TSMatTSMatSubExpr.h
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1 //=================================================================================================
33 //=================================================================================================
34 
35 #ifndef _BLAZE_MATH_EXPRESSIONS_TSMATTSMATSUBEXPR_H_
36 #define _BLAZE_MATH_EXPRESSIONS_TSMATTSMATSUBEXPR_H_
37 
38 
39 //*************************************************************************************************
40 // Includes
41 //*************************************************************************************************
42 
43 #include <blaze/math/Aliases.h>
50 #include <blaze/math/Exception.h>
72 #include <blaze/util/Assert.h>
73 #include <blaze/util/DisableIf.h>
74 #include <blaze/util/EnableIf.h>
76 #include <blaze/util/mpl/And.h>
77 #include <blaze/util/mpl/If.h>
78 #include <blaze/util/mpl/Maximum.h>
79 #include <blaze/util/Types.h>
81 
82 
83 namespace blaze {
84 
85 //=================================================================================================
86 //
87 // CLASS TSMATTSMATSUBEXPR
88 //
89 //=================================================================================================
90 
91 //*************************************************************************************************
98 template< typename MT1 // Type of the left-hand side sparse matrix
99  , typename MT2 > // Type of the right-hand side sparse matrix
100 class TSMatTSMatSubExpr
101  : public MatMatSubExpr< SparseMatrix< TSMatTSMatSubExpr<MT1,MT2>, true > >
102  , private Computation
103 {
104  private:
105  //**Type definitions****************************************************************************
112  //**********************************************************************************************
113 
114  //**Return type evaluation**********************************************************************
116 
121  enum : bool { returnExpr = !IsTemporary<RN1>::value && !IsTemporary<RN2>::value };
122 
125  //**********************************************************************************************
126 
127  //**Serial evaluation strategy******************************************************************
129 
134  template< typename T1, typename T2, typename T3 >
135  struct UseSymmetricKernel {
137  enum : bool { value = IsSymmetric<T2>::value && IsSymmetric<T3>::value };
138  };
140  //**********************************************************************************************
141 
142  //**Parallel evaluation strategy****************************************************************
144 
149  template< typename MT >
150  struct UseSMPAssign {
151  enum : bool { value = MT::smpAssignable };
152  };
154  //**********************************************************************************************
155 
156  public:
157  //**Type definitions****************************************************************************
163 
166 
168  using CompositeType = const ResultType;
169 
171  using LeftOperand = If_< IsExpression<MT1>, const MT1, const MT1& >;
172 
174  using RightOperand = If_< IsExpression<MT2>, const MT2, const MT2& >;
175  //**********************************************************************************************
176 
177  //**Compilation flags***************************************************************************
179  enum : bool { smpAssignable = false };
180  //**********************************************************************************************
181 
182  //**Constructor*********************************************************************************
188  explicit inline TSMatTSMatSubExpr( const MT1& lhs, const MT2& rhs ) noexcept
189  : lhs_( lhs ) // Left-hand side sparse matrix of the subtraction expression
190  , rhs_( rhs ) // Right-hand side sparse matrix of the subtraction expression
191  {
192  BLAZE_INTERNAL_ASSERT( lhs.rows() == rhs.rows() , "Invalid number of rows" );
193  BLAZE_INTERNAL_ASSERT( lhs.columns() == rhs.columns(), "Invalid number of columns" );
194  }
195  //**********************************************************************************************
196 
197  //**Access operator*****************************************************************************
204  inline ReturnType operator()( size_t i, size_t j ) const {
205  BLAZE_INTERNAL_ASSERT( i < lhs_.rows() , "Invalid row access index" );
206  BLAZE_INTERNAL_ASSERT( j < lhs_.columns(), "Invalid column access index" );
207  return lhs_(i,j) - rhs_(i,j);
208  }
209  //**********************************************************************************************
210 
211  //**At function*********************************************************************************
219  inline ReturnType at( size_t i, size_t j ) const {
220  if( i >= lhs_.rows() ) {
221  BLAZE_THROW_OUT_OF_RANGE( "Invalid row access index" );
222  }
223  if( j >= lhs_.columns() ) {
224  BLAZE_THROW_OUT_OF_RANGE( "Invalid column access index" );
225  }
226  return (*this)(i,j);
227  }
228  //**********************************************************************************************
229 
230  //**Rows function*******************************************************************************
