DMatDMatSchurExpr.h
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1 //=================================================================================================
33 //=================================================================================================
34 
35 #ifndef _BLAZE_MATH_EXPRESSIONS_DMATDMATSCHUREXPR_H_
36 #define _BLAZE_MATH_EXPRESSIONS_DMATDMATSCHUREXPR_H_
37 
38 
39 //*************************************************************************************************
40 // Includes
41 //*************************************************************************************************
42 
43 #include <iterator>
44 #include <blaze/math/Aliases.h>
49 #include <blaze/math/Exception.h>
55 #include <blaze/math/SIMD.h>
76 #include <blaze/system/Inline.h>
78 #include <blaze/util/Assert.h>
79 #include <blaze/util/DisableIf.h>
80 #include <blaze/util/EnableIf.h>
82 #include <blaze/util/mpl/And.h>
83 #include <blaze/util/mpl/If.h>
84 #include <blaze/util/mpl/Maximum.h>
85 #include <blaze/util/mpl/Or.h>
86 #include <blaze/util/Types.h>
87 #include <blaze/util/Unused.h>
88 
89 
90 namespace blaze {
91 
92 //=================================================================================================
93 //
94 // CLASS DMATDMATSCHUREXPR
95 //
96 //=================================================================================================
97 
98 //*************************************************************************************************
105 template< typename MT1 // Type of the left-hand side dense matrix
106  , typename MT2 // Type of the right-hand side dense matrix
107  , bool SO > // Storage order
109  : public SchurExpr< DenseMatrix< DMatDMatSchurExpr<MT1,MT2,SO>, SO > >
110  , private Computation
111 {
112  private:
113  //**Type definitions****************************************************************************
122  //**********************************************************************************************
123 
124  //**Return type evaluation**********************************************************************
126 
131  enum : bool { returnExpr = !IsTemporary<RN1>::value && !IsTemporary<RN2>::value };
132 
135  //**********************************************************************************************
136 
137  //**Serial evaluation strategy******************************************************************
139 
145  enum : bool { useAssign = RequiresEvaluation<MT1>::value || RequiresEvaluation<MT2>::value || !returnExpr };
146 
148  template< typename MT >
150  struct UseAssign {
151  enum : bool { value = useAssign };
152  };
154  //**********************************************************************************************
155 
156  //**Parallel evaluation strategy****************************************************************
158 
164  template< typename MT >
165  struct UseSMPAssign {
166  enum : bool { value = ( !MT1::smpAssignable || !MT2::smpAssignable ) && useAssign };
167  };
169  //**********************************************************************************************
170 
171  public:
172  //**Type definitions****************************************************************************
178 
181 
184 
186  using LeftOperand = If_< IsExpression<MT1>, const MT1, const MT1& >;
187 
189  using RightOperand = If_< IsExpression<MT2>, const MT2, const MT2& >;
190  //**********************************************************************************************
191 
192  //**ConstIterator class definition**************************************************************
196  {
197  public:
198  //**Type definitions*************************************************************************
199  using IteratorCategory = std::random_access_iterator_tag;
204 
205  // STL iterator requirements
211 
214 
217  //*******************************************************************************************
218 
219  //**Constructor******************************************************************************
225  explicit inline ConstIterator( LeftIteratorType left, RightIteratorType right )
226  : left_ ( left ) // Iterator to the current left-hand side element
227  , right_( right ) // Iterator to the current right-hand side element
228  {}
229  //*******************************************************************************************
230 
231  //**Addition assignment operator*************************************************************
237  inline ConstIterator& operator+=( size_t inc ) {
238  left_ += inc;
239  right_ += inc;
240  return *this;
241  }
242  //*******************************************************************************************
243 
244  //**Subtraction assignment operator**********************************************************
250  inline ConstIterator& operator-=( size_t dec ) {
251  left_ -= dec;
252  right_ -= dec;
253  return *this;
254  }
255  //*******************************************************************************************
256 
257  //**Prefix increment operator****************************************************************
263  ++left_;
264  ++right_;
265  return *this;
266  }
267  //*******************************************************************************************
268 
269  //**Postfix increment operator***************************************************************
274  inline const ConstIterator operator++( int ) {
275  return ConstIterator( left_++, right_++ );
276  }
277  //*******************************************************************************************
278 
279  //**Prefix decrement operator****************************************************************
285  --left_;
286  --right_;
287  return *this;
288  }
289  //*******************************************************************************************
290 
291  //**Postfix decrement operator***************************************************************
296  inline const ConstIterator operator--( int ) {
297  return ConstIterator( left_--, right_-- );
298  }
299  //*******************************************************************************************
300 
301  //**Element access operator******************************************************************
306  inline ReturnType operator*() const {
307  return (*left_) * (*right_);
308  }
309  //*******************************************************************************************
310 
311  //**Load function****************************************************************************
316  inline auto load() const noexcept {
317  return left_.load() * right_.load();
318  }
319  //*******************************************************************************************
320 
321  //**Equality operator************************************************************************
327  inline bool operator==( const ConstIterator& rhs ) const {
328  return left_ == rhs.left_;
329  }
330  //*******************************************************************************************
331 
332  //**Inequality operator**********************************************************************
338  inline bool operator!=( const ConstIterator& rhs ) const {
