//=================================================================================================
/*!
//  \file blaze/math/expressions/DVecSVecMultExpr.h
//  \brief Header file for the dense vector/sparse vector multiplication expression
//
//  Copyright (C) 2013 Klaus Iglberger - All Rights Reserved
//
//  This file is part of the Blaze library. You can redistribute it and/or modify it under
//  the terms of the New (Revised) BSD License. Redistribution and use in source and binary
//  forms, with or without modification, are permitted provided that the following conditions
//  are met:
//
//  1. Redistributions of source code must retain the above copyright notice, this list of
//     conditions and the following disclaimer.
//  2. Redistributions in binary form must reproduce the above copyright notice, this list
//     of conditions and the following disclaimer in the documentation and/or other materials
//     provided with the distribution.
//  3. Neither the names of the Blaze development group nor the names of its contributors
//     may be used to endorse or promote products derived from this software without specific
//     prior written permission.
//
//  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
//  EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
//  OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
//  SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
//  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
//  TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
//  BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
//  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
//  ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
//  DAMAGE.
*/
//=================================================================================================

#ifndef _BLAZE_MATH_EXPRESSIONS_DVECSVECMULTEXPR_H_
#define _BLAZE_MATH_EXPRESSIONS_DVECSVECMULTEXPR_H_


//*************************************************************************************************
// Includes
//*************************************************************************************************

#include <iterator>
#include <blaze/math/constraints/DenseVector.h>
#include <blaze/math/constraints/RequiresEvaluation.h>
#include <blaze/math/constraints/SparseVector.h>
#include <blaze/math/constraints/TransposeFlag.h>
#include <blaze/math/constraints/VecVecMultExpr.h>
#include <blaze/math/expressions/Computation.h>
#include <blaze/math/expressions/Forward.h>
#include <blaze/math/expressions/SparseVector.h>
#include <blaze/math/expressions/VecVecMultExpr.h>
#include <blaze/math/shims/Reset.h>
#include <blaze/math/shims/Serial.h>
#include <blaze/math/sparse/ValueIndexPair.h>
#include <blaze/math/traits/MultExprTrait.h>
#include <blaze/math/traits/MultTrait.h>
#include <blaze/math/traits/SubvectorExprTrait.h>
#include <blaze/math/typetraits/IsExpression.h>
#include <blaze/math/typetraits/IsTemporary.h>
#include <blaze/math/typetraits/RequiresEvaluation.h>
#include <blaze/math/typetraits/Size.h>
#include <blaze/util/Assert.h>
#include <blaze/util/constraints/Reference.h>
#include <blaze/util/EnableIf.h>
#include <blaze/util/Exception.h>
#include <blaze/util/logging/FunctionTrace.h>
#include <blaze/util/mpl/Max.h>
#include <blaze/util/SelectType.h>
#include <blaze/util/Types.h>
#include <blaze/util/typetraits/RemoveReference.h>


namespace blaze {

//=================================================================================================
//
//  CLASS DVECSVECMULTEXPR
//
//=================================================================================================

//*************************************************************************************************
/*!\brief Expression object for dense vector-sparse vector multiplications.
// \ingroup sparse_vector_expression
//
// The DVecSVecMultExpr class represents the compile time expression for componentwise
// multiplications between a dense vector and a sparse vector.
*/
template< typename VT1  // Type of the left-hand side dense vector
        , typename VT2  // Type of the right-hand side sparse vector
        , bool TF >     // Transpose flag
class DVecSVecMultExpr : public SparseVector< DVecSVecMultExpr<VT1,VT2,TF>, TF >
                       , private VecVecMultExpr
                       , private Computation
{
 private:
   //**Type definitions****************************************************************************
   typedef typename VT1::ResultType     RT1;  //!< Result type of the left-hand side dense vector expression.
   typedef typename VT2::ResultType     RT2;  //!< Result type of the right-hand side sparse vector expression.
   typedef typename VT1::ReturnType     RN1;  //!< Return type of the left-hand side dense vector expression.
   typedef typename VT2::ReturnType     RN2;  //!< Return type of the right-hand side sparse vector expression.
   typedef typename VT1::CompositeType  CT1;  //!< Composite type of the left-hand side dense vector expression.
   typedef typename VT2::CompositeType  CT2;  //!< Composite type of the right-hand side sparse vector expression.
   typedef typename VT1::TransposeType  TT1;  //!< Transpose type of the left-hand side dense vector expression.
   typedef typename VT2::TransposeType  TT2;  //!< Transpose type of the right-hand side sparse vector expression.
   //**********************************************************************************************