235  inline size_t rows() const noexcept {
236  return lhs_.rows();
237  }
238  //**********************************************************************************************
239 
240  //**Columns function****************************************************************************
245  inline size_t columns() const noexcept {
246  return lhs_.columns();
247  }
248  //**********************************************************************************************
249 
250  //**NonZeros function***************************************************************************
255  inline size_t nonZeros() const {
256  return lhs_.nonZeros() + rhs_.nonZeros();
257  }
258  //**********************************************************************************************
259 
260  //**NonZeros function***************************************************************************
266  inline size_t nonZeros( size_t i ) const {
267  return lhs_.nonZeros(i) + rhs_.nonZeros(i);
268  }
269  //**********************************************************************************************
270 
271  //**Left operand access*************************************************************************
276  inline LeftOperand leftOperand() const noexcept {
277  return lhs_;
278  }
279  //**********************************************************************************************
280 
281  //**Right operand access************************************************************************
286  inline RightOperand rightOperand() const noexcept {
287  return rhs_;
288  }
289  //**********************************************************************************************
290 
291  //**********************************************************************************************
297  template< typename T >
298  inline bool canAlias( const T* alias ) const noexcept {
299  return ( lhs_.canAlias( alias ) || rhs_.canAlias( alias ) );
300  }
301  //**********************************************************************************************
302 
303  //**********************************************************************************************
309  template< typename T >
310  inline bool isAliased( const T* alias ) const noexcept {
311  return ( lhs_.isAliased( alias ) || rhs_.isAliased( alias ) );
312  }
313  //**********************************************************************************************
314 
315  private:
316  //**Member variables****************************************************************************
319  //**********************************************************************************************
320 
321  //**Assignment to dense matrices****************************************************************
334  template< typename MT // Type of the target dense matrix
335  , bool SO > // Storage order of the target dense matrix
336  friend inline void assign( DenseMatrix<MT,SO>& lhs, const TSMatTSMatSubExpr& rhs )
337  {
339 
340  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
341  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
342 
343  using RightIterator = ConstIterator_< RemoveReference_<CT2> >;
344 
345  assign( ~lhs, rhs.lhs_ );
346 
347  if( !IsResizable< ElementType_<MT> >::value ) {
348  subAssign( ~lhs, rhs.rhs_ );
349  }
350  else
351  {
352  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
353 
354  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
355  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
356  BLAZE_INTERNAL_ASSERT( B.rows() == (~lhs).rows() , "Invalid number of rows" );
357  BLAZE_INTERNAL_ASSERT( B.columns() == (~lhs).columns() , "Invalid number of columns" );
358 
359  for( size_t j=0UL; j<(~lhs).columns(); ++j ) {
360  const RightIterator end( B.end(j) );
361  for( RightIterator element=B.begin(j); element!=end; ++element ) {
362  if( isDefault( (~lhs)(element->index(),j) ) )
363  (~lhs)(element->index(),j) = -element->value();
364  else
365  (~lhs)(element->index(),j) -= element->value();
366  }
367  }
368  }
369  }
371  //**********************************************************************************************
372 
373  //**Assignment to row-major sparse matrices*****************************************************
386  template< typename MT > // Type of the target sparse matrix
388  assign( SparseMatrix<MT,false>& lhs, const TSMatTSMatSubExpr& rhs )
389  {
391 
393 
394  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
395  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
396 
397  using LeftIterator = ConstIterator_< RemoveReference_<CT1> >;
398  using RightIterator = ConstIterator_< RemoveReference_<CT2> >;
399 
400  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
401  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
402 
403  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
404  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
405  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
406  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
407  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
408  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
409 
410  const size_t m( rhs.rows() );
411  const size_t n( rhs.columns() );
412 
413  // Counting the number of elements per column
