index() ) );
432  for( LeftIterator lelem=A.begin( relem->index() ); lelem!=lend; ++lelem )
433  {
434  if( IsResizable< ElementType_<MT3> >::value &&
435  isDefault( C(lelem->index(),j) ) ) {
436  C(lelem->index(),j) = lelem->value() * relem->value();
437  }
438  else {
439  C(lelem->index(),j) += lelem->value() * relem->value();
440  }
441  }
442  }
443  }
444  }
446  //**********************************************************************************************
447 
448  //**Assignment to row-major sparse matrices*****************************************************
461  template< typename MT > // Type of the target sparse matrix
463  assign( SparseMatrix<MT,false>& lhs, const TSMatTSMatMultExpr& rhs )
464  {
466 
468 
469  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
470  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
471 
474 
475  const ResultType tmp( serial( rhs ) );
476  (~lhs).reserve( tmp.nonZeros() );
477  assign( ~lhs, tmp );
478  }
480  //**********************************************************************************************
481 
482  //**Assignment to column-major sparse matrices**************************************************
495  template< typename MT > // Type of the target sparse matrix
496  friend inline void assign( SparseMatrix<MT,true>& lhs, const TSMatTSMatMultExpr& rhs )
497  {
499 
500  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
501  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
502 
503  using LeftIterator = ConstIterator_< RemoveReference_<CT1> >;
504  using RightIterator = ConstIterator_< RemoveReference_<CT2> >;
505 
506  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
507  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
508 
509  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
510  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
511  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
512  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
513  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
514  BLAZE_INTERNAL_ASSERT( B.columns() == (~lhs).columns() , "Invalid number of columns" );
515 
516  // (Over-)Estimating the number of non-zero entries in the resulting matrix
517  size_t nonzeros( 0UL );
518 
519  for( size_t j=0UL; j<(~lhs).columns(); ++j ) {
520  const RightIterator rend( B.end(j) );
521  for( RightIterator relem=B.begin(j); relem!=rend; ++relem ) {
522  nonzeros += A.nonZeros( relem->index() );
523  }
524  }
525 
526  if( nonzeros > (~lhs).rows() * (~lhs).columns() ) {
527  nonzeros = (~lhs).rows() * (~lhs).columns();
528  }
529 
530  (~lhs).reserve( nonzeros );
531  nonzeros = 0UL;
532 
533  // Performing the matrix-matrix multiplication
534  std::vector<ElementType> values ( (~lhs).rows(), ElementType() );
535  std::vector<byte_t> valid ( (~lhs).rows(), 0 );
536  std::vector<size_t> indices( (~lhs).rows(), 0UL );
537  size_t minIndex( inf ), maxIndex( 0UL );
538 
539  for( size_t j=0UL; j<(~lhs).columns(); ++j )
540  {
541  const RightIterator rend( B.end(j) );
542  for( RightIterator relem=B.begin(j); relem!=rend; ++relem )
543  {
544  const LeftIterator lend( A.end( relem->index() ) );
545  for( LeftIterator lelem=A.begin( relem->index() ); lelem!=lend; ++lelem )
546  {
547  if( !valid[lelem->index()] ) {
548  values[lelem->index()] = lelem->value() * relem->value();
549  valid [lelem->index()] = 1;
550  indices[nonzeros] = lelem->index();
551  ++nonzeros;
552  if( lelem->index() < minIndex ) minIndex = lelem->index();
553  if( lelem->index() > maxIndex ) maxIndex = lelem->index();
554  }
555  else {
556  values[lelem->index()] += lelem->value() * relem->value();
557  }
558  }
559  }
560 
561  BLAZE_INTERNAL_ASSERT( nonzeros <= (~lhs).rows(), "Invalid number of non-zero elements" );
562 
563  if( nonzeros > 0UL )
564  {
565  BLAZE_INTERNAL_ASSERT( minIndex <= maxIndex, "Invalid index detected" );
566 
567  if( ( nonzeros + nonzeros ) < ( maxIndex - minIndex ) )
568  {
569  std::sort( indices.begin(), indices.begin() + nonzeros );
570 
571  for( size_t i=0UL; i<nonzeros; ++i )