339  return left_ != rhs.left_;
340  }
341  //*******************************************************************************************
342 
343  //**Less-than operator***********************************************************************
349  inline bool operator<( const ConstIterator& rhs ) const {
350  return left_ < rhs.left_;
351  }
352  //*******************************************************************************************
353 
354  //**Greater-than operator********************************************************************
360  inline bool operator>( const ConstIterator& rhs ) const {
361  return left_ > rhs.left_;
362  }
363  //*******************************************************************************************
364 
365  //**Less-or-equal-than operator**************************************************************
371  inline bool operator<=( const ConstIterator& rhs ) const {
372  return left_ <= rhs.left_;
373  }
374  //*******************************************************************************************
375 
376  //**Greater-or-equal-than operator***********************************************************
382  inline bool operator>=( const ConstIterator& rhs ) const {
383  return left_ >= rhs.left_;
384  }
385  //*******************************************************************************************
386 
387  //**Subtraction operator*********************************************************************
393  inline DifferenceType operator-( const ConstIterator& rhs ) const {
394  return left_ - rhs.left_;
395  }
396  //*******************************************************************************************
397 
398  //**Addition operator************************************************************************
405  friend inline const ConstIterator operator+( const ConstIterator& it, size_t inc ) {
406  return ConstIterator( it.left_ + inc, it.right_ + inc );
407  }
408  //*******************************************************************************************
409 
410  //**Addition operator************************************************************************
417  friend inline const ConstIterator operator+( size_t inc, const ConstIterator& it ) {
418  return ConstIterator( it.left_ + inc, it.right_ + inc );
419  }
420  //*******************************************************************************************
421 
422  //**Subtraction operator*********************************************************************
429  friend inline const ConstIterator operator-( const ConstIterator& it, size_t dec ) {
430  return ConstIterator( it.left_ - dec, it.right_ - dec );
431  }
432  //*******************************************************************************************
433 
434  private:
435  //**Member variables*************************************************************************
438  //*******************************************************************************************
439  };
440  //**********************************************************************************************
441 
442  //**Compilation flags***************************************************************************
444  enum : bool { simdEnabled = MT1::simdEnabled && MT2::simdEnabled &&
446 
448  enum : bool { smpAssignable = MT1::smpAssignable && MT2::smpAssignable };
449  //**********************************************************************************************
450 
451  //**SIMD properties*****************************************************************************
453  enum : size_t { SIMDSIZE = SIMDTrait<ElementType>::size };
454  //**********************************************************************************************
455 
456  //**Constructor*********************************************************************************
462  explicit inline DMatDMatSchurExpr( const MT1& lhs, const MT2& rhs ) noexcept
463  : lhs_( lhs ) // Left-hand side dense matrix of the Schur product expression
464  , rhs_( rhs ) // Right-hand side dense matrix of the Schur product expression
465  {
466  BLAZE_INTERNAL_ASSERT( lhs.rows() == rhs.rows() , "Invalid number of rows" );
467  BLAZE_INTERNAL_ASSERT( lhs.columns() == rhs.columns(), "Invalid number of columns" );
468  }
469  //**********************************************************************************************
470 
471  //**Access operator*****************************************************************************
478  inline ReturnType operator()( size_t i, size_t j ) const {
479  BLAZE_INTERNAL_ASSERT( i < lhs_.rows() , "Invalid row access index" );
480  BLAZE_INTERNAL_ASSERT( j < lhs_.columns(), "Invalid column access index" );
481  return lhs_(i,j) * rhs_(i,j);
482  }
483  //**********************************************************************************************
484 
485  //**At function*********************************************************************************
493  inline ReturnType at( size_t i, size_t j ) const {
494  if( i >= lhs_.rows() ) {
495  BLAZE_THROW_OUT_OF_RANGE( "Invalid row access index" );
496  }
497  if( j >= lhs_.columns() ) {
498  BLAZE_THROW_OUT_OF_RANGE( "Invalid column access index" );
499  }
500  return (*this)(i,j);
501  }
502  //**********************************************************************************************
503 
504  //**Load function*******************************************************************************
511  BLAZE_ALWAYS_INLINE auto load( size_t i, size_t j ) const noexcept {
512  BLAZE_INTERNAL_ASSERT( i < lhs_.rows() , "Invalid row access index" );
513  BLAZE_INTERNAL_ASSERT( j < lhs_.columns(), "Invalid column access index" );
514  BLAZE_INTERNAL_ASSERT( !SO || ( i % SIMDSIZE == 0UL ), "Invalid row access index" );
515  BLAZE_INTERNAL_ASSERT( SO || ( j % SIMDSIZE == 0UL ), "Invalid column access index" );
516  return lhs_.load(i,j) * rhs_.load(i,j);
517  }
518  //**********************************************************************************************
519 
520  //**Begin function******************************************************************************
526  inline ConstIterator begin( size_t i ) const {
527  return ConstIterator( lhs_.begin(i), rhs_.begin(i) );
528  }
529  //**********************************************************************************************
530 
531  //**End function********************************************************************************
537  inline ConstIterator end( size_t i ) const {
538  return ConstIterator( lhs_.end(i), rhs_.end(i) );
539  }
540  //**********************************************************************************************
541 
542  //**Rows function*******************************************************************************
547  inline size_t rows() const noexcept {
548  return lhs_.rows();
549  }
550  //**********************************************************************************************
551 
552  //**Columns function****************************************************************************
557  inline size_t columns() const noexcept {
558  return lhs_.columns();
559  }
560  //**********************************************************************************************
