35 #ifndef _BLAZE_MATH_EXPRESSIONS_SMATSMATMULTEXPR_H_ 36 #define _BLAZE_MATH_EXPRESSIONS_SMATSMATMULTEXPR_H_ 107 template<
typename MT1
109 class SMatSMatMultExpr
110 :
public MatMatMultExpr< SparseMatrix< SMatSMatMultExpr<MT1,MT2>, false > >
111 ,
private Computation
138 template<
typename T1,
typename T2,
typename T3 >
139 struct CanExploitSymmetry {
153 template<
typename T1,
typename T2,
typename T3 >
154 struct IsEvaluationRequired {
155 enum :
bool { value = ( evaluateLeft || evaluateRight ) &&
156 !CanExploitSymmetry<T1,T2,T3>::value };
180 enum :
bool { smpAssignable = !evaluateLeft && MT1::smpAssignable &&
181 !evaluateRight && MT2::smpAssignable };
231 :(
lhs_.columns() ) ) );
235 const size_t n(
end - begin );
255 if( i >=
lhs_.rows() ) {
258 if( j >=
rhs_.columns() ) {
270 inline size_t rows() const noexcept {
281 return rhs_.columns();
290 inline constexpr
size_t nonZeros() const noexcept {
301 inline size_t nonZeros(
size_t i )
const noexcept {
333 template<
typename T >
334 inline bool canAlias(
const T* alias )
const noexcept {
335 return (
lhs_.isAliased( alias ) ||
rhs_.isAliased( alias ) );
345 template<
typename T >
346 inline bool isAliased(
const T* alias )
const noexcept {
347 return (
lhs_.isAliased( alias ) ||
rhs_.isAliased( alias ) );
357 return (
rows() *
columns() >= SMP_SMATSMATMULT_THRESHOLD );
380 template<
typename MT
400 SMatSMatMultExpr::selectAssignKernel( ~lhs, A, B );
418 template<
typename MT3
421 static inline void selectAssignKernel( MT3& C,
const MT4& A,
const MT5& B )
426 for(
size_t i=0UL; i<C.rows(); ++i ) {
427 const LeftIterator lend( A.end(i) );
428 for( LeftIterator lelem=A.begin(i); lelem!=lend; ++lelem ) {
429 const RightIterator rend( B.end( lelem->index() ) );
430 for( RightIterator relem=B.begin( lelem->index() ); relem!=rend; ++relem )
434 C(i,relem->index()) = lelem->value() * relem->value();
437 C(i,relem->index()) += lelem->value() * relem->value();
459 template<
typename MT >
481 size_t nonzeros( 0UL );
483 for(
size_t i=0UL; i<(~lhs).
rows(); ++i ) {
484 const LeftIterator lend( A.end(i) );
485 for( LeftIterator lelem=A.begin(i); lelem!=lend; ++lelem ) {
486 nonzeros += B.nonZeros( lelem->index() );
490 if( nonzeros > (~lhs).rows() * (~lhs).
columns() ) {
494 (~lhs).reserve( nonzeros );
501 size_t minIndex(
inf ), maxIndex( 0UL );
503 for(
size_t i=0UL; i<(~lhs).
rows(); ++i )
505 const LeftIterator lend( A.end(i) );
506 for( LeftIterator lelem=A.begin(i); lelem!=lend; ++lelem )
508 const RightIterator rend( B.end( lelem->index() ) );
509 for( RightIterator relem=B.begin( lelem->index() ); relem!=rend; ++relem )
511 if( !valid[relem->index()] ) {
512 values[relem->index()] = lelem->value() * relem->value();
513 valid [relem->index()] =
true;
514 indices[nonzeros] = relem->index();
516 if( relem->index() < minIndex ) minIndex = relem->index();
517 if( relem->index() > maxIndex ) maxIndex = relem->index();
520 values[relem->index()] += lelem->value() * relem->value();
531 if( ( nonzeros + nonzeros ) < ( maxIndex - minIndex ) )
533 std::sort( indices.
begin(), indices.
