// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2010 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_PRODUCTBASE_H
#define EIGEN_PRODUCTBASE_H

namespace Eigen { 

/** \class ProductBase
  * \ingroup Core_Module
  *
  */

namespace internal {
template<typename Derived, typename _Lhs, typename _Rhs>
struct traits<ProductBase<Derived,_Lhs,_Rhs> >
{
  typedef MatrixXpr XprKind;
  typedef typename remove_all<_Lhs>::type Lhs;
  typedef typename remove_all<_Rhs>::type Rhs;
  typedef typename scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
  typedef typename promote_storage_type<typename traits<Lhs>::StorageKind,
                                           typename traits<Rhs>::StorageKind>::ret StorageKind;
  typedef typename promote_index_type<typename traits<Lhs>::Index,
                                         typename traits<Rhs>::Index>::type Index;
  enum {
    RowsAtCompileTime = traits<Lhs>::RowsAtCompileTime,
    ColsAtCompileTime = traits<Rhs>::ColsAtCompileTime,
    MaxRowsAtCompileTime = traits<Lhs>::MaxRowsAtCompileTime,
    MaxColsAtCompileTime = traits<Rhs>::MaxColsAtCompileTime,
    Flags = (MaxRowsAtCompileTime==1 ? RowMajorBit : 0)
          | EvalBeforeNestingBit | EvalBeforeAssigningBit | NestByRefBit,
                  // Note that EvalBeforeNestingBit and NestByRefBit
                  // are not used in practice because nested is overloaded for products
    CoeffReadCost = 0 // FIXME why is it needed ?
  };
};
}

#define EIGEN_PRODUCT_PUBLIC_INTERFACE(Derived) \
  typedef ProductBase<Derived, Lhs, Rhs > Base; \
  EIGEN_DENSE_PUBLIC_INTERFACE(Derived) \
  typedef typename Base::LhsNested LhsNested; \
  typedef typename Base::_LhsNested _LhsNested; \
  typedef typename Base::LhsBlasTraits LhsBlasTraits; \
  typedef typename Base::ActualLhsType ActualLhsType; \
  typedef typename Base::_ActualLhsType _ActualLhsType; \
  typedef typename Base::RhsNested RhsNested; \
  typedef typename Base::_RhsNested _RhsNested; \
  typedef typename Base::RhsBlasTraits RhsBlasTraits; \
  typedef typename Base::ActualRhsType ActualRhsType; \
  typedef typename Base::_ActualRhsType _ActualRhsType; \
  using Base::m_lhs; \
  using Base::m_rhs;

template<typename Derived, typename Lhs, typename Rhs>
class ProductBase : public MatrixBase<Derived>
{
  public:
    typedef MatrixBase<Derived> Base;
    EIGEN_DENSE_PUBLIC_INTERFACE(ProductBase)
    
    typedef typename Lhs::Nested LhsNested;
    typedef typename internal::remove_all<LhsNested>::type _LhsNested;
    typedef internal::blas_traits<_LhsNested> LhsBlasTraits;
    typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
    typedef typename internal::remove_all<ActualLhsType>::type _ActualLhsType;
    typedef typename internal::traits<Lhs>::Scalar LhsScalar;

    typedef typename Rhs::Nested RhsNested;
    typedef typename internal::remove_all<RhsNested>::type _RhsNested;
    typedef internal::blas_traits<_RhsNested> RhsBlasTraits;
    typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
    typedef typename internal::remove_all<ActualRhsType>::type _ActualRhsType;
    typedef typename internal::traits<Rhs>::Scalar RhsScalar;

    // Diagonal of a product: no need to evaluate the arguments because they are going to be evaluated only once
    typedef CoeffBasedProduct<LhsNested, RhsNested, 0> FullyLazyCoeffBaseProductType;

  public:

    typedef typename Base::PlainObject PlainObject;

    ProductBase(const Lhs& a_lhs, const Rhs& a_rhs)
      : m_lhs(a_lhs), m_rhs(a_rhs)
    {
      eigen_assert(a_lhs.cols() == a_rhs.rows()
        && "invalid matrix product"
        && "if you wanted a coeff-wise or a dot product use the respective explicit functions");
    }

    inline Index rows() const { return m_lhs.rows(); }
    inline Index cols() const { return m_rhs.cols(); }

    template<typename Dest>
    inline void evalTo(Dest& dst) const { dst.setZero(); scaleAndAddTo(dst,Scalar(1)); }

    template<typename Dest>
    inline void addTo(Dest& dst) const { scaleAndAddTo(dst,Scalar(1)); }

    template<typename Dest>
    inline void subTo(Dest& dst) const { scaleAndAddTo(dst,Scalar(-1)); }

    template<typename Dest>
    inline void scaleAndAddTo(Dest& dst, const Scalar& alpha) const { derived().scaleAndAddTo(dst,alpha); }

    const _LhsNested& lhs() const { return m_lhs; }
    const _RhsNested& rhs() const { return m_rhs; }