561 
562  //**Left operand access*************************************************************************
567  inline LeftOperand leftOperand() const noexcept {
568  return lhs_;
569  }
570  //**********************************************************************************************
571 
572  //**Right operand access************************************************************************
577  inline RightOperand rightOperand() const noexcept {
578  return rhs_;
579  }
580  //**********************************************************************************************
581 
582  //**********************************************************************************************
588  template< typename T >
589  inline bool canAlias( const T* alias ) const noexcept {
590  return ( IsExpression<MT1>::value && ( RequiresEvaluation<MT1>::value ? lhs_.isAliased( alias ) : lhs_.canAlias( alias ) ) ) ||
591  ( IsExpression<MT2>::value && ( RequiresEvaluation<MT2>::value ? rhs_.isAliased( alias ) : rhs_.canAlias( alias ) ) );
592  }
593  //**********************************************************************************************
594 
595  //**********************************************************************************************
601  template< typename T >
602  inline bool isAliased( const T* alias ) const noexcept {
603  return ( lhs_.isAliased( alias ) || rhs_.isAliased( alias ) );
604  }
605  //**********************************************************************************************
606 
607  //**********************************************************************************************
612  inline bool isAligned() const noexcept {
613  return lhs_.isAligned() && rhs_.isAligned();
614  }
615  //**********************************************************************************************
616 
617  //**********************************************************************************************
622  inline bool canSMPAssign() const noexcept {
623  return lhs_.canSMPAssign() || rhs_.canSMPAssign() ||
624  ( rows() * columns() >= SMP_DMATDMATSCHUR_THRESHOLD );
625  }
626  //**********************************************************************************************
627 
628  private:
629  //**Member variables****************************************************************************
632  //**********************************************************************************************
633 
634  //**Assignment to dense matrices****************************************************************
648  template< typename MT // Type of the target dense matrix
649  , bool SO2 > // Storage order of the target dense matrix
650  friend inline EnableIf_< UseAssign<MT> >
651  assign( DenseMatrix<MT,SO2>& lhs, const DMatDMatSchurExpr& 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  if( !IsOperation<MT1>::value && isSame( ~lhs, rhs.lhs_ ) ) {
659  schurAssign( ~lhs, rhs.rhs_ );
660  }
661  else {
662  assign ( ~lhs, rhs.lhs_ );
663  schurAssign( ~lhs, rhs.rhs_ );
664  }
665  }
667  //**********************************************************************************************
668 
669  //**Assignment to sparse matrices***************************************************************
683  template< typename MT // Type of the target sparse matrix
684  , bool SO2 > // Storage order of the target sparse matrix
685  friend inline EnableIf_< UseAssign<MT> >
686  assign( SparseMatrix<MT,SO2>& lhs, const DMatDMatSchurExpr& rhs )
687  {
689 
691 
698 
699  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
700  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
701 
702  const TmpType tmp( serial( rhs ) );
703  assign( ~lhs, tmp );
704  }
706  //**********************************************************************************************
707 
708  //**Addition assignment to dense matrices*******************************************************
722  template< typename MT // Type of the target dense matrix
723  , bool SO2 > // Storage order of the target dense matrix
724  friend inline EnableIf_< UseAssign<MT> >
725  addAssign( DenseMatrix<MT,SO2>& lhs, const DMatDMatSchurExpr& rhs )
726  {
728 
732 
733  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
734  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
735 
736  const ResultType tmp( serial( rhs ) );
737  addAssign( ~lhs, tmp );
738  }
740  //**********************************************************************************************
741 
742  //**Addition assignment to sparse matrices******************************************************
743  // No special implementation for the addition assignment to sparse matrices.
744  //**********************************************************************************************
745 
746  //**Subtraction assignment to dense matrices****************************************************
760  template< typename MT // Type of the target dense matrix
761  , bool SO2 > // Storage order of the target dense matrix
762  friend inline EnableIf_< UseAssign<MT> >
763  subAssign( DenseMatrix<MT,SO2>& lhs, const DMatDMatSchurExpr& rhs )
764  {
766 
770 
771  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
772  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
773 
774  const ResultType tmp( serial( rhs ) );
775  subAssign( ~lhs, tmp );
776  }
778  //**********************************************************************************************
779 
780  //**Subtraction assignment to sparse matrices***************************************************
781  // No special implementation for the subtraction assignment to sparse matrices.
782  //**********************************************************************************************
783 
784  //**Schur product assignment to dense matrices**************************************************
798  template< typename MT // Type of the target dense matrix
799  , bool SO2 > // Storage order of the target dense matrix
800  friend inline EnableIf_< UseAssign<MT> >
801  schurAssign( DenseMatrix<MT,SO2>& lhs, const DMatDMatSchurExpr& rhs )
802  {
804 
805  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
806  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
807 
808  schurAssign( ~lhs, rhs.lhs_ );
809  schurAssign( ~lhs, rhs.rhs_ );
810  }
812  //**********************************************************************************************
813 
814  //**Schur product assignment to sparse matrices*************************************************
815  // No special implementation for the Schur product assignment to sparse matrices.
816  //**********************************************************************************************
817 
818  //**Multiplication assignment to dense matrices*************************************************
819  // No special implementation for the multiplication assignment to dense matrices.
820  //**********************************************************************************************
821 
822  //**Multiplication assignment to sparse matrices************************************************
823  // No special implementation for the multiplication assignment to sparse matrices.
