SMatSMatSubExpr.h
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1 //=================================================================================================
33 //=================================================================================================
34 
35 #ifndef _BLAZE_MATH_EXPRESSIONS_SMATSMATSUBEXPR_H_
36 #define _BLAZE_MATH_EXPRESSIONS_SMATSMATSUBEXPR_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 SMATSMATSUBEXPR
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 SMatSMatSubExpr
101  : public MatMatSubExpr< SparseMatrix< SMatSMatSubExpr<MT1,MT2>, false > >
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 SMatSMatSubExpr( 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****************************************************************
333  template< typename MT // Type of the target dense matrix
334  , bool SO > // Storage order of the target dense matrix
335  friend inline void assign( DenseMatrix<MT,SO>& lhs, const SMatSMatSubExpr& rhs )
336  {
338 
339  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
340  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
341 
342  using RightIterator = ConstIterator_< RemoveReference_<CT2> >;
343 
344  assign( ~lhs, rhs.lhs_ );
345 
346  if( !IsResizable< ElementType_<MT> >::value ) {
347  subAssign( ~lhs, rhs.rhs_ );
348  }
349  else
350  {
351  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
352 
353  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
354  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
355  BLAZE_INTERNAL_ASSERT( B.rows() == (~lhs).rows() , "Invalid number of rows" );
356  BLAZE_INTERNAL_ASSERT( B.columns() == (~lhs).columns() , "Invalid number of columns" );
357 
358  for( size_t i=0UL; i<(~lhs).rows(); ++i ) {
359  const RightIterator end( B.end(i) );
360  for( RightIterator element=B.begin(i); element!=end; ++element ) {
361  if( isDefault( (~lhs)(i,element->index()) ) )
362  (~lhs)(i,element->index()) = -element->value();
363  else
364  (~lhs)(i,element->index()) -= element->value();
365  }
366  }
367  }
368  }
370  //**********************************************************************************************
371 
372  //**Assignment to row-major sparse matrices*****************************************************
384  template< typename MT > // Type of the target sparse matrix
385  friend inline void assign( SparseMatrix<MT,false>& lhs, const SMatSMatSubExpr& rhs )
386  {
388 
389  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
390  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
391 
392  using LeftIterator = ConstIterator_< RemoveReference_<CT1> >;
393  using RightIterator = ConstIterator_< RemoveReference_<CT2> >;
394 
395  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
396  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
397 
398  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
399  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
400  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
401  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
402  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
403  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
404 
405  // Final memory allocation (based on the evaluated operands)
406  (~lhs).reserve( A.nonZeros() + B.nonZeros() );
407 
408  // Performing the matrix subtraction
409  for( size_t i=0UL; i<(~lhs).rows(); ++i )
410  {
411  const LeftIterator lend( A.end(i) );
412  const RightIterator rend( B.end(i) );
413 
414  LeftIterator l( A.begin(i) );
415  RightIterator r( B.begin(i) );
416 
417  while( l != lend && r != rend )
418  {
419  if( l->index() < r->index() ) {
420  (~lhs).append( i, l->index(), l->value() );
421  ++l;
422  }
423  else if( l->index() > r->index() ) {
424  (~lhs).append( i, r->index(), -r->value() );
425  ++r;
426  }
427  else {
428  (~lhs).append( i, l->index(), l->value() - r->value() );
429  ++l;
430  ++r;
431  }
432  }
433 
434  while( l != lend ) {
435  (~lhs).append( i, l->index(), l->value() );
436  ++l;
437  }
438 
439  while( r != rend ) {
440  (~lhs).append( i, r->index(), -r->value() );
441  ++r;
442  }
443 
444  (~lhs).finalize( i );
445  }
446  }
448  //**********************************************************************************************
449 
450  //**Assignment to column-major sparse matrices**************************************************