572  {
573  const size_t index( indices[i] );
574  if( !isDefault( values[index] ) ) {
575  (~lhs).append( index, j, values[index] );
576  reset( values[index] );
577  }
578 
579  reset( valid [index] );
580  }
581  }
582  else {
583  for( size_t i=minIndex; i<=maxIndex; ++i )
584  {
585  if( !isDefault( values[i] ) ) {
586  (~lhs).append( i, j, values[i] );
587  reset( values[i] );
588  }
589 
590  reset( valid [i] );
591  }
592  }
593 
594  nonzeros = 0UL;
595  minIndex = inf;
596  maxIndex = 0UL;
597  }
598 
599  (~lhs).finalize( j );
600  }
601  }
603  //**********************************************************************************************
604 
605  //**Restructuring assignment to row-major matrices**********************************************
620  template< typename MT > // Type of the target matrix
622  assign( Matrix<MT,false>& lhs, const TSMatTSMatMultExpr& rhs )
623  {
625 
627 
628  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
629  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
630 
631  assign( ~lhs, trans( rhs.lhs_ ) * trans( rhs.rhs_ ) );
632  }
634  //**********************************************************************************************
635 
636  //**Addition assignment to dense matrices*******************************************************
649  template< typename MT // Type of the target dense matrix
650  , bool SO > // Storage order of the target dense matarix
652  addAssign( DenseMatrix<MT,SO>& lhs, const TSMatTSMatMultExpr& rhs )
653  {
655 
656  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
657  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
658 
659  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
660  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
661 
662  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
663  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
664  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
665  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
666  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
667  BLAZE_INTERNAL_ASSERT( B.columns() == (~lhs).columns() , "Invalid number of columns" );
668 
669  TSMatTSMatMultExpr::selectAddAssignKernel( ~lhs, A, B );
670  }
672  //**********************************************************************************************
673 
674  //**Default addition assignment to dense matrices***********************************************
688  template< typename MT3 // Type of the left-hand side target matrix
689  , typename MT4 // Type of the left-hand side matrix operand
690  , typename MT5 > // Type of the right-hand side matrix operand
691  static inline void selectAddAssignKernel( MT3& C, const MT4& A, const MT5& B )
692  {
693  using LeftIterator = ConstIterator_<MT4>;
694  using RightIterator = ConstIterator_<MT5>;
695 
696  for( size_t j=0UL; j<C.columns(); ++j ) {
697  const RightIterator rend( B.end(j) );
698  for( RightIterator relem=B.begin(j); relem!=rend; ++relem ) {
699  const LeftIterator lend( A.end( relem->index() ) );
700  for( LeftIterator lelem=A.begin( relem->index() ); lelem!=lend; ++lelem ) {
701  C(lelem->index(),j) += lelem->value() * relem->value();
702  }
703  }
704  }
705  }
707  //**********************************************************************************************
708 
709  //**Restructuring addition assignment to row-major matrices*************************************
724  template< typename MT > // Type of the target matrix
726  addAssign( Matrix<MT,false>& lhs, const TSMatTSMatMultExpr& rhs )
727  {
729 
731 
732  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
733  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
734 
735  addAssign( ~lhs, trans( rhs.lhs_ ) * trans( rhs.rhs_ ) );
736  }
738  //**********************************************************************************************
739 
740  //**Addition assignment to sparse matrices******************************************************
741  // No special implementation for the addition assignment to sparse matrices.
