text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
  // Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
  //
  // This Source Code Form is subject to the terms of the Mozilla
  // Public License v. 2.0. If a copy of the MPL was not distributed
  // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
  
  #ifndef EIGEN_GENERAL_PRODUCT_H
  #define EIGEN_GENERAL_PRODUCT_H
  
  namespace Eigen { 
  
  /** \class GeneralProduct
    * \ingroup Core_Module
    *
    * \brief Expression of the product of two general matrices or vectors
    *
    * \param LhsNested the type used to store the left-hand side
    * \param RhsNested the type used to store the right-hand side
    * \param ProductMode the type of the product
    *
    * This class represents an expression of the product of two general matrices.
    * We call a general matrix, a dense matrix with full storage. For instance,
    * This excludes triangular, selfadjoint, and sparse matrices.
    * It is the return type of the operator* between general matrices. Its template
    * arguments are determined automatically by ProductReturnType. Therefore,
    * GeneralProduct should never be used direclty. To determine the result type of a
    * function which involves a matrix product, use ProductReturnType::Type.
    *
    * \sa ProductReturnType, MatrixBase::operator*(const MatrixBase<OtherDerived>&)
    */
  template<typename Lhs, typename Rhs, int ProductType = internal::product_type<Lhs,Rhs>::value>
  class GeneralProduct;
  
  enum {
    Large = 2,
    Small = 3
  };
  
  namespace internal {
  
  template<int Rows, int Cols, int Depth> struct product_type_selector;
  
  template<int Size, int MaxSize> struct product_size_category
  {
    enum { is_large = MaxSize == Dynamic ||
                      Size >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD,
           value = is_large  ? Large
                 : Size == 1 ? 1
                             : Small
    };
  };
  
  template<typename Lhs, typename Rhs> struct product_type
  {
    typedef typename remove_all<Lhs>::type _Lhs;
    typedef typename remove_all<Rhs>::type _Rhs;
    enum {
      MaxRows  = _Lhs::MaxRowsAtCompileTime,
      Rows  = _Lhs::RowsAtCompileTime,
      MaxCols  = _Rhs::MaxColsAtCompileTime,
      Cols  = _Rhs::ColsAtCompileTime,
      MaxDepth = EIGEN_SIZE_MIN_PREFER_FIXED(_Lhs::MaxColsAtCompileTime,
                                             _Rhs::MaxRowsAtCompileTime),
      Depth = EIGEN_SIZE_MIN_PREFER_FIXED(_Lhs::ColsAtCompileTime,
                                          _Rhs::RowsAtCompileTime),
      LargeThreshold = EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
    };
  
    // the splitting into different lines of code here, introducing the _select enums and the typedef below,
    // is to work around an internal compiler error with gcc 4.1 and 4.2.
  private:
    enum {
      rows_select = product_size_category<Rows,MaxRows>::value,
      cols_select = product_size_category<Cols,MaxCols>::value,
      depth_select = product_size_category<Depth,MaxDepth>::value
    };
    typedef product_type_selector<rows_select, cols_select, depth_select> selector;
  
  public:
    enum {
      value = selector::ret
    };
  #ifdef EIGEN_DEBUG_PRODUCT
    static void debug()
    {
        EIGEN_DEBUG_VAR(Rows);
        EIGEN_DEBUG_VAR(Cols);
        EIGEN_DEBUG_VAR(Depth);
        EIGEN_DEBUG_VAR(rows_select);
        EIGEN_DEBUG_VAR(cols_select);
        EIGEN_DEBUG_VAR(depth_select);
        EIGEN_DEBUG_VAR(value);
    }
  #endif
  };
  