   //**Return type evaluation**********************************************************************
   //! Compilation switch for the selection of the subscript operator return type.
   /*! The \a returnExpr compile time constant expression is a compilation switch for the
       selection of the \a ReturnType. If either vector operand returns a temporary vector
       or matrix, \a returnExpr will be set to \a false and the subscript operator will
       return it's result by value. Otherwise \a returnExpr will be set to \a true and
       the subscript operator may return it's result as an expression. */
   enum { returnExpr = !IsTemporary<RN1>::value && !IsTemporary<RN2>::value };

   //! Expression return type for the subscript operator.
   typedef typename MultExprTrait<RN1,RN2>::Type  ExprReturnType;
   //**********************************************************************************************

   //**Evaluation strategy*************************************************************************
   //! Compilation switch for the evaluation strategy of the multiplication expression.
   /*! The \a useAssign compile time constant expression represents a compilation switch for
       the evaluation strategy of the multiplication expression. In case either the dense or
       the sparse vector operand requires an intermediate evaluation, \a useAssign will be set
       to \a true and the multiplication expression will be evaluated via the \a assign function
       family. Otherwise \a useAssign will be set to \a false and the expression will be
       evaluated via the subscript operator. */
   enum { useAssign = ( RequiresEvaluation<VT1>::value || RequiresEvaluation<VT2>::value ) };

   /*! \cond BLAZE_INTERNAL */
   //! Helper structure for the explicit application of the SFINAE principle.
   template< typename VT >
   struct UseAssign {
      enum { value = useAssign };
   };
   /*! \endcond */
   //**********************************************************************************************

 public:
   //**Type definitions****************************************************************************
   typedef DVecSVecMultExpr<VT1,VT2,TF>        This;           //!< Type of this DVecSVecMultExpr instance.
   typedef typename MultTrait<RT1,RT2>::Type   ResultType;     //!< Result type for expression template evaluations.
   typedef typename ResultType::TransposeType  TransposeType;  //!< Transpose type for expression template evaluations.
   typedef typename ResultType::ElementType    ElementType;    //!< Resulting element type.

   //! Return type for expression template evaluations.
   typedef const typename SelectType< returnExpr, ExprReturnType, ElementType >::Type  ReturnType;

   //! Data type for composite expression templates.
   typedef typename SelectType< useAssign, const ResultType, const DVecSVecMultExpr& >::Type  CompositeType;

   //! Composite type of the left-hand side dense vector expression.
   typedef typename SelectType< IsExpression<VT1>::value, const VT1, const VT1& >::Type  LeftOperand;

   //! Composite type of the right-hand side sparse vector expression.
   typedef typename SelectType< IsExpression<VT2>::value, const VT2, const VT2& >::Type  RightOperand;
   //**********************************************************************************************

   //**Compilation flags***************************************************************************
   //! Compilation switch for the expression template assignment strategy.
   enum { smpAssignable = 0 };
   //**********************************************************************************************

   //**ConstIterator class definition**************************************************************
   /*!\brief Iterator over the elements of the dense vector-sparse vector multiplication expression.
   */
   class ConstIterator
   {
    public:
      //**Type definitions*************************************************************************
      //! Element type of the sparse vector expression.
      typedef ValueIndexPair<ElementType>  Element;

      //! Iterator type of the sparse vector expression.
      typedef typename RemoveReference<RightOperand>::Type::ConstIterator  IteratorType;

      typedef std::forward_iterator_tag  IteratorCategory;  //!< The iterator category.
      typedef Element                    ValueType;         //!< Type of the underlying pointers.
      typedef ValueType*                 PointerType;       //!< Pointer return type.
      typedef ValueType&                 ReferenceType;     //!< Reference return type.
      typedef ptrdiff_t                  DifferenceType;    //!< Difference between two iterators.