742  //**********************************************************************************************
743 
744  //**Subtraction assignment to dense matrices****************************************************
757  template< typename MT // Type of the target dense matrix
758  , bool SO > // Storage order of the target dense matarix
760  subAssign( DenseMatrix<MT,SO>& lhs, const TSMatTSMatMultExpr& rhs )
761  {
763 
764  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
765  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
766 
767  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
768  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
769 
770  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
771  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
772  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
773  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
774  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
775  BLAZE_INTERNAL_ASSERT( B.columns() == (~lhs).columns() , "Invalid number of columns" );
776 
777  TSMatTSMatMultExpr::selectSubAssignKernel( ~lhs, A, B );
778  }
780  //**********************************************************************************************
781 
782  //**Default subtraction assignment to dense matrices********************************************
796  template< typename MT3 // Type of the left-hand side target matrix
797  , typename MT4 // Type of the left-hand side matrix operand
798  , typename MT5 > // Type of the right-hand side matrix operand
799  static inline void selectSubAssignKernel( MT3& C, const MT4& A, const MT5& B )
800  {
801  using LeftIterator = ConstIterator_<MT4>;
802  using RightIterator = ConstIterator_<MT5>;
803 
804  for( size_t j=0UL; j<C.columns(); ++j ) {
805  const RightIterator rend( B.end(j) );
806  for( RightIterator relem=B.begin(j); relem!=rend; ++relem ) {
807  const LeftIterator lend( A.end( relem->index() ) );
808  for( LeftIterator lelem=A.begin( relem->index() ); lelem!=lend; ++lelem ) {
809  C(lelem->index(),j) -= lelem->value() * relem->value();
810  }
811  }
812  }
813  }
815  //**********************************************************************************************
816 
817  //**Restructuring subtraction assignment to row-major matrices**********************************
833  template< typename MT > // Type of the target matrix
835  subAssign( Matrix<MT,false>& lhs, const TSMatTSMatMultExpr& rhs )
836  {
838 
840 
841  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
842  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
843 
844  subAssign( ~lhs, trans( rhs.lhs_ ) * trans( rhs.rhs_ ) );
845  }
847  //**********************************************************************************************
848 
849  //**Subtraction assignment to sparse matrices***************************************************
850  // No special implementation for the subtraction assignment to sparse matrices.
851  //**********************************************************************************************
852 
853  //**Schur product assignment to dense matrices**************************************************
866  template< typename MT // Type of the target dense matrix
867  , bool SO > // Storage order of the target dense matarix
868  friend inline void schurAssign( DenseMatrix<MT,SO>& lhs, const TSMatTSMatMultExpr& rhs )
869  {
871 
875 
876  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
877  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
878 
879  const ResultType tmp( serial( rhs ) );
880  schurAssign( ~lhs, tmp );
881  }
883  //**********************************************************************************************
884 
885  //**Schur product assignment to sparse matrices*************************************************
886  // No special implementation for the Schur product assignment to sparse matrices.
887  //**********************************************************************************************
888 
889  //**Multiplication assignment to dense matrices*************************************************
890  // No special implementation for the multiplication assignment to dense matrices.
891  //**********************************************************************************************
892 
893  //**Multiplication assignment to sparse matrices************************************************
894  // No special implementation for the multiplication assignment to sparse matrices.