  
  /* The following allows to select the kind of product at compile time
   * based on the three dimensions of the product.
   * This is a compile time mapping from {1,Small,Large}^3 -> {product types} */
  // FIXME I'm not sure the current mapping is the ideal one.
  template<int M, int N>  struct product_type_selector<M,N,1>              { enum { ret = OuterProduct }; };
  template<int Depth>     struct product_type_selector<1,    1,    Depth>  { enum { ret = InnerProduct }; };
  template<>              struct product_type_selector<1,    1,    1>      { enum { ret = InnerProduct }; };
  template<>              struct product_type_selector<Small,1,    Small>  { enum { ret = CoeffBasedProductMode }; };
  template<>              struct product_type_selector<1,    Small,Small>  { enum { ret = CoeffBasedProductMode }; };
  template<>              struct product_type_selector<Small,Small,Small>  { enum { ret = CoeffBasedProductMode }; };
  template<>              struct product_type_selector<Small, Small, 1>    { enum { ret = LazyCoeffBasedProductMode }; };
  template<>              struct product_type_selector<Small, Large, 1>    { enum { ret = LazyCoeffBasedProductMode }; };
  template<>              struct product_type_selector<Large, Small, 1>    { enum { ret = LazyCoeffBasedProductMode }; };
  template<>              struct product_type_selector<1,    Large,Small>  { enum { ret = CoeffBasedProductMode }; };
  template<>              struct product_type_selector<1,    Large,Large>  { enum { ret = GemvProduct }; };
  template<>              struct product_type_selector<1,    Small,Large>  { enum { ret = CoeffBasedProductMode }; };
  template<>              struct product_type_selector<Large,1,    Small>  { enum { ret = CoeffBasedProductMode }; };
  template<>              struct product_type_selector<Large,1,    Large>  { enum { ret = GemvProduct }; };
  template<>              struct product_type_selector<Small,1,    Large>  { enum { ret = CoeffBasedProductMode }; };
  template<>              struct product_type_selector<Small,Small,Large>  { enum { ret = GemmProduct }; };
  template<>              struct product_type_selector<Large,Small,Large>  { enum { ret = GemmProduct }; };
  template<>              struct product_type_selector<Small,Large,Large>  { enum { ret = GemmProduct }; };
  template<>              struct product_type_selector<Large,Large,Large>  { enum { ret = GemmProduct }; };
  template<>              struct product_type_selector<Large,Small,Small>  { enum { ret = GemmProduct }; };
  template<>              struct product_type_selector<Small,Large,Small>  { enum { ret = GemmProduct }; };
  template<>              struct product_type_selector<Large,Large,Small>  { enum { ret = GemmProduct }; };
  
  } // end namespace internal
  
  /** \class ProductReturnType
    * \ingroup Core_Module
    *
    * \brief Helper class to get the correct and optimized returned type of operator*
    *
    * \param Lhs the type of the left-hand side
    * \param Rhs the type of the right-hand side
    * \param ProductMode the type of the product (determined automatically by internal::product_mode)
    *
    * This class defines the typename Type representing the optimized product expression
    * between two matrix expressions. In practice, using ProductReturnType<Lhs,Rhs>::Type
    * is the recommended way to define the result type of a function returning an expression
    * which involve a matrix product. The class Product should never be
    * used directly.
    *
    * \sa class Product, MatrixBase::operator*(const MatrixBase<OtherDerived>&)
    */
  template<typename Lhs, typename Rhs, int ProductType>
  struct ProductReturnType
  {
    // TODO use the nested type to reduce instanciations ????
  //   typedef typename internal::nested<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;
  //   typedef typename internal::nested<Rhs,Lhs::RowsAtCompileTime>::type RhsNested;
  
    typedef GeneralProduct<Lhs/*Nested*/, Rhs/*Nested*/, ProductType> Type;
  };
  
  template<typename Lhs, typename Rhs>
  struct ProductReturnType<Lhs,Rhs,CoeffBasedProductMode>
  {
    typedef typename internal::nested<Lhs, Rhs::ColsAtCompileTime, typename internal::plain_matrix_type<Lhs>::type >::type LhsNested;
    typedef typename internal::nested<Rhs, Lhs::RowsAtCompileTime, typename internal::plain_matrix_type<Rhs>::type >::type RhsNested;
    typedef CoeffBasedProduct<LhsNested, RhsNested, EvalBeforeAssigningBit | EvalBeforeNestingBit> Type;
  };
  