462  template< typename MT > // Type of the target sparse matrix
464  assign( SparseMatrix<MT,true>& lhs, const SMatSMatSubExpr& rhs )
465  {
467 
469 
470  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
471  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
472 
473  using LeftIterator = ConstIterator_< RemoveReference_<CT1> >;
474  using RightIterator = ConstIterator_< RemoveReference_<CT2> >;
475 
476  CT1 A( serial( rhs.lhs_ ) ); // Evaluation of the left-hand side sparse matrix operand
477  CT2 B( serial( rhs.rhs_ ) ); // Evaluation of the right-hand side sparse matrix operand
478 
479  BLAZE_INTERNAL_ASSERT( A.rows() == rhs.lhs_.rows() , "Invalid number of rows" );
480  BLAZE_INTERNAL_ASSERT( A.columns() == rhs.lhs_.columns(), "Invalid number of columns" );
481  BLAZE_INTERNAL_ASSERT( B.rows() == rhs.rhs_.rows() , "Invalid number of rows" );
482  BLAZE_INTERNAL_ASSERT( B.columns() == rhs.rhs_.columns(), "Invalid number of columns" );
483  BLAZE_INTERNAL_ASSERT( A.rows() == (~lhs).rows() , "Invalid number of rows" );
484  BLAZE_INTERNAL_ASSERT( A.columns() == (~lhs).columns() , "Invalid number of columns" );
485 
486  const size_t m( rhs.rows() );
487  const size_t n( rhs.columns() );
488 
489  // Counting the number of elements per column
490  std::vector<size_t> nonzeros( n, 0UL );
491  for( size_t i=0UL; i<m; ++i )
492  {
493  const LeftIterator lend( A.end(i) );
494  const RightIterator rend( B.end(i) );
495 
496  LeftIterator l( A.begin(i) );
497  RightIterator r( B.begin(i) );
498 
499  while( l != lend && r != rend )
500  {
501  if( l->index() < r->index() ) {
502  ++nonzeros[l->index()];
503  ++l;
504  }
505  else if( l->index() > r->index() ) {
506  ++nonzeros[r->index()];
507  ++r;
508  }
509  else {
510  ++nonzeros[l->index()];
511  ++l;
512  ++r;
513  }
514  }
515 
516  while( l != lend ) {
517  ++nonzeros[l->index()];
518  ++l;
519  }
520 
521  while( r != rend ) {
522  ++nonzeros[r->index()];
523  ++r;
524  }
525  }
526 
527  // Resizing the left-hand side sparse matrix
528  for( size_t j=0UL; j<n; ++j ) {
529  (~lhs).reserve( j, nonzeros[j] );
530  }
531 
532  // Performing the matrix subtraction
533  for( size_t i=0UL; i<m; ++i )
534  {
535  const LeftIterator lend( A.end(i) );
536  const RightIterator rend( B.end(i) );
537 
538  LeftIterator l( A.begin(i) );
539  RightIterator r( B.begin(i) );
540 
541  while( l != lend && r != rend )
542  {
543  if( l->index() < r->index() ) {
544  (~lhs).append( i, l->index(), l->value() );
545  ++l;
546  }
547  else if( l->index() > r->index() ) {
548  (~lhs).append( i, r->index(), -r->value() );
549  ++r;
550  }
551  else {
552  (~lhs).append( i, l->index(), l->value() - r->value() );
553  ++l;
554  ++r;
555  }
556  }
557 
558  while( l != lend ) {
559  (~lhs).append( i, l->index(), l->value() );
560  ++l;
561  }
562 
563  while( r != rend ) {
564  (~lhs).append( i, r->index(), -r->value() );
565  ++r;
566  }
567  }
568  }
570  //**********************************************************************************************
571 
572  //**Assignment to column-major sparse matrices**************************************************
584  template< typename MT > // Type of the target sparse matrix
586  assign( SparseMatrix<MT,true>& lhs, const SMatSMatSubExpr& rhs )
587  {
589 
591 
592  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
593  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
594 
595  assign( ~lhs, trans( rhs.lhs_ ) - trans( rhs.rhs_ ) );
596  }
598  //**********************************************************************************************
599 
600  //**Addition assignment to dense matrices*******************************************************
612  template< typename MT // Type of the target dense matrix
613  , bool SO > // Storage order of the target dense matrix
614  friend inline void addAssign( DenseMatrix<MT,SO>& lhs, const SMatSMatSubExpr& rhs )
615  {
617 
618  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
619  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
620 
621  addAssign( ~lhs, rhs.lhs_ );
622  subAssign( ~lhs, rhs.rhs_ );
623  }
625  //**********************************************************************************************
626 
627  //**Addition assignment to sparse matrices******************************************************
628  // No special implementation for the addition assignment to sparse matrices.