begin() + nonzeros );
535 for(
size_t j=0UL; j<nonzeros; ++j )
537 const size_t index( indices[j] );
539 (~lhs).append( i, index, values[index] );
540 reset( values[index] );
543 reset( valid[index] );
547 for(
size_t j=minIndex; j<=maxIndex; ++j )
550 (~lhs).append( i, j, values[j] );
563 (~lhs).finalize( i );
582 template<
typename MT >
597 (~lhs).reserve( tmp.nonZeros() );
618 template<
typename MT >
629 assign( ~lhs,
trans( rhs.lhs_ ) *
trans( rhs.rhs_ ) );
647 template<
typename MT
667 SMatSMatMultExpr::selectAddAssignKernel( ~lhs, A, B );
686 template<
typename MT3
689 static inline void selectAddAssignKernel( MT3& C,
const MT4& A,
const MT5& B )
694 for(
size_t i=0UL; i<C.rows(); ++i ) {
695 const LeftIterator lend( A.end(i) );
696 for( LeftIterator lelem=A.begin(i); lelem!=lend; ++lelem ) {
697 const RightIterator rend( B.end( lelem->index() ) );
698 for( RightIterator relem=B.begin( lelem->index() ); relem!=rend; ++relem ) {
699 C(i,relem->index()) += lelem->value() * relem->value();
722 template<
typename MT >
733 addAssign( ~lhs,
trans( rhs.lhs_ ) *
trans( rhs.rhs_ ) );
755 template<
typename MT
775 SMatSMatMultExpr::selectSubAssignKernel( ~lhs, A, B );
794 template<
typename MT3
797 static inline void selectSubAssignKernel( MT3& C,
const MT4& A,
const MT5& B )
802 for(
size_t i=0UL; i<C.rows(); ++i ) {
803 const LeftIterator lend( A.end(i) );
804 for( LeftIterator lelem=A.begin(i); lelem!=lend; ++lelem ) {
805 const RightIterator rend( B.end( lelem->index() ) );
806 for( RightIterator relem=B.begin( lelem->index() ); relem!=rend; ++relem ) {
807 C(i,relem->index()) -= lelem->value() * relem->value();
830 template<
typename MT >
841 subAssign( ~lhs,
trans( rhs.lhs_ ) *
trans( rhs.rhs_ ) );
863 template<
typename MT
877 schurAssign( ~lhs, tmp );
909 template<
typename MT
949 template<
typename MT >
981 template<
typename MT
1021 template<
typename MT >
1057 template<
typename MT
1097 template<
typename MT >
1130 template<
typename MT
1210 template<
typename MT1
1212 inline decltype(
auto)
1237 template<
typename MT1,
typename MT2 >
1238 struct Size< SMatSMatMultExpr<MT1,MT2>, 0UL >
1239 :
public Size<MT1,0UL>
1242 template<
typename MT1,
typename MT2 >
1243 struct Size< SMatSMatMultExpr<MT1,MT2>, 1UL >
1244 :
public Size<MT2,1UL>
1260 template<
typename MT1,
typename MT2 >
1261 struct IsLower< SMatSMatMultExpr<MT1,MT2> >
1262 :
public And< IsLower<MT1>, IsLower<MT2> >
1278 template<
typename MT1,
typename MT2 >
1279 struct IsUniLower< SMatSMatMultExpr<MT1,MT2> >
1280 :
public And< IsUniLower<MT1>, IsUniLower<MT2> >
1296 template<
typename MT1,
typename MT2 >
1298 :
public Or< And< IsStrictlyLower<MT1>, IsLower<MT2> >
1299 , And< IsStrictlyLower<MT2>, IsLower<MT1> > >
1315 template<
typename MT1,
typename MT2 >
1316 struct IsUpper< SMatSMatMultExpr<MT1,MT2> >
1317 :
public And< IsUpper<MT1>, IsUpper<MT2> >
1333 template<
typename MT1,
typename MT2 >
1334 struct IsUniUpper< SMatSMatMultExpr<MT1,MT2> >
1335 :
public And< IsUniUpper<MT1>, IsUniUpper<MT2> >
1351 template<
typename MT1,
typename MT2 >
1353 :
public Or< And< IsStrictlyUpper<MT1>, IsUpper<MT2> >
1354 , And< IsStrictlyUpper<MT2>, IsUpper<MT1> > >
ReturnType operator()(size_t i, size_t j) const
2D-access to the matrix elements.