  template<typename Lhs, typename Rhs>
  struct ProductReturnType<Lhs,Rhs,LazyCoeffBasedProductMode>
  {
    typedef typename internal::nested<Lhs, Rhs::ColsAtCompileTime, typename internal::plain_matrix_type<Lhs>::type >::type LhsNested;
    typedef typename internal::nested<Rhs, Lhs::RowsAtCompileTime, typename internal::plain_matrix_type<Rhs>::type >::type RhsNested;
    typedef CoeffBasedProduct<LhsNested, RhsNested, NestByRefBit> Type;
  };
  
  // this is a workaround for sun CC
  template<typename Lhs, typename Rhs>
  struct LazyProductReturnType : public ProductReturnType<Lhs,Rhs,LazyCoeffBasedProductMode>
  {};
  
  /***********************************************************************
  *  Implementation of Inner Vector Vector Product
  ***********************************************************************/
  
  // FIXME : maybe the "inner product" could return a Scalar
  // instead of a 1x1 matrix ??
  // Pro: more natural for the user
  // Cons: this could be a problem if in a meta unrolled algorithm a matrix-matrix
  // product ends up to a row-vector times col-vector product... To tackle this use
  // case, we could have a specialization for Block<MatrixType,1,1> with: operator=(Scalar x);
  
  namespace internal {
  
  template<typename Lhs, typename Rhs>
  struct traits<GeneralProduct<Lhs,Rhs,InnerProduct> >
   : traits<Matrix<typename scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType,1,1> >
  {};
  
  }
  
  template<typename Lhs, typename Rhs>
  class GeneralProduct<Lhs, Rhs, InnerProduct>
    : internal::no_assignment_operator,
      public Matrix<typename internal::scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType,1,1>
  {
      typedef Matrix<typename internal::scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType,1,1> Base;
    public:
      GeneralProduct(const Lhs& lhs, const Rhs& rhs)
      {
        EIGEN_STATIC_ASSERT((internal::is_same<typename Lhs::RealScalar, typename Rhs::RealScalar>::value),
          YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
  
        Base::coeffRef(0,0) = (lhs.transpose().cwiseProduct(rhs)).sum();
      }
  
      /** Convertion to scalar */
      operator const typename Base::Scalar() const {
        return Base::coeff(0,0);
      }
  };
  
  /***********************************************************************
  *  Implementation of Outer Vector Vector Product
  ***********************************************************************/
  
  namespace internal {
  
  // Column major
  template<typename ProductType, typename Dest, typename Func>
  EIGEN_DONT_INLINE void outer_product_selector_run(const ProductType& prod, Dest& dest, const Func& func, const false_type&)
  {
    typedef typename Dest::Index Index;
    // FIXME make sure lhs is sequentially stored
    // FIXME not very good if rhs is real and lhs complex while alpha is real too
    const Index cols = dest.cols();
    for (Index j=0; j<cols; ++j)
      func(dest.col(j), prod.rhs().coeff(j) * prod.lhs());
  }
  
  // Row major
  template<typename ProductType, typename Dest, typename Func>
  EIGEN_DONT_INLINE void outer_product_selector_run(const ProductType& prod, Dest& dest, const Func& func, const true_type&) {
    typedef typename Dest::Index Index;
    // FIXME make sure rhs is sequentially stored
    // FIXME not very good if lhs is real and rhs complex while alpha is real too
    const Index rows = dest.rows();
    for (Index i=0; i<rows; ++i)
      func(dest.row(i), prod.lhs().coeff(i) * prod.rhs());
  }
  
  template<typename Lhs, typename Rhs>
  struct traits<GeneralProduct<Lhs,Rhs,OuterProduct> >
   : traits<ProductBase<GeneralProduct<Lhs,Rhs,OuterProduct>, Lhs, Rhs> >
  {};
  