895  //**********************************************************************************************
896 
897  //**SMP assignment to matrices******************************************************************
913  template< typename MT // Type of the target matrix
914  , bool SO > // Storage order of the target matrix
916  smpAssign( Matrix<MT,SO>& lhs, const TSMatTSMatMultExpr& rhs )
917  {
919 
920  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
921  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
922 
923  CT1 A( rhs.lhs_ ); // Evaluation of the left-hand side sparse matrix operand
924  CT2 B( rhs.rhs_ ); // Evaluation of the right-hand side sparse matrix operand
925 
926  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
927  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
928  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
929  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
930  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
931  BLAZE_INTERNAL_ASSERT( B.columns() == (~lhs).columns() , "Invalid number of columns" );
932 
933  smpAssign( ~lhs, A * B );
934  }
936  //**********************************************************************************************
937 
938  //**Restructuring SMP assignment to row-major matrices******************************************
953  template< typename MT > // Type of the target matrix
955  smpAssign( Matrix<MT,false>& lhs, const TSMatTSMatMultExpr& rhs )
956  {
958 
960 
961  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
962  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
963 
964  smpAssign( ~lhs, trans( rhs.lhs_ ) * trans( rhs.rhs_ ) );
965  }
967  //**********************************************************************************************
968 
969  //**SMP addition assignment to dense matrices***************************************************
985  template< typename MT // Type of the target dense matrix
986  , bool SO > // Storage order of the target dense matarix
989  {
991 
992  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
993  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
994 
995  CT1 A( rhs.lhs_ ); // Evaluation of the left-hand side sparse matrix operand
996  CT2 B( rhs.rhs_ ); // Evaluation of the right-hand side sparse matrix operand
997 
998  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
999  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
1000  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
1001  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
1002  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
1003  BLAZE_INTERNAL_ASSERT( B.columns() == (~lhs).columns() , "Invalid number of columns" );
1004 
1005  smpAddAssign( ~lhs, A * B );
1006  }
1008  //**********************************************************************************************
1009 
1010  //**Restructuring SMP addition assignment to row-major matrices*********************************
1026  template< typename MT > // Type of the target matrix
1029  {
1031 
1033 
1034  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
1035  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
1036 
1037  smpAddAssign( ~lhs, trans( rhs.lhs_ ) * trans( rhs.rhs_ ) );
1038  }
1040  //**********************************************************************************************
1041 
1042  //**SMP addition assignment to sparse matrices**************************************************
1043  // No special implementation for the SMP addition assignment to sparse matrices.
1044  //**********************************************************************************************
1045 
1046  //**SMP subtraction assignment to dense matrices************************************************
1062  template< typename MT // Type of the target dense matrix
1063  , bool SO > // Storage order of the target dense matarix
1066  {
1068 
1069  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
1070  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
1071 
1072  CT1 A( rhs.lhs_ ); // Evaluation of the left-hand side sparse matrix operand
1073  CT2 B( rhs.rhs_ ); // Evaluation of the right-hand side sparse matrix operand
1074 
1075  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
1076  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
1077  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
1078  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
1079  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
1080  BLAZE_INTERNAL_ASSERT( B.columns() == (~lhs).columns() , "Invalid number of columns" );
1081 
1082  smpSubAssign( ~lhs, A * B );
1083  }
1085  //**********************************************************************************************
1086 
1087  //**Restructuring SMP subtraction assignment to row-major matrices******************************
1103  template< typename MT > // Type of the target matrix
1106  {
1108 
1110 
1111  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
1112  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
1113 
1114  smpSubAssign( ~lhs, trans( rhs.lhs_ ) * trans( rhs.rhs_ ) );
1115  }
1117  //**********************************************************************************************
1118 
1119  //**SMP subtraction assignment to sparse matrices***********************************************
1120  // No special implementation for the SMP subtraction assignment to sparse matrices.
1121  //**********************************************************************************************
1122 
1123  //**SMP Schur product assignment to dense matrices**********************************************
1136  template< typename MT // Type of the target dense matrix
1137  , bool SO > // Storage order of the target dense matarix
1138  friend inline void smpSchurAssign( DenseMatrix<MT,SO>& lhs, const TSMatTSMatMultExpr& rhs )
1139  {
1141 
1145 
1146  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
1147  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
1148 
1149  const ResultType tmp( rhs );
1150  smpSchurAssign( ~lhs, tmp );
1151  }
1153  //**********************************************************************************************
1154 
1155  //**SMP Schur product assignment to sparse matrices*********************************************
1156  // No special implementation for the SMP Schur product assignment to sparse matrices.
1157  //**********************************************************************************************
1158 
1159  //**SMP multiplication assignment to dense matrices*********************************************
1160  // No special implementation for the SMP multiplication assignment to dense matrices.