414  std::vector<size_t> nonzeros( m, 0UL );
415  for( size_t j=0UL; j<n; ++j )
416  {
417  const LeftIterator lend( A.end(j) );
418  const RightIterator rend( B.end(j) );
419 
420  LeftIterator l( A.begin(j) );
421  RightIterator r( B.begin(j) );
422 
423  while( l != lend && r != rend )
424  {
425  if( l->index() < r->index() ) {
426  ++nonzeros[l->index()];
427  ++l;
428  }
429  else if( l->index() > r->index() ) {
430  ++nonzeros[r->index()];
431  ++r;
432  }
433  else {
434  ++nonzeros[l->index()];
435  ++l;
436  ++r;
437  }
438  }
439 
440  while( l != lend ) {
441  ++nonzeros[l->index()];
442  ++l;
443  }
444 
445  while( r != rend ) {
446  ++nonzeros[r->index()];
447  ++r;
448  }
449  }
450 
451  // Resizing the left-hand side sparse matrix
452  for( size_t i=0UL; i<m; ++i ) {
453  (~lhs).reserve( i, nonzeros[i] );
454  }
455 
456  // Performing the matrix subtraction
457  for( size_t j=0UL; j<n; ++j )
458  {
459  const LeftIterator lend( A.end(j) );
460  const RightIterator rend( B.end(j) );
461 
462  LeftIterator l( A.begin(j) );
463  RightIterator r( B.begin(j) );
464 
465  while( l != lend && r != rend )
466  {
467  if( l->index() < r->index() ) {
468  (~lhs).append( l->index(), j, l->value() );
469  ++l;
470  }
471  else if( l->index() > r->index() ) {
472  (~lhs).append( r->index(), j, -r->value() );
473  ++r;
474  }
475  else {
476  (~lhs).append( l->index(), j, l->value() - r->value() );
477  ++l;
478  ++r;
479  }
480  }
481 
482  while( l != lend ) {
483  (~lhs).append( l->index(), j, l->value() );
484  ++l;
485  }
486 
487  while( r != rend ) {
488  (~lhs).append( r->index(), j, -r->value() );
489  ++r;
490  }
491  }
492  }
494  //**********************************************************************************************
495 
496  //**Assignment to row-major sparse matrices*****************************************************
509  template< typename MT > // Type of the target sparse matrix
511  assign( SparseMatrix<MT,false>& lhs, const TSMatTSMatSubExpr& rhs )
512  {
514 
516 
517  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
518  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
519 
520  assign( ~lhs, trans( rhs.lhs_ ) - trans( rhs.rhs_ ) );
521  }
523  //**********************************************************************************************
524 
525  //**Assignment to column-major sparse matrices**************************************************
538  template< typename MT > // Type of the target sparse matrix
539  friend inline void assign( SparseMatrix<MT,true>& lhs, const TSMatTSMatSubExpr& rhs )
540  {
542 
543  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
544  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
545 
546  using LeftIterator = ConstIterator_< RemoveReference_<CT1> >;
547  using RightIterator = ConstIterator_< RemoveReference_<CT2> >;
548 
549  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
550  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
551 
552  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
553  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
554  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
555  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
556  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
557  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
558 
559  // Final memory allocation (based on the evaluated operands)
560  (~lhs).reserve( A.nonZeros() + B.nonZeros() );
561 
562  // Performing the matrix subtraction
563  for( size_t j=0UL; j<(~lhs).columns(); ++j )
564  {
565  const LeftIterator lend( A.end(j) );
566  const RightIterator rend( B.end(j) );
567 
568  LeftIterator l( A.begin(j) );
569  RightIterator r( B.begin(j) );
570 
571  while( l != lend && r != rend )
572  {
573  if( l->index() < r->index() ) {
574  (~lhs).append( l->index(), j, l->value() );
575  ++l;
576  }
577  else if( l->index() > r->index() ) {
578  (~lhs).append( r->index(), j, -r->value() );
579  ++r;
580  }
581  else {
582  (~lhs).append( l->index(), j, l->value() - r->value() );
583  ++l;
584  ++r;
585  }
586  }
587 
588  while( l != lend ) {
589  (~lhs).append( l->index(), j, l->value() );
590  ++l;
591  }
592 
593  while( r != rend ) {
594  (~lhs).append( r->index(), j, -r->value() );
595  ++r;
596  }
597 
598  (~lhs).finalize( j );
599  }
600  }
602  //**********************************************************************************************
603 
604  //**Addition assignment to dense matrices*******************************************************
617  template< typename MT // Type of the target dense matrix
618  , bool SO > // Storage order of the target dense matrix
619  friend inline void addAssign( DenseMatrix<MT,SO>& lhs, const TSMatTSMatSubExpr& rhs )
620  {
622 
623  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
624  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
625 
626  addAssign( ~lhs, rhs.lhs_ );
627  subAssign( ~lhs, rhs.rhs_ );
628  }
630  //**********************************************************************************************
631 
632  //**Addition assignment to sparse matrices******************************************************
633  // No special implementation for the addition assignment to sparse matrices.