      // STL iterator requirements
      typedef IteratorCategory  iterator_category;  //!< The iterator category.
      typedef ValueType         value_type;         //!< Type of the underlying pointers.
      typedef PointerType       pointer;            //!< Pointer return type.
      typedef ReferenceType     reference;          //!< Reference return type.
      typedef DifferenceType    difference_type;    //!< Difference between two iterators.
      //*******************************************************************************************

      //**Constructor******************************************************************************
      /*!\brief Constructor for the ConstIterator class.
      */
      inline ConstIterator( LeftOperand vec, IteratorType it )
         : vec_( vec )  // Left-hand side dense vector expression
         , it_ ( it  )  // Iterator over the elements of the right-hand side sparse vector expression
      {}
      //*******************************************************************************************

      //**Prefix increment operator****************************************************************
      /*!\brief Pre-increment operator.
      //
      // \return Reference to the incremented expression iterator.
      */
      inline ConstIterator& operator++() {
         ++it_;
         return *this;
      }
      //*******************************************************************************************

      //**Element access operator******************************************************************
      /*!\brief Direct access to the sparse vector element at the current iterator position.
      //
      // \return The current value of the sparse element.
      */
      inline const Element operator*() const {
         return Element( vec_[it_->index()] * it_->value(), it_->index() );
      }
      //*******************************************************************************************

      //**Element access operator******************************************************************
      /*!\brief Direct access to the sparse vector element at the current iterator position.
      //
      // \return Reference to the sparse vector element at the current iterator position.
      */
      inline const ConstIterator* operator->() const {
         return this;
      }
      //*******************************************************************************************

      //**Value function***************************************************************************
      /*!\brief Access to the current value of the sparse element.
      //
      // \return The current value of the sparse element.
      */
      inline ReturnType value() const {
         return vec_[it_->index()] * it_->value();
      }
      //*******************************************************************************************

      //**Index function***************************************************************************
      /*!\brief Access to the current index of the sparse element.
      //
      // \return The current index of the sparse element.
      */
      inline size_t index() const {
         return it_->index();
      }
      //*******************************************************************************************

      //**Equality operator************************************************************************
      /*!\brief Equality comparison between two ConstIterator objects.
      //
      // \param rhs The right-hand side expression iterator.
      // \return \a true if the iterators refer to the same element, \a false if not.
      */
      inline bool operator==( const ConstIterator& rhs ) const {
         return it_ == rhs.it_;
      }
      //*******************************************************************************************

      //**Inequality operator**********************************************************************
      /*!\brief Inequality comparison between two ConstIterator objects.
      //
      // \param rhs The right-hand side expression iterator.
      // \return \a true if the iterators don't refer to the same element, \a false if they do.
      */
      inline bool operator!=( const ConstIterator& rhs ) const {
         return it_ != rhs.it_;
      }
      //*******************************************************************************************

      //**Subtraction operator*********************************************************************
      /*!\brief Calculating the number of elements between two expression iterators.
      //
      // \param rhs The right-hand side expression iterator.
      // \return The number of elements between the two expression iterators.
      */
      inline DifferenceType operator-( const ConstIterator& rhs ) const {
         return it_ - rhs.it_;
      }
      //*******************************************************************************************

    private:
      //**Member variables*************************************************************************
      LeftOperand vec_;  //!< Left-hand side dense vector expression.
      IteratorType it_;  //!< Iterator over the elements of the right-hand side sparse vector expression.
      //*******************************************************************************************
   };
   //**********************************************************************************************