1161  //**********************************************************************************************
1162 
1163  //**SMP multiplication assignment to sparse matrices********************************************
1164  // No special implementation for the SMP multiplication assignment to sparse matrices.
1165  //**********************************************************************************************
1166 
1167  //**Compile time checks*************************************************************************
1175  //**********************************************************************************************
1176 };
1177 //*************************************************************************************************
1178 
1179 
1180 
1181 
1182 //=================================================================================================
1183 //
1184 // GLOBAL BINARY ARITHMETIC OPERATORS
1185 //
1186 //=================================================================================================
1187 
1188 //*************************************************************************************************
1215 template< typename MT1 // Type of the left-hand side sparse matrix
1216  , typename MT2 > // Type of the right-hand side sparse matrix
1217 inline decltype(auto)
1218  operator*( const SparseMatrix<MT1,true>& lhs, const SparseMatrix<MT2,true>& rhs )
1219 {
1221 
1222  if( (~lhs).columns() != (~rhs).rows() ) {
1223  BLAZE_THROW_INVALID_ARGUMENT( "Matrix sizes do not match" );
1224  }
1225 
1227  return ReturnType( ~lhs, ~rhs );
1228 }
1229 //*************************************************************************************************
1230 
1231 
1232 
1233 
1234 //=================================================================================================
1235 //
1236 // ROWS SPECIALIZATIONS
1237 //
1238 //=================================================================================================
1239 
1240 //*************************************************************************************************
1242 template< typename MT1, typename MT2 >
1243 struct Rows< TSMatTSMatMultExpr<MT1,MT2> >
1244  : public Rows<MT1>
1245 {};
1247 //*************************************************************************************************
1248 
1249 
1250 
1251 
1252 //=================================================================================================
1253 //
1254 // COLUMNS SPECIALIZATIONS
1255 //
1256 //=================================================================================================
1257 
1258 //*************************************************************************************************
1260 template< typename MT1, typename MT2 >
1261 struct Columns< TSMatTSMatMultExpr<MT1,MT2> >
1262  : public Columns<MT2>
1263 {};
1265 //*************************************************************************************************
1266 
1267 
1268 
1269 
1270 //=================================================================================================
1271 //
1272 // ISLOWER SPECIALIZATIONS
1273 //
1274 //=================================================================================================
1275 
1276 //*************************************************************************************************
1278 template< typename MT1, typename MT2 >
1279 struct IsLower< TSMatTSMatMultExpr<MT1,MT2> >
1280  : public BoolConstant< And< IsLower<MT1>, IsLower<MT2> >::value >
1281 {};
1283 //*************************************************************************************************
1284 
1285 
1286 
1287 
1288 //=================================================================================================
1289 //
1290 // ISUNILOWER SPECIALIZATIONS
1291 //
1292 //=================================================================================================
1293 
1294 //*************************************************************************************************
1296 template< typename MT1, typename MT2 >
1297 struct IsUniLower< TSMatTSMatMultExpr<MT1,MT2> >
1298  : public BoolConstant< And< IsUniLower<MT1>, IsUniLower<MT2> >::value >
1299 {};
1301 //*************************************************************************************************
1302 
1303 
1304 
1305 
1306 //=================================================================================================
1307 //
1308 // ISSTRICTLYLOWER SPECIALIZATIONS
1309 //
1310 //=================================================================================================
1311 
1312 //*************************************************************************************************
1314 template< typename MT1, typename MT2 >
1315 struct IsStrictlyLower< TSMatTSMatMultExpr<MT1,MT2> >
1316  : public BoolConstant< Or< And< IsStrictlyLower<MT1>, IsLower<MT2> >
1317  , And< IsStrictlyLower<MT2>, IsLower<MT1> > >::value >