634  //**********************************************************************************************
635 
636  //**Subtraction assignment to dense matrices****************************************************
649  template< typename MT // Type of the target dense matrix
650  , bool SO > // Storage order of the target dense matrix
651  friend inline void subAssign( DenseMatrix<MT,SO>& lhs, const TSMatTSMatSubExpr& rhs )
652  {
654 
655  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
656  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
657 
658  subAssign( ~lhs, rhs.lhs_ );
659  addAssign( ~lhs, rhs.rhs_ );
660  }
662  //**********************************************************************************************
663 
664  //**Subtraction assignment to sparse matrices***************************************************
665  // No special implementation for the subtraction assignment to sparse matrices.
666  //**********************************************************************************************
667 
668  //**Schur product assignment to dense matrices**************************************************
681  template< typename MT // Type of the target dense matrix
682  , bool SO > // Storage order of the target dense matrix
683  friend inline void schurAssign( DenseMatrix<MT,SO>& lhs, const TSMatTSMatSubExpr& rhs )
684  {
686 
690 
691  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
692  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
693 
694  const ResultType tmp( serial( rhs ) );
695  schurAssign( ~lhs, tmp );
696  }
698  //**********************************************************************************************
699 
700  //**Schur product assignment to sparse matrices*************************************************
701  // No special implementation for the Schur product assignment to sparse matrices.
702  //**********************************************************************************************
703 
704  //**Multiplication assignment to dense matrices*************************************************
705  // No special implementation for the multiplication assignment to dense matrices.
706  //**********************************************************************************************
707 
708  //**Multiplication assignment to sparse matrices************************************************
709  // No special implementation for the multiplication assignment to sparse matrices.
710  //**********************************************************************************************
711 
712  //**SMP assignment to dense matrices************************************************************
713  // No special implementation for the SMP assignment to dense matrices.
714  //**********************************************************************************************
715 
716  //**SMP assignment to sparse matrices***********************************************************
717  // No special implementation for the SMP assignment to sparse matrices.
718  //**********************************************************************************************
719 
720  //**SMP addition assignment to dense matrices***************************************************
735  template< typename MT // Type of the target dense matrix
736  , bool SO > // Storage order of the target dense matrix
737  friend inline EnableIf_< UseSMPAssign<MT> >
739  {
741 
742  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
743  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
744 
745  smpAddAssign( ~lhs, rhs.lhs_ );
746  smpSubAssign( ~lhs, rhs.rhs_ );
747  }
749  //**********************************************************************************************
750 
751  //**SMP addition assignment to sparse matrices**************************************************
752  // No special implementation for the SMP addition assignment to sparse matrices.
753  //**********************************************************************************************
754 
755  //**SMP subtraction assignment to dense matrices************************************************
770  template< typename MT // Type of the target dense matrix
771  , bool SO > // Storage order of the target dense matrix
772  friend inline EnableIf_< UseSMPAssign<MT> >
774  {
776 
777  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
778  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
779 
780  smpSubAssign( ~lhs, rhs.lhs_ );
781  smpAddAssign( ~lhs, rhs.rhs_ );
782  }
784  //**********************************************************************************************
785 
786  //**SMP subtraction assignment to sparse matrices***********************************************
787  // No special implementation for the SMP subtraction assignment to sparse matrices.