   //**Constructor*********************************************************************************
   /*!\brief Constructor for the DVecSVecMultExpr class.
   //
   // \param lhs The left-hand side dense vector operand of the multiplication expression.
   // \param rhs The right-hand side sparse vector operand of the multiplication expression.
   */
   explicit inline DVecSVecMultExpr( const VT1& lhs, const VT2& rhs )
      : lhs_( lhs )  // Left-hand side dense vector of the multiplication expression
      , rhs_( rhs )  // Right-hand side sparse vector of the multiplication expression
   {
      BLAZE_INTERNAL_ASSERT( lhs.size() == rhs.size(), "Invalid vector sizes" );
   }
   //**********************************************************************************************

   //**Subscript operator**************************************************************************
   /*!\brief Subscript operator for the direct access to the vector elements.
   //
   // \param index Access index. The index has to be in the range \f$[0..N-1]\f$.
   // \return The resulting value.
   */
   inline ReturnType operator[]( size_t index ) const {
      BLAZE_INTERNAL_ASSERT( index < lhs_.size(), "Invalid vector access index" );
      return lhs_[index] * rhs_[index];
   }
   //**********************************************************************************************

   //**At function*********************************************************************************
   /*!\brief Checked access to the vector elements.
   //
   // \param index Access index. The index has to be in the range \f$[0..N-1]\f$.
   // \return The resulting value.
   // \exception std::out_of_range Invalid vector access index.
   */
   inline ReturnType at( size_t index ) const {
      if( index >= lhs_.size() ) {
         BLAZE_THROW_OUT_OF_RANGE( "Invalid vector access index" );
      }
      return (*this)[index];
   }
   //**********************************************************************************************

   //**Begin function******************************************************************************
   /*!\brief Returns an iterator to the first non-zero element of the sparse vector.
   //
   // \return Iterator to the first non-zero element of the sparse vector.
   */
   inline ConstIterator begin() const {
      return ConstIterator( lhs_, rhs_.begin() );
   }
   //**********************************************************************************************

   //**End function********************************************************************************
   /*!\brief Returns an iterator just past the last non-zero element of the sparse vector.
   //
   // \return Iterator just past the last non-zero element of the sparse vector.
   */
   inline ConstIterator end() const {
      return ConstIterator( lhs_, rhs_.end() );
   }
   //**********************************************************************************************

   //**Size function*******************************************************************************
   /*!\brief Returns the current size/dimension of the vector.
   //
   // \return The size of the vector.
   */
   inline size_t size() const {
      return lhs_.size();
   }
   //**********************************************************************************************

   //**NonZeros function***************************************************************************
   /*!\brief Returns the number of non-zero elements in the sparse vector.
   //
   // \return The number of non-zero elements in the sparse vector.
   */
   inline size_t nonZeros() const {
      return rhs_.nonZeros();
   }
   //**********************************************************************************************

   //**Find function*******************************************************************************
   /*!\brief Searches for a specific vector element.
   //
   // \param index The index of the search element.
   // \return Iterator to the element in case the index is found, end() iterator otherwise.
   */
   inline ConstIterator find( size_t index ) const {
      BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION( VT2 );
      return ConstIterator( lhs_, rhs_.find( index ) );
   }
   //**********************************************************************************************

   //**LowerBound function*************************************************************************
   /*!\brief Returns an iterator to the first index not less then the given index.
   //
   // \param index The index of the search element.
   // \return Iterator to the first index not less then the given index, end() iterator otherwise.
   */
   inline ConstIterator lowerBound( size_t index ) const {
      BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION( VT2 );
      return ConstIterator( lhs_, rhs_.lowerBound( index ) );
   }
   //**********************************************************************************************

   //**UpperBound function*************************************************************************
   /*!\brief Returns an iterator to the first index greater then the given index.
   //
   // \param index The index of the search element.
   // \return Iterator to the first index greater then the given index, end() iterator otherwise.
   */
   inline ConstIterator upperBound( size_t index ) const {
      BLAZE_CONSTRAINT_MUST_NOT_REQUIRE_EVALUATION( VT2 );
      return ConstIterator( lhs_, rhs_.upperBound( index ) );
   }
   //**********************************************************************************************