Definition: SMatSMatMultExpr.h:205
decltype(auto) subvector(Vector< VT, TF > &, RSAs...)
Creating a view on a specific subvector of the given vector.
Definition: Subvector.h:329
#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.
decltype(auto) column(Matrix< MT, SO > &matrix, RCAs... args)
Creating a view on a specific column of the given matrix.
Definition: Column.h:131
Headerfile for the generic min algorithm.
Header file for the blaze::checked and blaze::unchecked instances.
bool canAlias(const T *alias) const noexcept
Returns whether the expression can alias with the given address alias.
Definition: SMatSMatMultExpr.h:334
RightOperand rhs_
Right-hand side sparse matrix of the multiplication expression.
Definition: SMatSMatMultExpr.h:364
Header file for the UNUSED_PARAMETER function template.
Header file for the IsUniUpper type trait.
EnableIf_< IsDenseMatrix< MT1 > > smpSchurAssign(Matrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs)
Default implementation of the SMP Schur product assignment of a matrix to dense matrix.
Definition: DenseMatrix.h:196
Compile time check for triangular matrix types.This type trait tests whether or not the given templat...
Definition: IsTriangular.h:86
Header file for basic type definitions.
If_< IsExpression< MT2 >, const MT2, const MT2 &> RightOperand
Composite type of the right-hand side sparse matrix expression.
Definition: SMatSMatMultExpr.h:175
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.
Header file for the IsDiagonal type trait.
BLAZE_ALWAYS_INLINE MT::Iterator begin(Matrix< MT, SO > &matrix, size_t i)
Returns an iterator to the first element of row/column i.
Definition: Matrix.h:364
Header file for the IsColumnMajorMatrix type trait.
void reset(const DiagonalProxy< MT > &proxy)
Resetting the represented element to the default initial values.
Definition: DiagonalProxy.h:588
Implementation of a dynamic vector with small vector optimization.The SmallVector class template is a...
Definition: SmallVector.h:80
constexpr Unchecked unchecked
Global Unchecked instance.The blaze::unchecked instance is an optional token for the creation of view...
Definition: Check.h:138
typename DisableIf< Condition, T >::Type DisableIf_
Auxiliary type for the DisableIf class template.The DisableIf_ alias declaration provides a convenien...
Definition: DisableIf.h:224
Header file for the And class template.
const ElementType_< MT > min(const DenseMatrix< MT, SO > &dm)
Returns the smallest element of the dense matrix.
Definition: DenseMatrix.h:1903
Compile time check for lower triangular matrices.This type trait tests whether or not the given templ...
Definition: IsLower.h:87
CompositeType_< MT2 > CT2
Composite type of the right-hand side sparse matrix expression.
Definition: SMatSMatMultExpr.h:118
OppositeType_< ResultType > OppositeType
Result type with opposite storage order for expression template evaluations.
Definition: SMatSMatMultExpr.h:165
typename MultTrait< T1, T2 >::Type MultTrait_
Auxiliary alias declaration for the MultTrait class template.The MultTrait_ alias declaration provide...
Definition: MultTrait.h:291
Header file for the Computation base class.
Header file for the MatMatMultExpr base class.
Compile time check for upper triangular matrices.This type trait tests whether or not the given templ...
Definition: IsUpper.h:87
bool isAliased(const T *alias) const noexcept
Returns whether the expression is aliased with the given address alias.
Definition: SMatSMatMultExpr.h:346
Constraints on the storage order of matrix types.
Header file for the RequiresEvaluation type trait.
Header file for the IsUniLower type trait.
typename T::ResultType ResultType_
Alias declaration for nested ResultType type definitions.The ResultType_ alias declaration provides a...
Definition: Aliases.h:343
const ElementType_< MT > max(const DenseMatrix< MT, SO > &dm)
Returns the largest element of the dense matrix.
Definition: DenseMatrix.h:1950
EnableIf_< IsDenseMatrix< MT1 > > smpAddAssign(Matrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs)
Default implementation of the SMP addition assignment of a matrix to a dense matrix.