788  //**********************************************************************************************
789 
790  //**SMP Schur product assignment to dense matrices**********************************************
805  template< typename MT // Type of the target dense matrix
806  , bool SO > // Storage order of the target dense matrix
807  friend inline EnableIf_< UseSMPAssign<MT> >
809  {
811 
815 
816  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
817  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
818 
819  const ResultType tmp( rhs );
820  smpSchurAssign( ~lhs, tmp );
821  }
823  //**********************************************************************************************
824 
825  //**SMP Schur product assignment to sparse matrices*********************************************
826  // No special implementation for the SMP Schur product assignment to sparse matrices.
827  //**********************************************************************************************
828 
829  //**SMP multiplication assignment to dense matrices*********************************************
830  // No special implementation for the SMP multiplication assignment to dense matrices.
831  //**********************************************************************************************
832 
833  //**SMP multiplication assignment to sparse matrices********************************************
834  // No special implementation for the SMP multiplication assignment to sparse matrices.
835  //**********************************************************************************************
836 
837  //**Compile time checks*************************************************************************
845  //**********************************************************************************************
846 };
847 //*************************************************************************************************
848 
849 
850 
851 
852 //=================================================================================================
853 //
854 // GLOBAL BINARY ARITHMETIC OPERATORS
855 //
856 //=================================================================================================
857 
858 //*************************************************************************************************
885 template< typename MT1 // Type of the left-hand side sparse matrix
886  , typename MT2 > // Type of the right-hand side sparse matrix
887 inline decltype(auto)
888  operator-( const SparseMatrix<MT1,true>& lhs, const SparseMatrix<MT2,true>& rhs )
889 {
891 
892  if( (~lhs).rows() != (~rhs).rows() || (~lhs).columns() != (~rhs).columns() ) {
893  BLAZE_THROW_INVALID_ARGUMENT( "Matrix sizes do not match" );
894  }
895 
897  return ReturnType( ~lhs, ~rhs );
898 }
899 //*************************************************************************************************
900 
901 
902 
903 
904 //=================================================================================================
905 //
906 // SIZE SPECIALIZATIONS
907 //
908 //=================================================================================================
909 
910 //*************************************************************************************************
912 template< typename MT1, typename MT2 >
913 struct Size< TSMatTSMatSubExpr<MT1,MT2>, 0UL >
914  : public Maximum< Size<MT1,0UL>, Size<MT2,0UL> >
915 {};
916 
917 template< typename MT1, typename MT2 >
918 struct Size< TSMatTSMatSubExpr<MT1,MT2>, 1UL >
919  : public Maximum< Size<MT1,1UL>, Size<MT2,1UL> >
920 {};
922 //*************************************************************************************************
923 
924 
925 
926 
927 //=================================================================================================
928 //
929 // ISSYMMETRIC SPECIALIZATIONS
930 //
931 //=================================================================================================
932 
933 //*************************************************************************************************
935 template< typename MT1, typename MT2 >
936 struct IsSymmetric< TSMatTSMatSubExpr<MT1,MT2> >
937  : public And< IsSymmetric<MT1>, IsSymmetric<MT2> >
938 {};
940 //*************************************************************************************************
941 
942 
943 
944 
945 //=================================================================================================
946 //
947 // ISHERMITIAN SPECIALIZATIONS
948 //
949 //=================================================================================================
950 
951 //*************************************************************************************************
953 template< typename MT1, typename MT2 >
954 struct IsHermitian< TSMatTSMatSubExpr<MT1,MT2> >
955  : public And< IsHermitian<MT1>, IsHermitian<MT2> >
956 {};
958 //*************************************************************************************************
959 
960 
961 
962 
963 //=================================================================================================
964 //
965 // ISLOWER SPECIALIZATIONS
966 //
967 //=================================================================================================
968 
969 //*************************************************************************************************
971 template< typename MT1, typename MT2 >
972 struct IsLower< TSMatTSMatSubExpr<MT1,MT2> >
973  : public And< IsLower<MT1>, IsLower<MT2> >
974 {};
976 //*************************************************************************************************