   //**Left operand access*************************************************************************
   /*!\brief Returns the left-hand side dense vector operand.
   //
   // \return The left-hand side dense vector operand.
   */
   inline LeftOperand leftOperand() const {
      return lhs_;
   }
   //**********************************************************************************************

   //**Right operand access************************************************************************
   /*!\brief Returns the right-hand side sparse vector operand.
   //
   // \return The right-hand side sparse vector operand.
   */
   inline RightOperand rightOperand() const {
      return rhs_;
   }
   //**********************************************************************************************

   //**********************************************************************************************
   /*!\brief Returns whether the expression can alias with the given address \a alias.
   //
   // \param alias The alias to be checked.
   // \return \a true in case the expression can alias, \a false otherwise.
   */
   template< typename T >
   inline bool canAlias( const T* alias ) const {
      return ( lhs_.canAlias( alias ) || rhs_.canAlias( alias ) );
   }
   //**********************************************************************************************

   //**********************************************************************************************
   /*!\brief Returns whether the expression is aliased with the given address \a alias.
   //
   // \param alias The alias to be checked.
   // \return \a true in case an alias effect is detected, \a false otherwise.
   */
   template< typename T >
   inline bool isAliased( const T* alias ) const {
      return ( lhs_.isAliased( alias ) || rhs_.isAliased( alias ) );
   }
   //**********************************************************************************************

 private:
   //**Member variables****************************************************************************
   LeftOperand  lhs_;  //!< Left-hand side dense vector of the multiplication expression.
   RightOperand rhs_;  //!< Right-hand side sparse vector of the multiplication expression.
   //**********************************************************************************************

   //**Assignment to dense vectors*****************************************************************
   /*! \cond BLAZE_INTERNAL */
   /*!\brief Assignment of a dense vector-sparse vector multiplication to a dense vector.
   // \ingroup sparse_vector
   //
   // \param lhs The target left-hand side dense vector.
   // \param rhs The right-hand side multiplication expression to be assigned.
   // \return void
   //
   // This function implements the performance optimized assignment of a dense vector-sparse
   // vector multiplication expression to a dense vector. Due to the explicit application of
   // the SFINAE principle, this function can only be selected by the compiler in case either
   // of the two operands requires an intermediate evaluation.
   */
   template< typename VT >  // Type of the target dense vector
   friend inline typename EnableIf< UseAssign<VT> >::Type
      assign( DenseVector<VT,TF>& lhs, const DVecSVecMultExpr& rhs )
   {
      BLAZE_FUNCTION_TRACE;

      BLAZE_INTERNAL_ASSERT( (~lhs).size() == rhs.size(), "Invalid vector sizes" );

      typedef typename RemoveReference<CT2>::Type::ConstIterator  ConstIterator;

      CT1 x( serial( rhs.lhs_ ) );  // Evaluation of the left-hand side dense vector operand
      CT2 y( serial( rhs.rhs_ ) );  // Evaluation of the right-hand side sparse vector operand

      BLAZE_INTERNAL_ASSERT( x.size() == rhs.lhs_.size(), "Invalid vector size" );
      BLAZE_INTERNAL_ASSERT( y.size() == rhs.rhs_.size(), "Invalid vector size" );
      BLAZE_INTERNAL_ASSERT( x.size() == (~lhs).size()  , "Invalid vector size" );

      for( ConstIterator element=y.begin(); element!=y.end(); ++element )
         (~lhs)[element->index()] = x[element->index()] * element->value();
   }
   /*! \endcond */
   //**********************************************************************************************