1318 {};
1320 //*************************************************************************************************
1321 
1322 
1323 
1324 
1325 //=================================================================================================
1326 //
1327 // ISUPPER SPECIALIZATIONS
1328 //
1329 //=================================================================================================
1330 
1331 //*************************************************************************************************
1333 template< typename MT1, typename MT2 >
1334 struct IsUpper< TSMatTSMatMultExpr<MT1,MT2> >
1335  : public BoolConstant< And< IsUpper<MT1>, IsUpper<MT2> >::value >
1336 {};
1338 //*************************************************************************************************
1339 
1340 
1341 
1342 
1343 //=================================================================================================
1344 //
1345 // ISUNIUPPER SPECIALIZATIONS
1346 //
1347 //=================================================================================================
1348 
1349 //*************************************************************************************************
1351 template< typename MT1, typename MT2 >
1352 struct IsUniUpper< TSMatTSMatMultExpr<MT1,MT2> >
1353  : public BoolConstant< And< IsUniUpper<MT1>, IsUniUpper<MT2> >::value >
1354 {};
1356 //*************************************************************************************************
1357 
1358 
1359 
1360 
1361 //=================================================================================================
1362 //
1363 // ISSTRICTLYUPPER SPECIALIZATIONS
1364 //
1365 //=================================================================================================
1366 
1367 //*************************************************************************************************
1369 template< typename MT1, typename MT2 >
1370 struct IsStrictlyUpper< TSMatTSMatMultExpr<MT1,MT2> >
1371  : public BoolConstant< Or< And< IsStrictlyUpper<MT1>, IsUpper<MT2> >
1372  , And< IsStrictlyUpper<MT2>, IsUpper<MT1> > >::value >
1373 {};
1375 //*************************************************************************************************
1376 
1377 } // namespace blaze
1378 
1379 #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
Header file for auxiliary alias declarations.
Headerfile for the generic min algorithm.
size_t rows() const noexcept
Returns the current number of rows of the matrix.
Definition: TSMatTSMatMultExpr.h:271
Header file for the Rows type trait.
Header file for the UNUSED_PARAMETER function template.
TSMatTSMatMultExpr(const MT1 &lhs, const MT2 &rhs) noexcept
Constructor for the TSMatTSMatMultExpr class.
Definition: TSMatTSMatMultExpr.h:192
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
const ElementType ReturnType
Return type for expression template evaluations.
Definition: TSMatTSMatMultExpr.h:170
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
If_< IsExpression< MT1 >, const MT1, const MT1 &> LeftOperand
Composite type of the left-hand side sparse matrix expression.
Definition: TSMatTSMatMultExpr.h:174
void reset(const DiagonalProxy< MT > &proxy)
Resetting the represented element to the default initial values.
Definition: DiagonalProxy.h:560
LeftOperand leftOperand() const noexcept
Returns the left-hand side transpose sparse matrix operand.
Definition: TSMatTSMatMultExpr.h:313
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
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
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
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
bool canSMPAssign() const noexcept
Returns whether the expression can be used in SMP assignments.
Definition: TSMatTSMatMultExpr.h:357
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.
MultTrait_< RT1, RT2 > ResultType
Result type for expression template evaluations.
Definition: TSMatTSMatMultExpr.h:166
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.
ResultType_< MT1 > RT1
Result type of the left-hand side sparse matrix expression.
Definition: TSMatTSMatMultExpr.h:117
Header file for the multiplication trait.
Header file for the IsStrictlyUpper type trait.
Header file for the IsSymmetric type trait.
constexpr size_t nonZeros() const noexcept
Returns the number of non-zero elements in the sparse matrix.
Definition: TSMatTSMatMultExpr.h:291
Namespace of the Blaze C++ math library.
Definition: Blaze.h:57
Header file for the If class template.
size_t columns() const noexcept
Returns the current number of columns of the matrix.
Definition: TSMatTSMatMultExpr.h:281
Compile time check for row-major matrix types.This type trait tests whether or not the given template...
Definition: IsRowMajorMatrix.h:110
#define BLAZE_CONSTRAINT_MUST_BE_COLUMN_MAJOR_MATRIX_TYPE(T)
Constraint on the data type.In case the given data type T is not a column-major dense or sparse matri...