824  //**********************************************************************************************
825 
826  //**SMP assignment to dense matrices************************************************************
840  template< typename MT // Type of the target dense matrix
841  , bool SO2 > // Storage order of the target dense matrix
842  friend inline EnableIf_< UseSMPAssign<MT> >
844  {
846 
847  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
848  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
849 
850  if( !IsOperation<MT1>::value && isSame( ~lhs, rhs.lhs_ ) ) {
851  smpSchurAssign( ~lhs, rhs.rhs_ );
852  }
853  else {
854  smpAssign ( ~lhs, rhs.lhs_ );
855  smpSchurAssign( ~lhs, rhs.rhs_ );
856  }
857  }
859  //**********************************************************************************************
860 
861  //**SMP assignment to sparse matrices***********************************************************
875  template< typename MT // Type of the target sparse matrix
876  , bool SO2 > // Storage order of the target sparse matrix
877  friend inline EnableIf_< UseSMPAssign<MT> >
879  {
881 
883 
890 
891  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
892  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
893 
894  const TmpType tmp( rhs );
895  smpAssign( ~lhs, tmp );
896  }
898  //**********************************************************************************************
899 
900  //**SMP addition assignment to dense matrices***************************************************
914  template< typename MT // Type of the target dense matrix
915  , bool SO2 > // Storage order of the target dense matrix
916  friend inline EnableIf_< UseAssign<MT> >
918  {
920 
924 
925  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
926  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
927 
928  const ResultType tmp( rhs );
929  smpAddAssign( ~lhs, tmp );
930  }
932  //**********************************************************************************************
933 
934  //**SMP addition assignment to sparse matrices**************************************************
935  // No special implementation for the SMP addition assignment to sparse matrices.
936  //**********************************************************************************************
937 
938  //**SMP subtraction assignment to dense matrices************************************************
953  template< typename MT // Type of the target dense matrix
954  , bool SO2 > // Storage order of the target dense matrix
955  friend inline EnableIf_< UseSMPAssign<MT> >
957  {
959 
963 
964  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
965  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
966 
967  const ResultType tmp( rhs );
968  smpSubAssign( ~lhs, tmp );
969  }
971  //**********************************************************************************************
972 
973  //**SMP subtraction assignment to sparse matrices***********************************************
974  // No special implementation for the SMP subtraction assignment to sparse matrices.
975  //**********************************************************************************************
976 
977  //**SMP Schur product assignment to dense matrices**********************************************
992  template< typename MT // Type of the target dense matrix
993  , bool SO2 > // Storage order of the target dense matrix
994  friend inline EnableIf_< UseSMPAssign<MT> >
996  {
998 
999  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
1000  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
1001 
1002  smpSchurAssign( ~lhs, rhs.lhs_ );
1003  smpSchurAssign( ~lhs, rhs.rhs_ );
1004  }
1006  //**********************************************************************************************
1007 
1008  //**SMP Schur product assignment to sparse matrices*********************************************
1009  // No special implementation for the SMP Schur product assignment to sparse matrices.
1010  //**********************************************************************************************
1011 
1012  //**SMP multiplication assignment to dense matrices*********************************************
1013  // No special implementation for the SMP multiplication assignment to dense matrices.
1014  //**********************************************************************************************
1015 
1016  //**SMP multiplication assignment to sparse matrices********************************************
1017  // No special implementation for the SMP multiplication assignment to sparse matrices.
1018  //**********************************************************************************************
1019 
1020  //**Compile time checks*************************************************************************
1026  //**********************************************************************************************
1027 };
1028 //*************************************************************************************************
1029 
1030 
1031 
1032 
1033 //=================================================================================================
1034 //
1035 // GLOBAL BINARY ARITHMETIC OPERATORS
1036 //
1037 //=================================================================================================
1038 
1039 //*************************************************************************************************
1052 template< typename MT1 // Type of the left-hand side dense matrix
1053  , typename MT2 // Type of the right-hand side dense matrix
1054  , bool SO // Storage order
1057 inline const DMatDMatSchurExpr<MT1,MT2,SO>
1058  dmatdmatschur( const DenseMatrix<MT1,SO>& lhs, const DenseMatrix<MT2,SO>& rhs )
1059 {
1061 
1062  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
1063  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
1064 
1065  return DMatDMatSchurExpr<MT1,MT2,SO>( ~lhs, ~rhs );
1066 }
1068 //*************************************************************************************************
1069 
1070 
1071 //*************************************************************************************************
1084 template< typename MT1 // Type of the left-hand side dense matrix
1085  , typename MT2 // Type of the right-hand side dense matrix
1086  , bool SO // Storage order
1087  , typename = EnableIf_< Or< And< IsUniLower<MT1>, IsUniUpper<MT2> >
1088  , And< IsUniUpper<MT1>, IsUniLower<MT2> > > > >
1090  dmatdmatschur( const DenseMatrix<MT1,SO>& lhs, const DenseMatrix<MT2,SO>& rhs )
1091 {
1093 
1094  UNUSED_PARAMETER( rhs );
1095 
1096  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == (~rhs).rows() , "Invalid number of rows" );
1097  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == (~rhs).columns(), "Invalid number of columns" );
1098 
1099  return IdentityMatrix< MultTrait_< ElementType_<MT1>, ElementType_<MT2> >, SO >( (~lhs).rows() );
1100 }
1102 //*************************************************************************************************
1103 
1104 
1105 //*************************************************************************************************
1130 template< typename MT1 // Type of the left-hand side dense matrix
1131  , typename MT2 // Type of the right-hand side dense matrix
1132  , bool SO > // Storage order
1133 inline decltype(auto)
1134  operator%( const DenseMatrix<MT1,SO>& lhs, const DenseMatrix<MT2,SO>& rhs )
1135 {
1137 
1138  if( (~lhs).rows() != (~rhs).rows() || (~lhs).columns() != (~rhs).columns() ) {
1139  BLAZE_THROW_INVALID_ARGUMENT( "Matrix sizes do not match" );
1140  }
1141 
1142  return dmatdmatschur( ~lhs, ~rhs );
1143 }
1144 //*************************************************************************************************