  }
  
  template<typename Lhs, typename Rhs>
  class GeneralProduct<Lhs, Rhs, OuterProduct>
    : public ProductBase<GeneralProduct<Lhs,Rhs,OuterProduct>, Lhs, Rhs>
  {
      template<typename T> struct IsRowMajor : internal::conditional<(int(T::Flags)&RowMajorBit), internal::true_type, internal::false_type>::type {};
      
    public:
      EIGEN_PRODUCT_PUBLIC_INTERFACE(GeneralProduct)
  
      GeneralProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
      {
        EIGEN_STATIC_ASSERT((internal::is_same<typename Lhs::RealScalar, typename Rhs::RealScalar>::value),
          YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
      }
      
      struct set  { template<typename Dst, typename Src> void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived()  = src; } };
      struct add  { template<typename Dst, typename Src> void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() += src; } };
      struct sub  { template<typename Dst, typename Src> void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() -= src; } };
      struct adds {
        Scalar m_scale;
        adds(const Scalar& s) : m_scale(s) {}
        template<typename Dst, typename Src> void operator()(const Dst& dst, const Src& src) const {
          dst.const_cast_derived() += m_scale * src;
        }
      };
      
      template<typename Dest>
      inline void evalTo(Dest& dest) const {
        internal::outer_product_selector_run(*this, dest, set(), IsRowMajor<Dest>());
      }
      
      template<typename Dest>
      inline void addTo(Dest& dest) const {
        internal::outer_product_selector_run(*this, dest, add(), IsRowMajor<Dest>());
      }
  
      template<typename Dest>
      inline void subTo(Dest& dest) const {
        internal::outer_product_selector_run(*this, dest, sub(), IsRowMajor<Dest>());
      }
  
      template<typename Dest> void scaleAndAddTo(Dest& dest, const Scalar& alpha) const
      {
        internal::outer_product_selector_run(*this, dest, adds(alpha), IsRowMajor<Dest>());
      }
  };
  
  /***********************************************************************
  *  Implementation of General Matrix Vector Product
  ***********************************************************************/
  
  /*  According to the shape/flags of the matrix we have to distinghish 3 different cases:
   *   1 - the matrix is col-major, BLAS compatible and M is large => call fast BLAS-like colmajor routine
   *   2 - the matrix is row-major, BLAS compatible and N is large => call fast BLAS-like rowmajor routine
   *   3 - all other cases are handled using a simple loop along the outer-storage direction.
   *  Therefore we need a lower level meta selector.
   *  Furthermore, if the matrix is the rhs, then the product has to be transposed.
   */
  namespace internal {
  
  template<typename Lhs, typename Rhs>
  struct traits<GeneralProduct<Lhs,Rhs,GemvProduct> >
   : traits<ProductBase<GeneralProduct<Lhs,Rhs,GemvProduct>, Lhs, Rhs> >
  {};
  
  template<int Side, int StorageOrder, bool BlasCompatible>
  struct gemv_selector;
  
  } // end namespace internal
  
  template<typename Lhs, typename Rhs>
  class GeneralProduct<Lhs, Rhs, GemvProduct>
    : public ProductBase<GeneralProduct<Lhs,Rhs,GemvProduct>, Lhs, Rhs>
  {
    public:
      EIGEN_PRODUCT_PUBLIC_INTERFACE(GeneralProduct)
  
      typedef typename Lhs::Scalar LhsScalar;
      typedef typename Rhs::Scalar RhsScalar;
  
      GeneralProduct(const Lhs& a_lhs, const Rhs& a_rhs) : Base(a_lhs,a_rhs)
      {
  //       EIGEN_STATIC_ASSERT((internal::is_same<typename Lhs::Scalar, typename Rhs::Scalar>::value),
  //         YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
      }
  
      enum { Side = Lhs::IsVectorAtCompileTime ? OnTheLeft : OnTheRight };
      typedef typename internal::conditional<int(Side)==OnTheRight,_LhsNested,_RhsNested>::type MatrixType;
  
