text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // 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_PRODUCT_H
  #define EIGEN_PRODUCT_H
  
  namespace Eigen {
  
  template<typename Lhs, typename Rhs, int Option, typename StorageKind> class ProductImpl;
  
  namespace internal {
  
  template<typename Lhs, typename Rhs, int Option>
  struct traits<Product<Lhs, Rhs, Option> >
  {
    typedef typename remove_all<Lhs>::type LhsCleaned;
    typedef typename remove_all<Rhs>::type RhsCleaned;
    typedef traits<LhsCleaned> LhsTraits;
    typedef traits<RhsCleaned> RhsTraits;
    
    typedef MatrixXpr XprKind;
    
    typedef typename ScalarBinaryOpTraits<typename traits<LhsCleaned>::Scalar, typename traits<RhsCleaned>::Scalar>::ReturnType Scalar;
    typedef typename product_promote_storage_type<typename LhsTraits::StorageKind,
                                                  typename RhsTraits::StorageKind,
                                                  internal::product_type<Lhs,Rhs>::ret>::ret StorageKind;
    typedef typename promote_index_type<typename LhsTraits::StorageIndex,
                                        typename RhsTraits::StorageIndex>::type StorageIndex;
    
    enum {
      RowsAtCompileTime    = LhsTraits::RowsAtCompileTime,
      ColsAtCompileTime    = RhsTraits::ColsAtCompileTime,
      MaxRowsAtCompileTime = LhsTraits::MaxRowsAtCompileTime,
      MaxColsAtCompileTime = RhsTraits::MaxColsAtCompileTime,
      
      // FIXME: only needed by GeneralMatrixMatrixTriangular
      InnerSize = EIGEN_SIZE_MIN_PREFER_FIXED(LhsTraits::ColsAtCompileTime, RhsTraits::RowsAtCompileTime),
      
      // The storage order is somewhat arbitrary here. The correct one will be determined through the evaluator.
      Flags = (MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1) ? RowMajorBit
            : (MaxColsAtCompileTime==1 && MaxRowsAtCompileTime!=1) ? 0
            : (   ((LhsTraits::Flags&NoPreferredStorageOrderBit) && (RhsTraits::Flags&RowMajorBit))
               || ((RhsTraits::Flags&NoPreferredStorageOrderBit) && (LhsTraits::Flags&RowMajorBit)) ) ? RowMajorBit
            : NoPreferredStorageOrderBit
    };
  };
  
  } // end namespace internal
  
  /** \class Product
    * \ingroup Core_Module
    *
    * \brief Expression of the product of two arbitrary matrices or vectors
    *
    * \tparam _Lhs the type of the left-hand side expression
    * \tparam _Rhs the type of the right-hand side expression
    *
    * This class represents an expression of the product of two arbitrary matrices.
    *
    * The other template parameters are:
    * \tparam Option     can be DefaultProduct, AliasFreeProduct, or LazyProduct
    *
    */
  template<typename _Lhs, typename _Rhs, int Option>
  class Product : public ProductImpl<_Lhs,_Rhs,Option,
                                     typename internal::product_promote_storage_type<typename internal::traits<_Lhs>::StorageKind,
                                                                                     typename internal::traits<_Rhs>::StorageKind,
                                                                                     internal::product_type<_Lhs,_Rhs>::ret>::ret>
  {
    public:
      
      typedef _Lhs Lhs;
      typedef _Rhs Rhs;
      
      typedef typename ProductImpl<
          Lhs, Rhs, Option,
          typename internal::product_promote_storage_type<typename internal::traits<Lhs>::StorageKind,
                                                          typename internal::traits<Rhs>::StorageKind,
                                                          internal::product_type<Lhs,Rhs>::ret>::ret>::Base Base;
      EIGEN_GENERIC_PUBLIC_INTERFACE(Product)
  
      typedef typename internal::ref_selector<Lhs>::type LhsNested;
      typedef typename internal::ref_selector<Rhs>::type RhsNested;
      typedef typename internal::remove_all<LhsNested>::type LhsNestedCleaned;
      typedef typename internal::remove_all<RhsNested>::type RhsNestedCleaned;
  