Definition: DenseMatrix.h:133
size_t rows() const noexcept
Returns the current number of rows of the matrix.
Definition: SMatSMatMultExpr.h:270
Base class for dense matrices.The DenseMatrix class is a base class for all dense matrix classes...
Definition: DenseMatrix.h:80
Base class for sparse matrices.The SparseMatrix class is a base class for all sparse matrix classes...
Definition: Forward.h:129
RightOperand rightOperand() const noexcept
Returns the right-hand side sparse matrix operand.
Definition: SMatSMatMultExpr.h:322
Header file for the SparseMatrix base class.
Constraint on the data type.
Compile time check to query the requirement to evaluate an expression.Via this type trait it is possi...
Definition: RequiresEvaluation.h: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
Headerfile for the generic max algorithm.
Header file for the DisableIf class template.
LeftOperand lhs_
Left-hand side sparse matrix of the multiplication expression.
Definition: SMatSMatMultExpr.h:363
Header file for the multiplication trait.
Header file for the IsStrictlyUpper type trait.
Header file for the IsSymmetric type trait.
Namespace of the Blaze C++ math library.
Definition: Blaze.h:58
Header file for the If class template.
EnableIf_< IsDenseMatrix< MT1 > > smpAssign(Matrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs)
Default implementation of the SMP assignment of a matrix to a dense matrix.
Definition: DenseMatrix.h:102
Header file for the Or class template.
#define BLAZE_THROW_OUT_OF_RANGE(MESSAGE)
Macro for the emission of a std::out_of_range exception.This macro encapsulates the default way of Bl...
Definition: Exception.h:331
ReturnType at(size_t i, size_t j) const
Checked access to the matrix elements.
Definition: SMatSMatMultExpr.h:254
Numerical infinity for built-in data types.
typename T::ElementType ElementType_
Alias declaration for nested ElementType type definitions.The ElementType_ alias declaration provides...
Definition: Aliases.h:163
Header file for the IsLower type trait.
Compile time check for diagonal matrices.This type trait tests whether or not the given template para...
Definition: IsDiagonal.h:89
Header file for the IsTriangular type trait.
LeftOperand leftOperand() const noexcept
Returns the left-hand side sparse matrix operand.
Definition: SMatSMatMultExpr.h:312
Compile time check for symmetric matrices.This type trait tests whether or not the given template par...
Definition: IsSymmetric.h:85
Header file for the exception macros of the math module.
Compile time check for strictly upper triangular matrices.This type trait tests whether or not the gi...
Definition: IsStrictlyUpper.h:86
BLAZE_ALWAYS_INLINE MT::Iterator end(Matrix< MT, SO > &matrix, size_t i)
Returns an iterator just past the last element of row/column i.
Definition: Matrix.h:430
Constraint on the data type.
Header file for all forward declarations for expression class templates.
Header file for the EnableIf class template.
Header file for the IsStrictlyLower type trait.
size_t nonZeros(size_t i) const noexcept
Returns the number of non-zero elements in the specified row.
Definition: SMatSMatMultExpr.h:301
#define BLAZE_CONSTRAINT_MUST_FORM_VALID_MATMATMULTEXPR(T1, T2)
Constraint on the data type.In case the given data types T1 and T2 do not form a valid matrix/matrix ...
Definition: MatMatMultExpr.h:107
MultTrait_< RT1, RT2 > ResultType
Result type for expression template evaluations.
Definition: SMatSMatMultExpr.h:164
Compile time check for lower unitriangular matrices.This type trait tests whether or not the given te...
Definition: IsUniLower.h:86
Compile time check for resizable data types.This type trait tests whether the given data type is a re...
Definition: IsResizable.h:75
size_t columns() const noexcept
Returns the current number of columns of the matrix.
Definition: SMatSMatMultExpr.h:280
#define BLAZE_CONSTRAINT_MUST_NOT_BE_SYMMETRIC_MATRIX_TYPE(T)
Constraint on the data type.In case the given data type T is a symmetric matrix type, a compilation error is created.
Definition: Symmetric.h:79
#define BLAZE_CONSTRAINT_MUST_BE_ROW_MAJOR_MATRIX_TYPE(T)
Constraint on the data type.In case the given data type T is not a row-major dense or sparse matrix t...