Definition: ColumnMajorMatrix.h:61
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.
ElementType_< ResultType > ElementType
Resulting element type.
Definition: TSMatTSMatMultExpr.h:169
Numerical infinity for built-in data types.
RightOperand rhs_
Right-hand side sparse matrix of the multiplication expression.
Definition: TSMatTSMatMultExpr.h:365
typename T::ElementType ElementType_
Alias declaration for nested ElementType type definitions.The ElementType_ alias declaration provides...
Definition: Aliases.h:163
Expression object for transpose sparse matrix-transpose sparse matrix multiplications.The TSMatTSMatMultExpr class represents the compile time expression for multiplications between two column-major sparse matrices.
Definition: Forward.h:170
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
LeftOperand lhs_
Left-hand side sparse matrix of the multiplication expression.
Definition: TSMatTSMatMultExpr.h:364
ReturnType at(size_t i, size_t j) const
Checked access to the matrix elements.
Definition: TSMatTSMatMultExpr.h:255
OppositeType_< ResultType > OppositeType
Result type with opposite storage order for expression template evaluations.
Definition: TSMatTSMatMultExpr.h:167
Header file for the IsTriangular type trait.
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.
ResultType_< MT2 > RT2
Result type of the right-hand side sparse matrix expression.
Definition: TSMatTSMatMultExpr.h:118
#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
Compile time check for lower unitriangular matrices.This type trait tests whether or not the given te...
Definition: IsUniLower.h:86
bool canAlias(const T *alias) const noexcept
Returns whether the expression can alias with the given address alias.
Definition: TSMatTSMatMultExpr.h:335
size_t nonZeros(size_t i) const noexcept
Returns the number of non-zero elements in the specified row.
Definition: TSMatTSMatMultExpr.h:302
Compile time check for resizable data types.This type trait tests whether the given data type is a re...
Definition: IsResizable.h:75
#define BLAZE_CONSTRAINT_MUST_NOT_BE_SYMMETRIC_MATRIX_TYPE(T)
Constraint on the data type.In case the given data type T is a symmetric matrix type, a compilation error is created.
Definition: Symmetric.h:79
Header file for run time assertion macros.
Utility type for generic codes.
CompositeType_< MT1 > CT1
Composite type of the left-hand side sparse matrix expression.
Definition: TSMatTSMatMultExpr.h:119
RightOperand rightOperand() const noexcept
Returns the right-hand side transpose sparse matrix operand.
Definition: TSMatTSMatMultExpr.h:323
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
bool isAliased(const T *alias) const noexcept
Returns whether the expression is aliased with the given address alias.
Definition: TSMatTSMatMultExpr.h:347
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
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.
Constraints on the storage order of matrix types.
decltype(auto) serial(const DenseMatrix< MT, SO > &dm)
Forces the serial evaluation of the given dense matrix expression dm.
Definition: DMatSerialExpr.h:819
#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
CompositeType_< MT2 > CT2
Composite type of the right-hand side sparse matrix expression.
Definition: TSMatTSMatMultExpr.h:120
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
const ResultType CompositeType
Data type for composite expression templates.
Definition: TSMatTSMatMultExpr.h:171
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
Header file for the IsRowMajorMatrix type trait.
Header file for the IsComputation type trait class.
Header file for the IsBuiltin type trait.
TransposeType_< ResultType > TransposeType
Transpose type for expression template evaluations.
Definition: TSMatTSMatMultExpr.h:168
ReturnType operator()(size_t i, size_t j) const
2D-access to the matrix elements.
Definition: TSMatTSMatMultExpr.h:207
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
If_< IsExpression< MT2 >, const MT2, const MT2 &> RightOperand
Composite type of the right-hand side sparse matrix expression.
Definition: TSMatTSMatMultExpr.h:177
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
Constraint on the data type.
Header file for the IsResizable type trait.
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.