   //**Assignment to sparse vectors****************************************************************
   /*! \cond BLAZE_INTERNAL */
   /*!\brief Assignment of a dense vector-sparse vector multiplication to a sparse vector.
   // \ingroup sparse_vector
   //
   // \param lhs The target left-hand side sparse vector.
   // \param rhs The right-hand side multiplication expression to be assigned.
   // \return void
   //
   // This function implements the performance optimized assignment of a dense vector-sparse
   // vector multiplication expression to a sparse vector. Due to the explicit application of
   // the SFINAE principle, this function can only be selected by the compiler in case either
   // of the two operands requires an intermediate evaluation.
   */
   template< typename VT >  // Type of the target sparse vector
   friend inline typename EnableIf< UseAssign<VT> >::Type
      assign( SparseVector<VT,TF>& lhs, const DVecSVecMultExpr& rhs )
   {
      BLAZE_FUNCTION_TRACE;

      BLAZE_INTERNAL_ASSERT( (~lhs).size() == rhs.size(), "Invalid vector sizes" );

      typedef typename RemoveReference<CT2>::Type::ConstIterator  ConstIterator;

      CT1 x( serial( rhs.lhs_ ) );  // Evaluation of the left-hand side dense vector operand
      CT2 y( serial( rhs.rhs_ ) );  // Evaluation of the right-hand side sparse vector operand

      BLAZE_INTERNAL_ASSERT( x.size() == rhs.lhs_.size(), "Invalid vector size" );
      BLAZE_INTERNAL_ASSERT( y.size() == rhs.rhs_.size(), "Invalid vector size" );
      BLAZE_INTERNAL_ASSERT( x.size() == (~lhs).size()  , "Invalid vector size" );

      for( ConstIterator element=y.begin(); element!=y.end(); ++element )
         (~lhs).append( element->index(), x[element->index()] * element->value() );
   }
   /*! \endcond */
   //**********************************************************************************************

   //**Addition assignment to dense vectors********************************************************
   /*! \cond BLAZE_INTERNAL */
   /*!\brief Addition assignment of a dense vector-sparse vector multiplication to a dense vector.
   // \ingroup sparse_vector
   //
   // \param lhs The target left-hand side dense vector.
   // \param rhs The right-hand side multiplication expression to be added.
   // \return void
   //
   // This function implements the performance optimized addition assignment of a dense vector-
   // sparse vector multiplication expression to a dense vector. Due to the explicit application
   // of the SFINAE principle, this function can only be selected by the compiler in case either
   // of the two operands requires an intermediate evaluation.
   */
   template< typename VT >  // Type of the target dense vector
   friend inline typename EnableIf< UseAssign<VT> >::Type
      addAssign( DenseVector<VT,TF>& lhs, const DVecSVecMultExpr& rhs )
   {
      BLAZE_FUNCTION_TRACE;

      BLAZE_INTERNAL_ASSERT( (~lhs).size() == rhs.size(), "Invalid vector sizes" );

      typedef typename RemoveReference<CT2>::Type::ConstIterator  ConstIterator;

      CT1 x( serial( rhs.lhs_ ) );  // Evaluation of the left-hand side dense vector operand
      CT2 y( serial( rhs.rhs_ ) );  // Evaluation of the right-hand side sparse vector operand

      BLAZE_INTERNAL_ASSERT( x.size() == rhs.lhs_.size(), "Invalid vector size" );
      BLAZE_INTERNAL_ASSERT( y.size() == rhs.rhs_.size(), "Invalid vector size" );
      BLAZE_INTERNAL_ASSERT( x.size() == (~lhs).size()  , "Invalid vector size" );

      for( ConstIterator element=y.begin(); element!=y.end(); ++element )
         (~lhs)[element->index()] += x[element->index()] * element->value();
   }
   /*! \endcond */
   //**********************************************************************************************

   //**Addition assignment to sparse vectors*******************************************************
   // No special implementation for the addition assignment to sparse vectors.
   //**********************************************************************************************