977 
978 
979 
980 
981 //=================================================================================================
982 //
983 // ISUNILOWER SPECIALIZATIONS
984 //
985 //=================================================================================================
986 
987 //*************************************************************************************************
989 template< typename MT1, typename MT2 >
990 struct IsUniLower< TSMatTSMatSubExpr<MT1,MT2> >
991  : public And< IsUniLower<MT1>, IsStrictlyLower<MT2> >
992 {};
994 //*************************************************************************************************
995 
996 
997 
998 
999 //=================================================================================================
1000 //
1001 // ISSTRICTLYLOWER SPECIALIZATIONS
1002 //
1003 //=================================================================================================
1004 
1005 //*************************************************************************************************
1007 template< typename MT1, typename MT2 >
1008 struct IsStrictlyLower< TSMatTSMatSubExpr<MT1,MT2> >
1009  : public And< IsStrictlyLower<MT1>, IsStrictlyLower<MT2> >
1010 {};
1012 //*************************************************************************************************
1013 
1014 
1015 
1016 
1017 //=================================================================================================
1018 //
1019 // ISUPPER SPECIALIZATIONS
1020 //
1021 //=================================================================================================
1022 
1023 //*************************************************************************************************
1025 template< typename MT1, typename MT2 >
1026 struct IsUpper< TSMatTSMatSubExpr<MT1,MT2> >
1027  : public And< IsUpper<MT1>, IsUpper<MT2> >
1028 {};
1030 //*************************************************************************************************
1031 
1032 
1033 
1034 
1035 //=================================================================================================
1036 //
1037 // ISUNIUPPER SPECIALIZATIONS
1038 //
1039 //=================================================================================================
1040 
1041 //*************************************************************************************************
1043 template< typename MT1, typename MT2 >
1044 struct IsUniUpper< TSMatTSMatSubExpr<MT1,MT2> >
1045  : public And< IsUniUpper<MT1>, IsStrictlyUpper<MT2> >
1046 {};
1048 //*************************************************************************************************
1049 
1050 
1051 
1052 
1053 //=================================================================================================
1054 //
1055 // ISSTRICTLYUPPER SPECIALIZATIONS
1056 //
1057 //=================================================================================================
1058 
1059 //*************************************************************************************************
1061 template< typename MT1, typename MT2 >
1062 struct IsStrictlyUpper< TSMatTSMatSubExpr<MT1,MT2> >
1063  : public And< IsStrictlyUpper<MT1>, IsStrictlyUpper<MT2> >
1064 {};
1066 //*************************************************************************************************
1067 
1068 } // namespace blaze
1069 
1070 #endif
Constraint on the data type.
#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.
size_t nonZeros(size_t i) const
Returns the number of non-zero elements in the specified row.
Definition: TSMatTSMatSubExpr.h:266
Compile time check whether the given type is a temporary vector or matrix type.This type trait class ...
Definition: IsTemporary.h:69
Header file for the IsUniUpper type trait.
EnableIf_< IsDenseMatrix< MT1 > > smpSchurAssign(Matrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs)
Default implementation of the SMP Schur product assignment of a matrix to dense matrix.
Definition: DenseMatrix.h:196
Header file for the subtraction trait.
Header file for basic type definitions.
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.
SubExprTrait_< RN1, RN2 > ExprReturnType
Expression return type for the subscript operator.
Definition: TSMatTSMatSubExpr.h:124
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.
Compile time value evaluation.The Maximum alias declaration selects the larger of the two given templ...
Definition: Maximum.h:73
Compile time check for lower triangular matrices.This type trait tests whether or not the given templ...
Definition: IsLower.h:87
ReturnType at(size_t i, size_t j) const
Checked access to the matrix elements.
Definition: TSMatTSMatSubExpr.h:219
Header file for the Computation base class.
ReturnType operator()(size_t i, size_t j) const
2D-access to the matrix elements.
Definition: TSMatTSMatSubExpr.h:204
Compile time check for upper triangular matrices.This type trait tests whether or not the given templ...
Definition: IsUpper.h:87
Constraints on the storage order of matrix types.
bool isAliased(const T *alias) const noexcept
Returns whether the expression is aliased with the given address alias.
Definition: TSMatTSMatSubExpr.h:310
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
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
TransposeType_< ResultType > TransposeType
Transpose type for expression template evaluations.
Definition: TSMatTSMatSubExpr.h:161
Base class for dense matrices.The DenseMatrix class is a base class for all dense matrix classes...