1145 
1146 
1147 
1148 
1149 //=================================================================================================
1150 //
1151 // SIZE SPECIALIZATIONS
1152 //
1153 //=================================================================================================
1154 
1155 //*************************************************************************************************
1157 template< typename MT1, typename MT2, bool SO >
1158 struct Size< DMatDMatSchurExpr<MT1,MT2,SO>, 0UL >
1159  : public Maximum< Size<MT1,0UL>, Size<MT2,0UL> >
1160 {};
1161 
1162 template< typename MT1, typename MT2, bool SO >
1163 struct Size< DMatDMatSchurExpr<MT1,MT2,SO>, 1UL >
1164  : public Maximum< Size<MT1,1UL>, Size<MT2,1UL> >
1165 {};
1167 //*************************************************************************************************
1168 
1169 
1170 
1171 
1172 //=================================================================================================
1173 //
1174 // ISALIGNED SPECIALIZATIONS
1175 //
1176 //=================================================================================================
1177 
1178 //*************************************************************************************************
1180 template< typename MT1, typename MT2, bool SO >
1181 struct IsAligned< DMatDMatSchurExpr<MT1,MT2,SO> >
1182  : public And< IsAligned<MT1>, IsAligned<MT2> >
1183 {};
1185 //*************************************************************************************************
1186 
1187 
1188 
1189 
1190 //=================================================================================================
1191 //
1192 // ISPADDED SPECIALIZATIONS
1193 //
1194 //=================================================================================================
1195 
1196 //*************************************************************************************************
1198 template< typename MT1, typename MT2, bool SO >
1199 struct IsPadded< DMatDMatSchurExpr<MT1,MT2,SO> >
1200  : public And< IsPadded<MT1>, IsPadded<MT2> >
1201 {};
1203 //*************************************************************************************************
1204 
1205 
1206 
1207 
1208 //=================================================================================================
1209 //
1210 // ISSYMMETRIC SPECIALIZATIONS
1211 //
1212 //=================================================================================================
1213 
1214 //*************************************************************************************************
1216 template< typename MT1, typename MT2, bool SO >
1217 struct IsSymmetric< DMatDMatSchurExpr<MT1,MT2,SO> >
1218  : public And< IsSymmetric<MT1>, IsSymmetric<MT2> >
1219 {};
1221 //*************************************************************************************************
1222 
1223 
1224 
1225 
1226 //=================================================================================================
1227 //
1228 // ISHERMITIAN SPECIALIZATIONS
1229 //
1230 //=================================================================================================
1231 
1232 //*************************************************************************************************
1234 template< typename MT1, typename MT2, bool SO >
1235 struct IsHermitian< DMatDMatSchurExpr<MT1,MT2,SO> >
1236  : public And< IsHermitian<MT1>, IsHermitian<MT2> >
1237 {};
1239 //*************************************************************************************************
1240 
1241 
1242 
1243 
1244 //=================================================================================================
1245 //
1246 // ISLOWER SPECIALIZATIONS
1247 //
1248 //=================================================================================================
1249 
1250 //*************************************************************************************************
1252 template< typename MT1, typename MT2, bool SO >
1253 struct IsLower< DMatDMatSchurExpr<MT1,MT2,SO> >
1254  : public Or< IsLower<MT1>, IsLower<MT2> >
1255 {};
1257 //*************************************************************************************************
1258 
1259 
1260 
1261 
1262 //=================================================================================================
1263 //
1264 // ISUNILOWER SPECIALIZATIONS
1265 //
1266 //=================================================================================================
1267 
1268 //*************************************************************************************************
1270 template< typename MT1, typename MT2, bool SO >
1271 struct IsUniLower< DMatDMatSchurExpr<MT1,MT2,SO> >
1272  : public And< IsUniLower<MT1>, IsUniLower<MT2> >
1273 {};
1275 //*************************************************************************************************
1276 
1277 
1278 
1279 
1280 //=================================================================================================
1281 //
1282 // ISSTRICTLYLOWER SPECIALIZATIONS
1283 //
1284 //=================================================================================================
1285 
1286 //*************************************************************************************************
1288 template< typename MT1, typename MT2, bool SO >
1289 struct IsStrictlyLower< DMatDMatSchurExpr<MT1,MT2,SO> >
1290  : public Or< IsStrictlyLower<MT1>, IsStrictlyLower<MT2> >
1291 {};
1293 //*************************************************************************************************
1294 
1295 
1296 
1297 
1298 //=================================================================================================
1299 //
1300 // ISUPPER SPECIALIZATIONS
1301 //
1302 //=================================================================================================
1303 
1304 //*************************************************************************************************
1306 template< typename MT1, typename MT2, bool SO >
1307 struct IsUpper< DMatDMatSchurExpr<MT1,MT2,SO> >
1308  : public Or< IsUpper<MT1>, IsUpper<MT2> >
1309 {};
1311 //*************************************************************************************************
1312 
1313 
1314 
1315 
1316 //=================================================================================================
1317 //
1318 // ISUNIUPPER SPECIALIZATIONS
1319 //
1320 //=================================================================================================
1321 
1322 //*************************************************************************************************
1324 template< typename MT1, typename MT2, bool SO >
1325 struct IsUniUpper< DMatDMatSchurExpr<MT1,MT2,SO> >
1326  : public And< IsUniUpper<MT1>, IsUniUpper<MT2> >
1327 {};
1329 //*************************************************************************************************
1330 
1331 
1332 
1333 
1334 //=================================================================================================
1335 //
1336 // ISSTRICTLYUPPER SPECIALIZATIONS
1337 //
1338 //=================================================================================================
1339 
1340 //*************************************************************************************************
1342 template< typename MT1, typename MT2, bool SO >
1343 struct IsStrictlyUpper< DMatDMatSchurExpr<MT1,MT2,SO> >
1344  : public Or< IsStrictlyUpper<MT1>, IsStrictlyUpper<MT2> >
1345 {};
1347 //*************************************************************************************************
1348 
1349 } // namespace blaze
1350 
1351 #endif
CompositeType_< MT1 > CT1
Composite type of the left-hand side dense matrix expression.