629  //**********************************************************************************************
630 
631  //**Subtraction assignment to dense matrices****************************************************
643  template< typename MT // Type of the target dense matrix
644  , bool SO > // Storage order of the target dense matrix
645  friend inline void subAssign( DenseMatrix<MT,SO>& lhs, const SMatSMatSubExpr& rhs )
646  {
648 
649  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
650  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
651 
652  subAssign( ~lhs, rhs.lhs_ );
653  addAssign( ~lhs, rhs.rhs_ );
654  }
656  //**********************************************************************************************
657 
658  //**Subtraction assignment to sparse matrices***************************************************
659  // No special implementation for the subtraction assignment to sparse matrices.
660  //**********************************************************************************************
661 
662  //**Schur product assignment to dense matrices**************************************************
675  template< typename MT // Type of the target dense matrix
676  , bool SO > // Storage order of the target dense matrix
677  friend inline void schurAssign( DenseMatrix<MT,SO>& lhs, const SMatSMatSubExpr& rhs )
678  {
680 
684 
685  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
686  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
687 
688  const ResultType tmp( serial( rhs ) );
689  schurAssign( ~lhs, tmp );
690  }
692  //**********************************************************************************************
693 
694  //**Schur product assignment to sparse matrices*************************************************
695  // No special implementation for the Schur product assignment to sparse matrices.
696  //**********************************************************************************************
697 
698  //**Multiplication assignment to dense matrices*************************************************
699  // No special implementation for the multiplication assignment to dense matrices.
700  //**********************************************************************************************
701 
702  //**Multiplication assignment to sparse matrices************************************************
703  // No special implementation for the multiplication assignment to sparse matrices.
704  //**********************************************************************************************
705 
706  //**SMP assignment to dense matrices************************************************************
707  // No special implementation for the SMP assignment to dense matrices.
708  //**********************************************************************************************
709 
710  //**SMP assignment to sparse matrices***********************************************************
711  // No special implementation for the SMP assignment to sparse matrices.
712  //**********************************************************************************************
713 
714  //**SMP addition assignment to dense matrices***************************************************
728  template< typename MT // Type of the target dense matrix
729  , bool SO > // Storage order of the target dense matrix
730  friend inline EnableIf_< UseSMPAssign<MT> >
732  {
734 
735  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
736  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
737 
738  smpAddAssign( ~lhs, rhs.lhs_ );
739  smpSubAssign( ~lhs, rhs.rhs_ );
740  }
742  //**********************************************************************************************
743 
744  //**SMP addition assignment to sparse matrices**************************************************
745  // No special implementation for the SMP addition assignment to sparse matrices.
746  //**********************************************************************************************
747 
748  //**SMP subtraction assignment to dense matrices************************************************
763  template< typename MT // Type of the target dense matrix
764  , bool SO > // Storage order of the target dense matrix
765  friend inline EnableIf_< UseSMPAssign<MT> >
767  {
769 
770  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
771  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
772 
773  smpSubAssign( ~lhs, rhs.lhs_ );
774  smpAddAssign( ~lhs, rhs.rhs_ );
775  }
777  //**********************************************************************************************
778 
779  //**SMP subtraction assignment to sparse matrices***********************************************
780  // No special implementation for the SMP subtraction assignment to sparse matrices.
781  //**********************************************************************************************
782 
783  //**SMP Schur product assignment to dense matrices**********************************************
798  template< typename MT // Type of the target dense matrix
799  , bool SO > // Storage order of the target dense matrix
800  friend inline EnableIf_< UseSMPAssign<MT> >
802  {
804 
808 
809  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
810  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
811 
812  const ResultType tmp( rhs );
813  smpSchurAssign( ~lhs, tmp );
814  }
816  //**********************************************************************************************
817 
818  //**SMP Schur product assignment to sparse matrices*********************************************
819  // No special implementation for the SMP Schur product assignment to sparse matrices.