Definition: RowMajorMatrix.h:61
Expression object for sparse matrix-sparse matrix multiplications.The SMatSMatMultExpr class represen...
Definition: Forward.h:117
SMatSMatMultExpr(const MT1 &lhs, const MT2 &rhs) noexcept
Constructor for the SMatSMatMultExpr class.
Definition: SMatSMatMultExpr.h:190
Header file for run time assertion macros.
Compile time check for column-major matrix types.This type trait tests whether or not the given templ...
Definition: IsColumnMajorMatrix.h:110
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
decltype(auto) row(Matrix< MT, SO > &, RRAs...)
Creating a view on a specific row of the given matrix.
Definition: Row.h:131
Header file for the reset shim.
#define BLAZE_FUNCTION_TRACE
Function trace macro.This macro can be used to reliably trace function calls. In case function tracin...
Definition: FunctionTrace.h:94
const ResultType CompositeType
Data type for composite expression templates.
Definition: SMatSMatMultExpr.h:169
Header file for the isDefault shim.
Base class for matrices.The Matrix class is a base class for all dense and sparse matrix classes with...
Definition: Forward.h:101
Constraint on the data type.
decltype(auto) serial(const DenseMatrix< MT, SO > &dm)
Forces the serial evaluation of the given dense matrix expression dm.
Definition: DMatSerialExpr.h: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
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
If_< IsExpression< MT1 >, const MT1, const MT1 &> LeftOperand
Composite type of the left-hand side sparse matrix expression.
Definition: SMatSMatMultExpr.h:172
Header file for the IsComputation type trait class.
Compile time logical 'or' evaluation.The Or alias declaration performs at compile time a logical 'or'...
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
const ElementType ReturnType
Return type for expression template evaluations.
Definition: SMatSMatMultExpr.h:168
TransposeType_< ResultType > TransposeType
Transpose type for expression template evaluations.
Definition: SMatSMatMultExpr.h:166
Iterator begin() noexcept
Returns an iterator to the first element of the small vector.
Definition: SmallVector.h:572
constexpr Infinity inf
Global Infinity instance.The blaze::inf instance can be used wherever a built-in data type is expecte...
Definition: Infinity.h:1073
CompositeType_< MT1 > CT1
Composite type of the left-hand side sparse matrix expression.
Definition: SMatSMatMultExpr.h:117
Compile time logical 'and' evaluation.The And alias declaration performs at compile time a logical 'a...
Definition: And.h:76
Header file for the SmallVector implementation.
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.
void UNUSED_PARAMETER(const Args &...)
Suppression of unused parameter warnings.
Definition: Unused.h:81
constexpr size_t nonZeros() const noexcept
Returns the number of non-zero elements in the sparse matrix.
Definition: SMatSMatMultExpr.h:290
Constraint on the data type.
ElementType_< ResultType > ElementType
Resulting element type.
Definition: SMatSMatMultExpr.h:167
Header file for the IsResizable type trait.
bool canSMPAssign() const noexcept
Returns whether the expression can be used in SMP assignments.
Definition: SMatSMatMultExpr.h:356
Header file for the Size type trait.
ResultType_< MT1 > RT1
Result type of the left-hand side sparse matrix expression.
Definition: SMatSMatMultExpr.h:115
Header file for the thresholds for matrix/vector and matrix/matrix multiplications.
#define BLAZE_INTERNAL_ASSERT(expr, msg)
Run time assertion macro for internal checks.In case of an invalid run time expression, the program execution is terminated. The BLAZE_INTERNAL_ASSERT macro can be disabled by setting the BLAZE_USER_ASSERTION flag to zero or by defining NDEBUG during the compilation.
Definition: Assert.h:101
#define BLAZE_CONSTRAINT_MUST_BE_SPARSE_MATRIX_TYPE(T)
Constraint on the data type.In case the given data type T is not a sparse, N-dimensional matrix type...
Definition: SparseMatrix.h:61
Header file for the IsExpression type trait class.
Header file for the function trace functionality.
ResultType_< MT2 > RT2
Result type of the right-hand side sparse matrix expression.
Definition: SMatSMatMultExpr.h:116