Definition: DMatDMatSchurExpr.h:118
#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
Pointer difference type of the Blaze library.
size_t rows() const noexcept
Returns the current number of rows of the matrix.
Definition: DMatDMatSchurExpr.h:547
RightIteratorType right_
Iterator to the current right-hand side element.
Definition: DMatDMatSchurExpr.h:437
Header file for auxiliary alias declarations.
Header file for the Schur product trait.
ReturnType_< MT2 > RN2
Return type of the right-hand side dense matrix expression.
Definition: DMatDMatSchurExpr.h:117
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 UNUSED_PARAMETER function template.
Header file for the IsUniUpper type trait.
EnableIf_< IsDenseMatrix< MT1 > > smpSchurAssign(Matrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs)
Default implementation of the SMP Schur product assignment of a matrix to dense matrix.
Definition: DenseMatrix.h:196
BLAZE_ALWAYS_INLINE bool isSame(const Matrix< MT1, SO1 > &a, const Matrix< MT2, SO2 > &b) noexcept
Returns whether the two given matrices represent the same observable state.
Definition: Matrix.h:949
Header file for basic type definitions.
Compile time check whether the given type is an operational expression template.This type trait class...
Definition: IsOperation.h:70
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.
#define BLAZE_CONSTRAINT_MUST_BE_MATRIX_WITH_STORAGE_ORDER(T, SO)
Constraint on the data type.In case the given data type T is not a dense or sparse matrix type and in...
Definition: StorageOrder.h:63
friend const ConstIterator operator+(size_t inc, const ConstIterator &it)
Addition between an integral value and a ConstIterator.
Definition: DMatDMatSchurExpr.h:417
ReturnType operator()(size_t i, size_t j) const
2D-access to the matrix elements.
Definition: DMatDMatSchurExpr.h:478
#define BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE(T)
Constraint on the data type.In case the given data type T is not a dense, N-dimensional matrix type...
Definition: DenseMatrix.h:61
CompositeType_< MT2 > CT2
Composite type of the right-hand side dense matrix expression.
Definition: DMatDMatSchurExpr.h:119
Availability of a SIMD multiplication for the given data types.Depending on the available instruction...
Definition: HasSIMDMult.h:172
bool operator<=(const ConstIterator &rhs) const
Less-than comparison between two ConstIterator objects.
Definition: DMatDMatSchurExpr.h:371
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
IfTrue_< useAssign, const ResultType, const DMatDMatSchurExpr &> CompositeType
Data type for composite expression templates.
Definition: DMatDMatSchurExpr.h:183
Header file for the Computation base class.
ConstIterator_< MT1 > LeftIteratorType
ConstIterator type of the left-hand side dense matrix expression.
Definition: DMatDMatSchurExpr.h:213
Compile time check for upper triangular matrices.This type trait tests whether or not the given templ...
Definition: IsUpper.h:87
Header file for the RequiresEvaluation type trait.
If_< IsExpression< MT1 >, const MT1, const MT1 &> LeftOperand
Composite type of the left-hand side dense matrix expression.
Definition: DMatDMatSchurExpr.h:186
ElementType_< MT1 > ET1
Element type of the left-hand side dense matrix expression.
Definition: DMatDMatSchurExpr.h:120
ConstIterator_< MT2 > RightIteratorType
ConstIterator type of the right-hand side dense matrix expression.
Definition: DMatDMatSchurExpr.h:216
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
#define BLAZE_CONSTRAINT_MUST_FORM_VALID_SCHUREXPR(T1, T2)
Constraint on the data type.In case the given data types T1 and T2 do not form a valid matrix/matrix ...
Definition: SchurExpr.h:107
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
Header file for all forward declarations for sparse vectors and matrices.
size_t columns() const noexcept
Returns the current number of columns of the matrix.
Definition: DMatDMatSchurExpr.h:557
ReturnType at(size_t i, size_t j) const
Checked access to the matrix elements.
Definition: DMatDMatSchurExpr.h:493
typename IfTrue< Condition, T1, T2 >::Type IfTrue_
Auxiliary alias declaration for the IfTrue class template.The IfTrue_ alias declaration provides a co...
Definition: If.h:109
typename T::ReturnType ReturnType_
Alias declaration for nested ReturnType type definitions.The ReturnType_ alias declaration provides a...
Definition: Aliases.h:363
ConstIterator & operator--()
Pre-decrement operator.
Definition: DMatDMatSchurExpr.h:284
Compile time check for the alignment of data types.This type trait tests whether the given data type ...
Definition: IsAligned.h:87
Constraint on the data type.
If_< IsExpression< MT2 >, const MT2, const MT2 &> RightOperand
Composite type of the right-hand side dense matrix expression.