820  //**********************************************************************************************
821 
822  //**SMP multiplication assignment to dense matrices*********************************************
823  // No special implementation for the SMP multiplication assignment to dense matrices.
824  //**********************************************************************************************
825 
826  //**SMP multiplication assignment to sparse matrices********************************************
827  // No special implementation for the SMP multiplication assignment to sparse matrices.
828  //**********************************************************************************************
829 
830  //**Compile time checks*************************************************************************
838  //**********************************************************************************************
839 };
840 //*************************************************************************************************
841 
842 
843 
844 
845 //=================================================================================================
846 //
847 // GLOBAL BINARY ARITHMETIC OPERATORS
848 //
849 //=================================================================================================
850 
851 //*************************************************************************************************
877 template< typename MT1 // Type of the left-hand side sparse matrix
878  , typename MT2 > // Type of the right-hand side sparse matrix
879 inline decltype(auto)
880  operator-( const SparseMatrix<MT1,false>& lhs, const SparseMatrix<MT2,false>& rhs )
881 {
883 
884  if( (~lhs).rows() != (~rhs).rows() || (~lhs).columns() != (~rhs).columns() ) {
885  BLAZE_THROW_INVALID_ARGUMENT( "Matrix sizes do not match" );
886  }
887 
888  using ReturnType = const SMatSMatSubExpr<MT1,MT2>;
889  return ReturnType( ~lhs, ~rhs );
890 }
891 //*************************************************************************************************
892 
893 
894 
895 
896 //=================================================================================================
897 //
898 // SIZE SPECIALIZATIONS
899 //
900 //=================================================================================================
901 
902 //*************************************************************************************************
904 template< typename MT1, typename MT2 >
905 struct Size< SMatSMatSubExpr<MT1,MT2>, 0UL >
906  : public Maximum< Size<MT1,0UL>, Size<MT2,0UL> >
907 {};
908 
909 template< typename MT1, typename MT2 >
910 struct Size< SMatSMatSubExpr<MT1,MT2>, 1UL >
911  : public Maximum< Size<MT1,1UL>, Size<MT2,1UL> >
912 {};
914 //*************************************************************************************************
915 
916 
917 
918 
919 //=================================================================================================
920 //
921 // ISSYMMETRIC SPECIALIZATIONS
922 //
923 //=================================================================================================
924 
925 //*************************************************************************************************
927 template< typename MT1, typename MT2 >
928 struct IsSymmetric< SMatSMatSubExpr<MT1,MT2> >
929  : public And< IsSymmetric<MT1>, IsSymmetric<MT2> >
930 {};
932 //*************************************************************************************************
933 
934 
935 
936 
937 //=================================================================================================
938 //
939 // ISHERMITIAN SPECIALIZATIONS
940 //
941 //=================================================================================================
942 
943 //*************************************************************************************************
945 template< typename MT1, typename MT2 >
946 struct IsHermitian< SMatSMatSubExpr<MT1,MT2> >
947  : public And< IsHermitian<MT1>, IsHermitian<MT2> >
948 {};
950 //*************************************************************************************************
951 
952 
953 
954 
955 //=================================================================================================
956 //
957 // ISLOWER SPECIALIZATIONS
958 //
959 //=================================================================================================
960 
961 //*************************************************************************************************
963 template< typename MT1, typename MT2 >
964 struct IsLower< SMatSMatSubExpr<MT1,MT2> >
965  : public And< IsLower<MT1>, IsLower<MT2> >
966 {};
968 //*************************************************************************************************
969 
970 
971 
972 
973 //=================================================================================================
974 //
975 // ISUNILOWER SPECIALIZATIONS
976 //
977 //=================================================================================================
978 
979 //*************************************************************************************************
981 template< typename MT1, typename MT2 >
982 struct IsUniLower< SMatSMatSubExpr<MT1,MT2> >
983  : public And< IsUniLower<MT1>, IsStrictlyLower<MT2> >
984 {};