      EIGEN_DEVICE_FUNC Product(const Lhs& lhs, const Rhs& rhs) : m_lhs(lhs), m_rhs(rhs)
      {
        eigen_assert(lhs.cols() == rhs.rows()
          && "invalid matrix product"
          && "if you wanted a coeff-wise or a dot product use the respective explicit functions");
      }
  
      EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index rows() const { return m_lhs.rows(); }
      EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index cols() const { return m_rhs.cols(); }
  
      EIGEN_DEVICE_FUNC const LhsNestedCleaned& lhs() const { return m_lhs; }
      EIGEN_DEVICE_FUNC const RhsNestedCleaned& rhs() const { return m_rhs; }
  
    protected:
  
      LhsNested m_lhs;
      RhsNested m_rhs;
  };
  
  namespace internal {
    
  template<typename Lhs, typename Rhs, int Option, int ProductTag = internal::product_type<Lhs,Rhs>::ret>
  class dense_product_base
   : public internal::dense_xpr_base<Product<Lhs,Rhs,Option> >::type
  {};
  
  /** Convertion to scalar for inner-products */
  template<typename Lhs, typename Rhs, int Option>
  class dense_product_base<Lhs, Rhs, Option, InnerProduct>
   : public internal::dense_xpr_base<Product<Lhs,Rhs,Option> >::type
  {
    typedef Product<Lhs,Rhs,Option> ProductXpr;
    typedef typename internal::dense_xpr_base<ProductXpr>::type Base;
  public:
    using Base::derived;
    typedef typename Base::Scalar Scalar;
    
    EIGEN_STRONG_INLINE operator const Scalar() const
    {
      return internal::evaluator<ProductXpr>(derived()).coeff(0,0);
    }
  };
  
  } // namespace internal
  
  // Generic API dispatcher
  template<typename Lhs, typename Rhs, int Option, typename StorageKind>
  class ProductImpl : public internal::generic_xpr_base<Product<Lhs,Rhs,Option>, MatrixXpr, StorageKind>::type
  {
    public:
      typedef typename internal::generic_xpr_base<Product<Lhs,Rhs,Option>, MatrixXpr, StorageKind>::type Base;
  };
  
  template<typename Lhs, typename Rhs, int Option>
  class ProductImpl<Lhs,Rhs,Option,Dense>
    : public internal::dense_product_base<Lhs,Rhs,Option>
  {
      typedef Product<Lhs, Rhs, Option> Derived;
      
    public:
      
      typedef typename internal::dense_product_base<Lhs, Rhs, Option> Base;
      EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
    protected:
      enum {
        IsOneByOne = (RowsAtCompileTime == 1 || RowsAtCompileTime == Dynamic) && 
                     (ColsAtCompileTime == 1 || ColsAtCompileTime == Dynamic),
        EnableCoeff = IsOneByOne || Option==LazyProduct
      };
      
    public:
    
      EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(Index row, Index col) const
      {
        EIGEN_STATIC_ASSERT(EnableCoeff, THIS_METHOD_IS_ONLY_FOR_INNER_OR_LAZY_PRODUCTS);
        eigen_assert( (Option==LazyProduct) || (this->rows() == 1 && this->cols() == 1) );
        
        return internal::evaluator<Derived>(derived()).coeff(row,col);
      }
  
      EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar coeff(Index i) const
      {
        EIGEN_STATIC_ASSERT(EnableCoeff, THIS_METHOD_IS_ONLY_FOR_INNER_OR_LAZY_PRODUCTS);
        eigen_assert( (Option==LazyProduct) || (this->rows() == 1 && this->cols() == 1) );
        
        return internal::evaluator<Derived>(derived()).coeff(i);
      }
      
    
  };
  
  } // end namespace Eigen
  
  #endif // EIGEN_PRODUCT_H
  