Definition: DMatDMatSchurExpr.h:189
Header file for the Maximum class template.
typename MultExprTrait< T1, T2 >::Type MultExprTrait_
Auxiliary alias declaration for the MultExprTrait class template.The MultExprTrait_ alias declaration...
Definition: MultExprTrait.h:112
Header file for the MultExprTrait class template.
Compile time check to query the requirement to evaluate an expression.Via this type trait it is possi...
Definition: RequiresEvaluation.h:71
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
bool operator>(const ConstIterator &rhs) const
Greater-than comparison between two ConstIterator objects.
Definition: DMatDMatSchurExpr.h:360
DifferenceType operator-(const ConstIterator &rhs) const
Calculating the number of elements between two iterators.
Definition: DMatDMatSchurExpr.h:393
Efficient implementation of an identity matrix.The IdentityMatrix class template is the representati...
Definition: Forward.h:49
Header file for the DisableIf class template.
Header file for the IsTemporary type trait class.
IteratorCategory iterator_category
The iterator category.
Definition: DMatDMatSchurExpr.h:206
Header file for the multiplication trait.
Header file for the IsStrictlyUpper type trait.
Header file for the IsSymmetric type trait.
Namespace of the Blaze C++ math library.
Definition: Blaze.h:58
#define BLAZE_ALWAYS_INLINE
Platform dependent setup of an enforced inline keyword.
Definition: Inline.h:85
Header file for the If class template.
SchurTrait_< RT1, RT2 > ResultType
Result type for expression template evaluations.
Definition: DMatDMatSchurExpr.h:174
ReturnType operator*() const
Direct access to the element at the current iterator position.
Definition: DMatDMatSchurExpr.h:306
ElementType * PointerType
Pointer return type.
Definition: DMatDMatSchurExpr.h:201
Compile time check for data types with padding.This type trait tests whether the given data type empl...
Definition: IsPadded.h:76
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
ResultType_< MT1 > RT1
Result type of the left-hand side dense matrix expression.
Definition: DMatDMatSchurExpr.h:114
Header file for the DenseMatrix base class.
PointerType pointer
Pointer return type.
Definition: DMatDMatSchurExpr.h:208
const Element * ConstIterator
Iterator over constant elements.
Definition: CompressedMatrix.h:3085
bool operator<(const ConstIterator &rhs) const
Less-than comparison between two ConstIterator objects.
Definition: DMatDMatSchurExpr.h:349
typename T::ElementType ElementType_
Alias declaration for nested ElementType type definitions.The ElementType_ alias declaration provides...
Definition: Aliases.h:163
Header file for all SIMD functionality.
bool isAliased(const T *alias) const noexcept
Returns whether the expression is aliased with the given address alias.
Definition: DMatDMatSchurExpr.h:602
Header file for the IsOperation type trait class.
Header file for the IsLower type trait.
typename SchurTrait< T1, T2 >::Type SchurTrait_
Auxiliary alias declaration for the SchurTrait class template.The SchurTrait_ alias declaration provi...
Definition: SchurTrait.h:208
ConstIterator begin(size_t i) const
Returns an iterator to the first non-zero element of row i.
Definition: DMatDMatSchurExpr.h:526
Header file for the IsAligned type trait.
ReferenceType reference
Reference return type.
Definition: DMatDMatSchurExpr.h:209
bool operator>=(const ConstIterator &rhs) const
Greater-than comparison between two ConstIterator objects.
Definition: DMatDMatSchurExpr.h:382
Constraints on the storage order of matrix types.
Compile time check for symmetric matrices.This type trait tests whether or not the given template par...
Definition: IsSymmetric.h:85
ElementType & ReferenceType
Reference return type.
Definition: DMatDMatSchurExpr.h:202
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
friend const ConstIterator operator+(const ConstIterator &it, size_t inc)
Addition between a ConstIterator and an integral value.
Definition: DMatDMatSchurExpr.h:405
Constraint on the data type.
Expression object for dense matrix-dense matrix Schur products.The DMatDMatSchurExpr class represents...
Definition: DMatDMatSchurExpr.h:108
Header file for all forward declarations for expression class templates.
Header file for the EnableIf class template.
Header file for the IsStrictlyLower type trait.
Header file for the IsPadded type trait.
Compile time check for lower unitriangular matrices.This type trait tests whether or not the given te...
Definition: IsUniLower.h:86
ConstIterator & operator+=(size_t inc)
Addition assignment operator.
Definition: DMatDMatSchurExpr.h:237
TransposeType_< ResultType > TransposeType
Transpose type for expression template evaluations.
Definition: DMatDMatSchurExpr.h:176
Header file for the HasSIMDMult type trait.
Base class for all Schur product expression templates.The SchurExpr class serves as a tag for all exp...
Definition: SchurExpr.h:66
Header file for run time assertion macros.
const ConstIterator operator--(int)
Post-decrement operator.
Definition: DMatDMatSchurExpr.h:296
ConstIterator & operator++()
Pre-increment operator.
Definition: DMatDMatSchurExpr.h:262
const IfTrue_< returnExpr, ExprReturnType, ElementType > ReturnType
Return type for expression template evaluations.
Definition: DMatDMatSchurExpr.h:180
const ConstIterator operator++(int)
Post-increment operator.
Definition: DMatDMatSchurExpr.h:274
std::random_access_iterator_tag IteratorCategory
The iterator category.
Definition: DMatDMatSchurExpr.h:199
Header file for the SchurExpr base class.
typename If< T1, T2, T3 >::Type If_
Auxiliary alias declaration for the If class template.The If_ alias declaration provides a convenient...