      template<typename Dest> void scaleAndAddTo(Dest& dst, const Scalar& alpha) const
      {
        eigen_assert(m_lhs.rows() == dst.rows() && m_rhs.cols() == dst.cols());
        internal::gemv_selector<Side,(int(MatrixType::Flags)&RowMajorBit) ? RowMajor : ColMajor,
                         bool(internal::blas_traits<MatrixType>::HasUsableDirectAccess)>::run(*this, dst, alpha);
      }
  };
  
  namespace internal {
  
  // The vector is on the left => transposition
  template<int StorageOrder, bool BlasCompatible>
  struct gemv_selector<OnTheLeft,StorageOrder,BlasCompatible>
  {
    template<typename ProductType, typename Dest>
    static void run(const ProductType& prod, Dest& dest, const typename ProductType::Scalar& alpha)
    {
      Transpose<Dest> destT(dest);
      enum { OtherStorageOrder = StorageOrder == RowMajor ? ColMajor : RowMajor };
      gemv_selector<OnTheRight,OtherStorageOrder,BlasCompatible>
        ::run(GeneralProduct<Transpose<const typename ProductType::_RhsNested>,Transpose<const typename ProductType::_LhsNested>, GemvProduct>
          (prod.rhs().transpose(), prod.lhs().transpose()), destT, alpha);
    }
  };
  
  template<typename Scalar,int Size,int MaxSize,bool Cond> struct gemv_static_vector_if;
  
  template<typename Scalar,int Size,int MaxSize>
  struct gemv_static_vector_if<Scalar,Size,MaxSize,false>
  {
    EIGEN_STRONG_INLINE  Scalar* data() { eigen_internal_assert(false && "should never be called"); return 0; }
  };
  
  template<typename Scalar,int Size>
  struct gemv_static_vector_if<Scalar,Size,Dynamic,true>
  {
    EIGEN_STRONG_INLINE Scalar* data() { return 0; }
  };
  
  template<typename Scalar,int Size,int MaxSize>
  struct gemv_static_vector_if<Scalar,Size,MaxSize,true>
  {
    #if EIGEN_ALIGN_STATICALLY
    internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize),0> m_data;
    EIGEN_STRONG_INLINE Scalar* data() { return m_data.array; }
    #else
    // Some architectures cannot align on the stack,
    // => let's manually enforce alignment by allocating more data and return the address of the first aligned element.
    enum {
      ForceAlignment  = internal::packet_traits<Scalar>::Vectorizable,
      PacketSize      = internal::packet_traits<Scalar>::size
    };
    internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize)+(ForceAlignment?PacketSize:0),0> m_data;
    EIGEN_STRONG_INLINE Scalar* data() {
      return ForceAlignment
              ? reinterpret_cast<Scalar*>((reinterpret_cast<size_t>(m_data.array) & ~(size_t(15))) + 16)
              : m_data.array;
    }
    #endif
  };
  
  template<> struct gemv_selector<OnTheRight,ColMajor,true>
  {
    template<typename ProductType, typename Dest>
    static inline void run(const ProductType& prod, Dest& dest, const typename ProductType::Scalar& alpha)
    {
      typedef typename ProductType::Index Index;
      typedef typename ProductType::LhsScalar   LhsScalar;
      typedef typename ProductType::RhsScalar   RhsScalar;
      typedef typename ProductType::Scalar      ResScalar;
      typedef typename ProductType::RealScalar  RealScalar;
      typedef typename ProductType::ActualLhsType ActualLhsType;
      typedef typename ProductType::ActualRhsType ActualRhsType;
      typedef typename ProductType::LhsBlasTraits LhsBlasTraits;
      typedef typename ProductType::RhsBlasTraits RhsBlasTraits;
      typedef Map<Matrix<ResScalar,Dynamic,1>, Aligned> MappedDest;
  
      ActualLhsType actualLhs = LhsBlasTraits::extract(prod.lhs());
      ActualRhsType actualRhs = RhsBlasTraits::extract(prod.rhs());
  
      ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs())
                                    * RhsBlasTraits::extractScalarFactor(prod.rhs());
  
      enum {
        // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
        // on, the other hand it is good for the cache to pack the vector anyways...
        EvalToDestAtCompileTime = Dest::InnerStrideAtCompileTime==1,
        ComplexByReal = (NumTraits<LhsScalar>::IsComplex) && (!NumTraits<RhsScalar>::IsComplex),
        MightCannotUseDest = (Dest::InnerStrideAtCompileTime!=1) || ComplexByReal
      };
  
      gemv_static_vector_if<ResScalar,Dest::SizeAtCompileTime,Dest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;
  
      bool alphaIsCompatible = (!ComplexByReal) || (numext::imag(actualAlpha)==RealScalar(0));
      bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;
      
      RhsScalar compatibleAlpha = get_factor<ResScalar,RhsScalar>::run(actualAlpha);
  
      ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),
                                                    evalToDest ? dest.data() : static_dest.data());
      
      if(!evalToDest)
      {
        #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
        int size = dest.size();
        EIGEN_DENSE_STORAGE_CTOR_PLUGIN
        #endif
        if(!alphaIsCompatible)
        {
          MappedDest(actualDestPtr, dest.size()).setZero();
          compatibleAlpha = RhsScalar(1);
        }
        else
          MappedDest(actualDestPtr, dest.size()) = dest;
      }
  
      general_matrix_vector_product
        <Index,LhsScalar,ColMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsBlasTraits::NeedToConjugate>::run(
          actualLhs.rows(), actualLhs.cols(),
          actualLhs.data(), actualLhs.outerStride(),
          actualRhs.data(), actualRhs.innerStride(),
          actualDestPtr, 1,
          compatibleAlpha);
  
      if (!evalToDest)
      {
        if(!alphaIsCompatible)
          dest += actualAlpha * MappedDest(actualDestPtr, dest.size());
        else
          dest = MappedDest(actualDestPtr, dest.size());
      }
    }
  };
  
  template<> struct gemv_selector<OnTheRight,RowMajor,true>
  {
    template<typename ProductType, typename Dest>
    static void run(const ProductType& prod, Dest& dest, const typename ProductType::Scalar& alpha)
    {
      typedef typename ProductType::LhsScalar LhsScalar;
      typedef typename ProductType::RhsScalar RhsScalar;
      typedef typename ProductType::Scalar    ResScalar;
      typedef typename ProductType::Index Index;
      typedef typename ProductType::ActualLhsType ActualLhsType;
      typedef typename ProductType::ActualRhsType ActualRhsType;
      typedef typename ProductType::_ActualRhsType _ActualRhsType;
      typedef typename ProductType::LhsBlasTraits LhsBlasTraits;
      typedef typename ProductType::RhsBlasTraits RhsBlasTraits;
  
      typename add_const<ActualLhsType>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
      typename add_const<ActualRhsType>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
  
      ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs())
                                    * RhsBlasTraits::extractScalarFactor(prod.rhs());
  
      enum {
        // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
        // on, the other hand it is good for the cache to pack the vector anyways...
        DirectlyUseRhs = _ActualRhsType::InnerStrideAtCompileTime==1
      };
  
      gemv_static_vector_if<RhsScalar,_ActualRhsType::SizeAtCompileTime,_ActualRhsType::MaxSizeAtCompileTime,!DirectlyUseRhs> static_rhs;
  
      ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,actualRhs.size(),
          DirectlyUseRhs ? const_cast<RhsScalar*>(actualRhs.data()) : static_rhs.data());
  
      if(!DirectlyUseRhs)
      {
        #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
        int size = actualRhs.size();
        EIGEN_DENSE_STORAGE_CTOR_PLUGIN
        #endif
        Map<typename _ActualRhsType::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
      }
  
      general_matrix_vector_product
        <Index,LhsScalar,RowMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsBlasTraits::NeedToConjugate>::run(
          actualLhs.rows(), actualLhs.cols(),
          actualLhs.data(), actualLhs.outerStride(),
          actualRhsPtr, 1,
          dest.data(), dest.innerStride(),
          actualAlpha);
    }
  };
  