   //**Subtraction assignment to dense vectors*****************************************************
   /*! \cond BLAZE_INTERNAL */
   /*!\brief Subtraction assignment of a dense vector-sparse vector multiplication to a dense vector.
   // \ingroup sparse_vector
   //
   // \param lhs The target left-hand side dense vector.
   // \param rhs The right-hand side multiplication expression to be subtracted.
   // \return void
   //
   // This function implements the performance optimized subtraction assignment of a dense vector-
   // sparse vector multiplication expression to a dense vector. Due to the explicit application
   // of the SFINAE principle, this function can only be selected by the compiler in case either
   // of the two operands requires an intermediate evaluation.
   */
   template< typename VT >  // Type of the target dense vector
   friend inline typename EnableIf< UseAssign<VT> >::Type
      subAssign( DenseVector<VT,TF>& lhs, const DVecSVecMultExpr& rhs )
   {
      BLAZE_FUNCTION_TRACE;

      BLAZE_INTERNAL_ASSERT( (~lhs).size() == rhs.size(), "Invalid vector sizes" );

      typedef typename RemoveReference<CT2>::Type::ConstIterator  ConstIterator;

      CT1 x( serial( rhs.lhs_ ) );  // Evaluation of the left-hand side dense vector operand
      CT2 y( serial( rhs.rhs_ ) );  // Evaluation of the right-hand side sparse vector operand

      BLAZE_INTERNAL_ASSERT( x.size() == rhs.lhs_.size(), "Invalid vector size" );
      BLAZE_INTERNAL_ASSERT( y.size() == rhs.rhs_.size(), "Invalid vector size" );
      BLAZE_INTERNAL_ASSERT( x.size() == (~lhs).size()  , "Invalid vector size" );

      for( ConstIterator element=y.begin(); element!=y.end(); ++element )
         (~lhs)[element->index()] -= x[element->index()] * element->value();
   }
   /*! \endcond */
   //**********************************************************************************************

   //**Subtraction assignment to sparse vectors****************************************************
   // No special implementation for the subtraction assignment to sparse vectors.
   //**********************************************************************************************

   //**Multiplication assignment to dense vectors**************************************************
   /*! \cond BLAZE_INTERNAL */
   /*!\brief Multiplication assignment of a dense vector-sparse vector multiplication to a dense vector.
   // \ingroup sparse_vector
   //
   // \param lhs The target left-hand side dense vector.
   // \param rhs The right-hand side multiplication expression to be multiplied.
   // \return void
   //
   // This function implements the performance optimized multiplication assignment of a dense
   // vector-sparse vector multiplication expression to a dense vector. Due to the explicit
   // application of the SFINAE principle, this function can only be selected by the compiler
   // in case either of the two operands requires an intermediate evaluation.
   */
   template< typename VT >  // Type of the target dense vector
   friend inline typename EnableIf< UseAssign<VT> >::Type
      multAssign( DenseVector<VT,TF>& lhs, const DVecSVecMultExpr& rhs )
   {
      BLAZE_FUNCTION_TRACE;

      BLAZE_INTERNAL_ASSERT( (~lhs).size() == rhs.size(), "Invalid vector sizes" );

      typedef typename RemoveReference<CT2>::Type::ConstIterator  ConstIterator;

      CT1 x( serial( rhs.lhs_ ) );  // Evaluation of the left-hand side dense vector operand
      CT2 y( serial( rhs.rhs_ ) );  // Evaluation of the right-hand side sparse vector operand

      BLAZE_INTERNAL_ASSERT( x.size() == rhs.lhs_.size(), "Invalid vector size" );
      BLAZE_INTERNAL_ASSERT( y.size() == rhs.rhs_.size(), "Invalid vector size" );
      BLAZE_INTERNAL_ASSERT( x.size() == (~lhs).size()  , "Invalid vector size" );

      const ConstIterator end( y.end() );
      ConstIterator begin( y.begin() );
      size_t i( 0UL );

      for( ; begin!=end; ++begin ) {
         const size_t index( begin->index() );
         for( ; i<index; ++i )
            reset( (~lhs)[i] );
         (~lhs)[index] *= x[index] * begin->value();
         ++i;
      }

      for( ; i<(~lhs).size(); ++i )
         reset( (~lhs)[i] );
   }
   /*! \endcond */
   //**********************************************************************************************