Definition: DenseMatrix.h:80
Base class for sparse matrices.The SparseMatrix class is a base class for all sparse matrix classes...
Definition: Forward.h:129
typename IfTrue< Condition, T1, T2 >::Type IfTrue_
Auxiliary alias declaration for the IfTrue class template.The IfTrue_ alias declaration provides a co...
Definition: If.h:109
LeftOperand lhs_
Left-hand side sparse matrix of the subtraction expression.
Definition: TSMatTSMatSubExpr.h:317
typename T::ReturnType ReturnType_
Alias declaration for nested ReturnType type definitions.The ReturnType_ alias declaration provides a...
Definition: Aliases.h:363
size_t rows() const noexcept
Returns the current number of rows of the matrix.
Definition: TSMatTSMatSubExpr.h:235
Header file for the SparseMatrix base class.
CompositeType_< MT1 > CT1
Composite type of the left-hand side sparse matrix expression.
Definition: TSMatTSMatSubExpr.h:110
typename SubExprTrait< T1, T2 >::Type SubExprTrait_
Auxiliary alias declaration for the SubExprTrait class template.The SubExprTrait_ alias declaration p...
Definition: SubExprTrait.h:112
Constraint on the data type.
Header file for the Maximum class template.
typename T::CompositeType CompositeType_
Alias declaration for nested CompositeType type definitions.The CompositeType_ alias declaration prov...
Definition: Aliases.h:83
Compile time check for upper unitriangular matrices.This type trait tests whether or not the given te...
Definition: IsUniUpper.h:86
const ResultType CompositeType
Data type for composite expression templates.
Definition: TSMatTSMatSubExpr.h:168
Header file for the DisableIf class template.
Header file for the IsTemporary type trait class.
Header file for the IsStrictlyUpper type trait.
Header file for the IsSymmetric type trait.
ReturnType_< MT1 > RN1
Return type of the left-hand side sparse matrix expression.
Definition: TSMatTSMatSubExpr.h:108
Namespace of the Blaze C++ math library.
Definition: Blaze.h:58
Header file for the If class template.
#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
TSMatTSMatSubExpr(const MT1 &lhs, const MT2 &rhs) noexcept
Constructor for the TSMatTSMatSubExpr class.
Definition: TSMatTSMatSubExpr.h:188
#define BLAZE_THROW_OUT_OF_RANGE(MESSAGE)
Macro for the emission of a std::out_of_range exception.This macro encapsulates the default way of Bl...
Definition: Exception.h:331
const IfTrue_< returnExpr, ExprReturnType, ElementType > ReturnType
Return type for expression template evaluations.
Definition: TSMatTSMatSubExpr.h:165
SubTrait_< RT1, RT2 > ResultType
Result type for expression template evaluations.
Definition: TSMatTSMatSubExpr.h:159
typename T::ElementType ElementType_
Alias declaration for nested ElementType type definitions.The ElementType_ alias declaration provides...
Definition: Aliases.h:163
Header file for the MatMatSubExpr base class.
Header file for the IsLower type trait.
ElementType_< ResultType > ElementType
Resulting element type.
Definition: TSMatTSMatSubExpr.h:162
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.
RightOperand rhs_
Right-hand side sparse matrix of the subtraction expression.
Definition: TSMatTSMatSubExpr.h:318
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:430
Constraint on the data type.
Header file for all forward declarations for expression class templates.
Header file for the EnableIf class template.
Header file for the IsStrictlyLower type trait.
Compile time check for lower unitriangular matrices.This type trait tests whether or not the given te...
Definition: IsUniLower.h:86
Compile time check for resizable data types.This type trait tests whether the given data type is a re...
Definition: IsResizable.h:75
bool canAlias(const T *alias) const noexcept
Returns whether the expression can alias with the given address alias.
Definition: TSMatTSMatSubExpr.h:298
#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
ResultType_< MT2 > RT2
Result type of the right-hand side sparse matrix expression.
Definition: TSMatTSMatSubExpr.h:107
Header file for run time assertion macros.
Expression object for transpose sparse matrix-transpose sparse matrix subtractions.The TSMatTSMatSubExpr class represents the compile time expression for subtractions between two column-major sparse matrices.