  template<> struct gemv_selector<OnTheRight,ColMajor,false>
  {
    template<typename ProductType, typename Dest>
    static void run(const ProductType& prod, Dest& dest, const typename ProductType::Scalar& alpha)
    {
      typedef typename Dest::Index Index;
      // TODO makes sure dest is sequentially stored in memory, otherwise use a temp
      const Index size = prod.rhs().rows();
      for(Index k=0; k<size; ++k)
        dest += (alpha*prod.rhs().coeff(k)) * prod.lhs().col(k);
    }
  };
  
  template<> struct gemv_selector<OnTheRight,RowMajor,false>
  {
    template<typename ProductType, typename Dest>
    static void run(const ProductType& prod, Dest& dest, const typename ProductType::Scalar& alpha)
    {
      typedef typename Dest::Index Index;
      // TODO makes sure rhs is sequentially stored in memory, otherwise use a temp
      const Index rows = prod.rows();
      for(Index i=0; i<rows; ++i)
        dest.coeffRef(i) += alpha * (prod.lhs().row(i).cwiseProduct(prod.rhs().transpose())).sum();
    }
  };
  
  } // end namespace internal
  
  /***************************************************************************
  * Implementation of matrix base methods
  ***************************************************************************/
  
  /** \returns the matrix product of \c *this and \a other.
    *
    * \note If instead of the matrix product you want the coefficient-wise product, see Cwise::operator*().
    *
    * \sa lazyProduct(), operator*=(const MatrixBase&), Cwise::operator*()
    */
  template<typename Derived>
  template<typename OtherDerived>
  inline const typename ProductReturnType<Derived, OtherDerived>::Type
  MatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const
  {
    // A note regarding the function declaration: In MSVC, this function will sometimes
    // not be inlined since DenseStorage is an unwindable object for dynamic
    // matrices and product types are holding a member to store the result.
    // Thus it does not help tagging this function with EIGEN_STRONG_INLINE.
    enum {
      ProductIsValid =  Derived::ColsAtCompileTime==Dynamic
                     || OtherDerived::RowsAtCompileTime==Dynamic
                     || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
      AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
      SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
    };
    // note to the lost user:
    //    * for a dot product use: v1.dot(v2)
    //    * for a coeff-wise product use: v1.cwiseProduct(v2)
    EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
      INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
    EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
      INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
    EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
  #ifdef EIGEN_DEBUG_PRODUCT
    internal::product_type<Derived,OtherDerived>::debug();
  #endif
    return typename ProductReturnType<Derived,OtherDerived>::Type(derived(), other.derived());
  }
  
  /** \returns an expression of the matrix product of \c *this and \a other without implicit evaluation.
    *
    * The returned product will behave like any other expressions: the coefficients of the product will be
    * computed once at a time as requested. This might be useful in some extremely rare cases when only
    * a small and no coherent fraction of the result's coefficients have to be computed.
    *
    * \warning This version of the matrix product can be much much slower. So use it only if you know
    * what you are doing and that you measured a true speed improvement.
    *
    * \sa operator*(const MatrixBase&)
    */
  template<typename Derived>
  template<typename OtherDerived>
  const typename LazyProductReturnType<Derived,OtherDerived>::Type
  MatrixBase<Derived>::lazyProduct(const MatrixBase<OtherDerived> &other) const
  {
    enum {
      ProductIsValid =  Derived::ColsAtCompileTime==Dynamic
                     || OtherDerived::RowsAtCompileTime==Dynamic
                     || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
      AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
      SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
    };
    // note to the lost user:
    //    * for a dot product use: v1.dot(v2)
    //    * for a coeff-wise product use: v1.cwiseProduct(v2)
    EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
      INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
    EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
      INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
    EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
  
    return typename LazyProductReturnType<Derived,OtherDerived>::Type(derived(), other.derived());
  }
  
  } // end namespace Eigen
  
  #endif // EIGEN_PRODUCT_H
  