Definition: If.h:154
ValueType value_type
Type of the underlying elements.
Definition: DMatDMatSchurExpr.h:207
SIMD characteristics of data types.The SIMDTrait class template provides the SIMD characteristics of ...
Definition: SIMDTrait.h:296
#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
LeftOperand lhs_
Left-hand side dense matrix of the Schur product expression.
Definition: DMatDMatSchurExpr.h:630
ConstIterator & operator-=(size_t dec)
Subtraction assignment operator.
Definition: DMatDMatSchurExpr.h:250
Compile time check for Hermitian matrices.This type trait tests whether or not the given template par...
Definition: IsHermitian.h:85
bool canSMPAssign() const noexcept
Returns whether the expression can be used in SMP assignments.
Definition: DMatDMatSchurExpr.h:622
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
ElementType ValueType
Type of the underlying elements.
Definition: DMatDMatSchurExpr.h:200
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
#define BLAZE_CONSTRAINT_MATRICES_MUST_HAVE_SAME_STORAGE_ORDER(T1, T2)
Constraint on the data type.In case either of the two given data types T1 or T2 is not a matrix type ...
Definition: StorageOrder.h:84
BLAZE_ALWAYS_INLINE auto load(size_t i, size_t j) const noexcept
Access to the SIMD elements of the matrix.
Definition: DMatDMatSchurExpr.h:511
ElementType_< ResultType > ElementType
Resulting element type.
Definition: DMatDMatSchurExpr.h:177
Compile time check for strictly lower triangular matrices.This type trait tests whether or not the gi...
Definition: IsStrictlyLower.h:86
typename T::ConstIterator ConstIterator_
Alias declaration for nested ConstIterator type definitions.The ConstIterator_ alias declaration prov...
Definition: Aliases.h:103
bool operator!=(const ConstIterator &rhs) const
Inequality comparison between two ConstIterator objects.
Definition: DMatDMatSchurExpr.h:338
bool operator==(const ConstIterator &rhs) const
Equality comparison between two ConstIterator objects.
Definition: DMatDMatSchurExpr.h:327
LeftOperand leftOperand() const noexcept
Returns the left-hand side dense matrix operand.
Definition: DMatDMatSchurExpr.h:567
Iterator over the elements of the dense matrix.
Definition: DMatDMatSchurExpr.h:195
Base class for all compute expression templates.The Computation class serves as a tag for all computa...
Definition: Computation.h:66
Compile time logical &#39;or&#39; evaluation.The Or alias declaration performs at compile time a logical &#39;or&#39;...
Definition: Or.h:76
Compile time evaluation of the size of vectors and matrices.The Size type trait evaluates the size of...
Definition: Size.h:80
ConstIterator(LeftIteratorType left, RightIteratorType right)
Constructor for the ConstIterator class.
Definition: DMatDMatSchurExpr.h:225
friend const ConstIterator operator-(const ConstIterator &it, size_t dec)
Subtraction between a ConstIterator and an integral value.
Definition: DMatDMatSchurExpr.h:429
Compile time logical &#39;and&#39; evaluation.The And alias declaration performs at compile time a logical &#39;a...
Definition: And.h:76
ConstIterator end(size_t i) const
Returns an iterator just past the last non-zero element of row i.
Definition: DMatDMatSchurExpr.h:537
OppositeType_< ResultType > OppositeType
Result type with opposite storage order for expression template evaluations.
Definition: DMatDMatSchurExpr.h:175
auto load() const noexcept
Access to the SIMD elements of the matrix.
Definition: DMatDMatSchurExpr.h:316
RightOperand rhs_
Right-hand side dense matrix of the Schur product expression.
Definition: DMatDMatSchurExpr.h:631
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.
ReturnType_< MT1 > RN1
Return type of the left-hand side dense matrix expression.
Definition: DMatDMatSchurExpr.h:116
void UNUSED_PARAMETER(const Args &...)
Suppression of unused parameter warnings.
Definition: Unused.h:81
bool canAlias(const T *alias) const noexcept
Returns whether the expression can alias with the given address alias.
Definition: DMatDMatSchurExpr.h:589
Header file for the IsHermitian type trait.
DMatDMatSchurExpr(const MT1 &lhs, const MT2 &rhs) noexcept
Constructor for the DMatDMatSchurExpr class.
Definition: DMatDMatSchurExpr.h:462
ResultType_< MT2 > RT2
Result type of the right-hand side dense matrix expression.
Definition: DMatDMatSchurExpr.h:115
System settings for the inline keywords.
Header file for the Size 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
ElementType_< MT2 > ET2
Element type of the right-hand side dense matrix expression.
Definition: DMatDMatSchurExpr.h:121
MultExprTrait_< RN1, RN2 > ExprReturnType
Expression return type for the subscript operator.
Definition: DMatDMatSchurExpr.h:134
Compile time check whether the given type is an expression template.This type trait class tests wheth...
Definition: IsExpression.h:95
Header file for the IsExpression type trait class.
Header file for the function trace functionality.
RightOperand rightOperand() const noexcept
Returns the right-hand side dense matrix operand.
Definition: DMatDMatSchurExpr.h:577
bool isAligned() const noexcept
Returns whether the operands of the expression are properly aligned in memory.
Definition: DMatDMatSchurExpr.h:612
LeftIteratorType left_
Iterator to the current left-hand side element.
Definition: DMatDMatSchurExpr.h:436
Constraint on the data type.