Definition: Forward.h:172
If_< IsExpression< MT2 >, const MT2, const MT2 &> RightOperand
Composite type of the right-hand side sparse matrix expression.
Definition: TSMatTSMatSubExpr.h:174
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
ReturnType_< MT2 > RN2
Return type of the right-hand side sparse matrix expression.
Definition: TSMatTSMatSubExpr.h:109
#define BLAZE_FUNCTION_TRACE
Function trace macro.This macro can be used to reliably trace function calls. In case function tracin...
Definition: FunctionTrace.h:94
Header file for the isDefault shim.
Compile time check for Hermitian matrices.This type trait tests whether or not the given template par...
Definition: IsHermitian.h:85
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:816
OppositeType_< ResultType > OppositeType
Result type with opposite storage order for expression template evaluations.
Definition: TSMatTSMatSubExpr.h:160
#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
LeftOperand leftOperand() const noexcept
Returns the left-hand side transpose sparse matrix operand.
Definition: TSMatTSMatSubExpr.h:276
Header file for the RemoveReference type trait.
typename EnableIf< Condition, T >::Type EnableIf_
Auxiliary alias declaration for the EnableIf class template.The EnableIf_ alias declaration provides ...
Definition: EnableIf.h:224
typename T::OppositeType OppositeType_
Alias declaration for nested OppositeType type definitions.The OppositeType_ alias declaration provid...
Definition: Aliases.h:263
RightOperand rightOperand() const noexcept
Returns the right-hand side transpose sparse matrix operand.
Definition: TSMatTSMatSubExpr.h:286
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:3080
typename T::ConstIterator ConstIterator_
Alias declaration for nested ConstIterator type definitions.The ConstIterator_ alias declaration prov...
Definition: Aliases.h:103
size_t columns() const noexcept
Returns the current number of columns of the matrix.
Definition: TSMatTSMatSubExpr.h:245
decltype(auto) trans(const DenseMatrix< MT, SO > &dm)
Calculation of the transpose of the given dense matrix.
Definition: DMatTransExpr.h:789
CompositeType_< MT2 > CT2
Composite type of the right-hand side sparse matrix expression.
Definition: TSMatTSMatSubExpr.h:111
Header file for the IsComputation type trait class.
typename SubTrait< T1, T2 >::Type SubTrait_
Auxiliary alias declaration for the SubTrait class template.The SubTrait_ alias declaration provides ...
Definition: SubTrait.h:291
Compile time evaluation of the size of vectors and matrices.The Size type trait evaluates the size of...
Definition: Size.h:80
Compile time logical &#39;and&#39; evaluation.The And alias declaration performs at compile time a logical &#39;a...
Definition: And.h:76
#define BLAZE_CONSTRAINT_MUST_FORM_VALID_MATMATSUBEXPR(T1, T2)
Constraint on the data type.In case the given data types T1 and T2 do not form a valid matrix/matrix ...
Definition: MatMatSubExpr.h:107
bool isDefault(const DiagonalProxy< MT > &proxy)
Returns whether the represented element is in default state.
Definition: DiagonalProxy.h:628
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.
Header file for the IsHermitian type trait.
Header file for the IsResizable type trait.
Header file for the SubExprTrait class template.
If_< IsExpression< MT1 >, const MT1, const MT1 &> LeftOperand
Composite type of the left-hand side sparse matrix expression.
Definition: TSMatTSMatSubExpr.h:171
size_t nonZeros() const
Returns the number of non-zero elements in the sparse matrix.
Definition: TSMatTSMatSubExpr.h:255
Header file for the Size type trait.
#define BLAZE_INTERNAL_ASSERT(expr, msg)
Run time assertion macro for internal checks.In case of an invalid run time expression, the program execution is terminated. The BLAZE_INTERNAL_ASSERT macro can be disabled by setting the BLAZE_USER_ASSERTION flag to zero or by defining NDEBUG during the compilation.
Definition: Assert.h:101
#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
ResultType_< MT1 > RT1
Result type of the left-hand side sparse matrix expression.
Definition: TSMatTSMatSubExpr.h:106
Header file for the IsExpression type trait class.
Header file for the function trace functionality.