986 //*************************************************************************************************
987 
988 
989 
990 
991 //=================================================================================================
992 //
993 // ISSTRICTLYLOWER SPECIALIZATIONS
994 //
995 //=================================================================================================
996 
997 //*************************************************************************************************
999 template< typename MT1, typename MT2 >
1000 struct IsStrictlyLower< SMatSMatSubExpr<MT1,MT2> >
1001  : public And< IsStrictlyLower<MT1>, IsStrictlyLower<MT2> >
1002 {};
1004 //*************************************************************************************************
1005 
1006 
1007 
1008 
1009 //=================================================================================================
1010 //
1011 // ISUPPER SPECIALIZATIONS
1012 //
1013 //=================================================================================================
1014 
1015 //*************************************************************************************************
1017 template< typename MT1, typename MT2 >
1018 struct IsUpper< SMatSMatSubExpr<MT1,MT2> >
1019  : public And< IsUpper<MT1>, IsUpper<MT2> >
1020 {};
1022 //*************************************************************************************************
1023 
1024 
1025 
1026 
1027 //=================================================================================================
1028 //
1029 // ISUNIUPPER SPECIALIZATIONS
1030 //
1031 //=================================================================================================
1032 
1033 //*************************************************************************************************
1035 template< typename MT1, typename MT2 >
1036 struct IsUniUpper< SMatSMatSubExpr<MT1,MT2> >
1037  : public And< IsUniUpper<MT1>, IsStrictlyUpper<MT2> >
1038 {};
1040 //*************************************************************************************************
1041 
1042 
1043 
1044 
1045 //=================================================================================================
1046 //
1047 // ISSTRICTLYUPPER SPECIALIZATIONS
1048 //
1049 //=================================================================================================
1050 
1051 //*************************************************************************************************
1053 template< typename MT1, typename MT2 >
1054 struct IsStrictlyUpper< SMatSMatSubExpr<MT1,MT2> >
1055  : public And< IsStrictlyUpper<MT1>, IsStrictlyUpper<MT2> >
1056 {};
1058 //*************************************************************************************************
1059 
1060 } // namespace blaze
1061 
1062 #endif
If_< IsExpression< MT2 >, const MT2, const MT2 &> RightOperand
Composite type of the right-hand side sparse matrix expression.
Definition: SMatSMatSubExpr.h:174
size_t rows() const noexcept
Returns the current number of rows of the matrix.
Definition: SMatSMatSubExpr.h:235
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.
ResultType_< MT2 > RT2
Result type of the right-hand side sparse matrix expression.
Definition: SMatSMatSubExpr.h:107
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.
SubTrait_< RT1, RT2 > ResultType
Result type for expression template evaluations.
Definition: SMatSMatSubExpr.h:159
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.
ReturnType_< MT1 > RN1
ReturnType type of the left-hand side sparse matrix expression.
Definition: SMatSMatSubExpr.h:108
bool isAliased(const T *alias) const noexcept
Returns whether the expression is aliased with the given address alias.
Definition: SMatSMatSubExpr.h:310
size_t columns() const noexcept
Returns the current number of columns of the matrix.
Definition: SMatSMatSubExpr.h:245
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
const ResultType CompositeType
Data type for composite expression templates.
Definition: SMatSMatSubExpr.h:168
Header file for the Computation base class.
Compile time check for upper triangular matrices.This type trait tests whether or not the given templ...
Definition: IsUpper.h:87
Constraints on the storage order of matrix types.
size_t nonZeros(size_t i) const
Returns the number of non-zero elements in the specified row.
Definition: SMatSMatSubExpr.h:266
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
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
ReturnType at(size_t i, size_t j) const
Checked access to the matrix elements.
Definition: SMatSMatSubExpr.h:219
typename T::ReturnType ReturnType_
Alias declaration for nested ReturnType type definitions.The ReturnType_ alias declaration provides a...
Definition: Aliases.h:363
Header file for the SparseMatrix base class.
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
Header file for the DisableIf class template.
Header file for the IsTemporary type trait class.
Header file for the IsStrictlyUpper type trait.
Header file for the IsSymmetric type trait.
Namespace of the Blaze C++ math library.
Definition: Blaze.h: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
bool canAlias(const T *alias) const noexcept
Returns whether the expression can alias with the given address alias.
Definition: SMatSMatSubExpr.h:298
ResultType_< MT1 > RT1
Result type of the left-hand side sparse matrix expression.