   //**Multiplication assignment to sparse vectors*************************************************
   // No special implementation for the multiplication assignment to sparse vectors.
   //**********************************************************************************************

   //**Compile time checks*************************************************************************
   /*! \cond BLAZE_INTERNAL */
   BLAZE_CONSTRAINT_MUST_BE_DENSE_VECTOR_TYPE ( VT1 );
   BLAZE_CONSTRAINT_MUST_BE_SPARSE_VECTOR_TYPE( VT2 );
   BLAZE_CONSTRAINT_MUST_BE_VECTOR_WITH_TRANSPOSE_FLAG( VT1, TF );
   BLAZE_CONSTRAINT_MUST_BE_VECTOR_WITH_TRANSPOSE_FLAG( VT2, TF );
   BLAZE_CONSTRAINT_MUST_FORM_VALID_VECVECMULTEXPR( VT1, VT2 );
   /*! \endcond */
   //**********************************************************************************************
};
//*************************************************************************************************




//=================================================================================================
//
//  GLOBAL BINARY ARITHMETIC OPERATORS
//
//=================================================================================================

//*************************************************************************************************
/*!\brief Multiplication operator for the componentwise product of a dense vector and a sparse
//        vector (\f$ \vec{a}=\vec{b}*\vec{c} \f$).
// \ingroup sparse_vector
//
// \param lhs The left-hand side dense vector for the component product.
// \param rhs The right-hand side sparse vector for the component product.
// \return The product of the two vectors.
// \exception std::invalid_argument Vector sizes do not match.
//
// This operator represents the componentwise multiplication of a dense vector and a sparse
// vector:

   \code
   blaze::DynamicVector<double> a;
   blaze::CompressedVector<double> b, c;
   // ... Resizing and initialization
   c = a * b;
   \endcode

// The operator returns an expression representing a sparse vector of the higher-order element
// type of the two involved vector element types \a T1::ElementType and \a T2::ElementType.
// Both vector types \a T1 and \a T2 as well as the two element types \a T1::ElementType and
// \a T2::ElementType have to be supported by the MultTrait class template.\n
// In case the current sizes of the two given vectors don't match, a \a std::invalid_argument
// is thrown.
*/
template< typename T1  // Type of the left-hand side dense vector
        , typename T2  // Type of the right-hand side sparse vector
        , bool TF >    // Transpose flag
inline const DVecSVecMultExpr<T1,T2,TF>
   operator*( const DenseVector<T1,TF>& lhs, const SparseVector<T2,TF>& rhs )
{
   BLAZE_FUNCTION_TRACE;

   if( (~lhs).size() != (~rhs).size() ) {
      BLAZE_THROW_INVALID_ARGUMENT( "Vector sizes do not match" );
   }

   return DVecSVecMultExpr<T1,T2,TF>( ~lhs, ~rhs );
}
//*************************************************************************************************




//=================================================================================================
//
//  SIZE SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename VT1, typename VT2, bool TF >
struct Size< DVecSVecMultExpr<VT1,VT2,TF> >
   : public Max< Size<VT1>, Size<VT2> >
{};
/*! \endcond */
//*************************************************************************************************




//=================================================================================================
//
//  EXPRESSION TRAIT SPECIALIZATIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
template< typename VT1, typename VT2, bool TF, bool AF >
struct SubvectorExprTrait< DVecSVecMultExpr<VT1,VT2,TF>, AF >
{
 public:
   //**********************************************************************************************
   typedef typename MultExprTrait< typename SubvectorExprTrait<const VT1,AF>::Type
                                 , typename SubvectorExprTrait<const VT2,AF>::Type >::Type  Type;
   //**********************************************************************************************
};
/*! \endcond */
//*************************************************************************************************

} // namespace blaze

#endif