Definition: SMatSMatSubExpr.h:106
#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
CompositeType_< MT2 > CT2
Composite type of the right-hand side sparse matrix expression.
Definition: SMatSMatSubExpr.h:111
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.
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:430
LeftOperand lhs_
Left-hand side sparse matrix of the subtraction expression.
Definition: SMatSMatSubExpr.h:317
const IfTrue_< returnExpr, ExprReturnType, ElementType > ReturnType
Return type for expression template evaluations.
Definition: SMatSMatSubExpr.h:165
Constraint on the data type.
Header file for all forward declarations for expression class templates.
SubExprTrait_< RN1, RN2 > ExprReturnType
Expression return type for the subscript operator.
Definition: SMatSMatSubExpr.h:124
Header file for the EnableIf class template.
Header file for the IsStrictlyLower type trait.
ReturnType_< MT2 > RN2
ReturnType type of the right-hand side sparse matrix expression.
Definition: SMatSMatSubExpr.h:109
Compile time check for lower unitriangular matrices.This type trait tests whether or not the given te...
Definition: IsUniLower.h:86
CompositeType_< MT1 > CT1
Composite type of the left-hand side sparse matrix expression.
Definition: SMatSMatSubExpr.h:110
Compile time check for resizable data types.This type trait tests whether the given data type is a re...
Definition: IsResizable.h:75
OppositeType_< ResultType > OppositeType
Result type with opposite storage order for expression template evaluations.
Definition: SMatSMatSubExpr.h:160
#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
If_< IsExpression< MT1 >, const MT1, const MT1 &> LeftOperand
Composite type of the left-hand side sparse matrix expression.
Definition: SMatSMatSubExpr.h:171
Header file for run time assertion macros.
ElementType_< ResultType > ElementType
Resulting element type.
Definition: SMatSMatSubExpr.h:162
Expression object for sparse matrix-sparse matrix subtractions.The SMatSMatSubExpr class represents t...
Definition: Forward.h:119
RightOperand rhs_
Right-hand side sparse matrix of the subtraction expression.
Definition: SMatSMatSubExpr.h:318
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
RightOperand rightOperand() const noexcept
Returns the right-hand side sparse matrix operand.
Definition: SMatSMatSubExpr.h:286
#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
ReturnType operator()(size_t i, size_t j) const
2D-access to the matrix elements.
Definition: SMatSMatSubExpr.h:204
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
#define BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION(T)
Constraint on the data type.In case the given data type T requires an intermediate evaluation within ...
Definition: RequiresEvaluation.h:81
Header file for the RemoveReference type trait.
typename EnableIf< Condition, T >::Type EnableIf_
Auxiliary alias declaration for the EnableIf class template.The EnableIf_ alias declaration provides ...
Definition: EnableIf.h:224
typename T::OppositeType OppositeType_
Alias declaration for nested OppositeType type definitions.The OppositeType_ alias declaration provid...
Definition: Aliases.h:263
Compile time check for strictly lower triangular matrices.This type trait tests whether or not the gi...
Definition: IsStrictlyLower.h:86
LeftOperand leftOperand() const noexcept
Returns the left-hand side sparse matrix operand.
Definition: SMatSMatSubExpr.h:276
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
decltype(auto) trans(const DenseMatrix< MT, SO > &dm)
Calculation of the transpose of the given dense matrix.
Definition: DMatTransExpr.h:789
Header file for the IsComputation type trait class.
size_t nonZeros() const
Returns the number of non-zero elements in the sparse matrix.
Definition: SMatSMatSubExpr.h:255
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
SMatSMatSubExpr(const MT1 &lhs, const MT2 &rhs) noexcept
Constructor for the SMatSMatSubExpr class.
Definition: SMatSMatSubExpr.h:188
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.
TransposeType_< ResultType > TransposeType
Transpose type for expression template evaluations.
Definition: SMatSMatSubExpr.h:161
Header file for the IsHermitian type trait.
Header file for the IsResizable type trait.
Header file for the SubExprTrait class template.
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
Header file for the IsExpression type trait class.
Header file for the function trace functionality.