    // Implicit conversion to the nested type (trigger the evaluation of the product)
    operator const PlainObject& () const
    {
      m_result.resize(m_lhs.rows(), m_rhs.cols());
      derived().evalTo(m_result);
      return m_result;
    }

    const Diagonal<const FullyLazyCoeffBaseProductType,0> diagonal() const
    { return FullyLazyCoeffBaseProductType(m_lhs, m_rhs); }

    template<int Index>
    const Diagonal<const FullyLazyCoeffBaseProductType,Index> diagonal() const
    { return FullyLazyCoeffBaseProductType(m_lhs, m_rhs); }

    const Diagonal<const FullyLazyCoeffBaseProductType, DynamicIndex> diagonal(Index index) const {
      return Diagonal<const FullyLazyCoeffBaseProductType, DynamicIndex>(
          FullyLazyCoeffBaseProductType(m_lhs, m_rhs), index);
    }

    // restrict coeff accessors to 1x1 expressions. No need to care about mutators here since this isnt a Lvalue expression
    typename Base::CoeffReturnType coeff(Index row, Index col) const
    {
#ifdef EIGEN2_SUPPORT
      return lhs().row(row).cwiseProduct(rhs().col(col).transpose()).sum();
#else
      EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
      eigen_assert(this->rows() == 1 && this->cols() == 1);
      Matrix<Scalar,1,1> result = *this;
      return result.coeff(row,col);
#endif
    }

    typename Base::CoeffReturnType coeff(Index i) const
    {
      EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
      eigen_assert(this->rows() == 1 && this->cols() == 1);
      Matrix<Scalar,1,1> result = *this;
      return result.coeff(i);
    }

    const Scalar& coeffRef(Index row, Index col) const
    {
      EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
      eigen_assert(this->rows() == 1 && this->cols() == 1);
      return derived().coeffRef(row,col);
    }

    const Scalar& coeffRef(Index i) const
    {
      EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
      eigen_assert(this->rows() == 1 && this->cols() == 1);
      return derived().coeffRef(i);
    }

  protected:

    LhsNested m_lhs;
    RhsNested m_rhs;

    mutable PlainObject m_result;
};

// here we need to overload the nested rule for products
// such that the nested type is a const reference to a plain matrix
namespace internal {
template<typename Lhs, typename Rhs, int Mode, int N, typename PlainObject>
struct nested<GeneralProduct<Lhs,Rhs,Mode>, N, PlainObject>
{
  typedef PlainObject const& type;
};
}

template<typename NestedProduct>
class ScaledProduct;

// Note that these two operator* functions are not defined as member
// functions of ProductBase, because, otherwise we would have to
// define all overloads defined in MatrixBase. Furthermore, Using
// "using Base::operator*" would not work with MSVC.
//
// Also note that here we accept any compatible scalar types
template<typename Derived,typename Lhs,typename Rhs>
const ScaledProduct<Derived>
operator*(const ProductBase<Derived,Lhs,Rhs>& prod, const typename Derived::Scalar& x)
{ return ScaledProduct<Derived>(prod.derived(), x); }

template<typename Derived,typename Lhs,typename Rhs>
typename internal::enable_if<!internal::is_same<typename Derived::Scalar,typename Derived::RealScalar>::value,
                      const ScaledProduct<Derived> >::type
operator*(const ProductBase<Derived,Lhs,Rhs>& prod, const typename Derived::RealScalar& x)
{ return ScaledProduct<Derived>(prod.derived(), x); }


template<typename Derived,typename Lhs,typename Rhs>
const ScaledProduct<Derived>
operator*(const typename Derived::Scalar& x,const ProductBase<Derived,Lhs,Rhs>& prod)
{ return ScaledProduct<Derived>(prod.derived(), x); }

template<typename Derived,typename Lhs,typename Rhs>
typename internal::enable_if<!internal::is_same<typename Derived::Scalar,typename Derived::RealScalar>::value,
                      const ScaledProduct<Derived> >::type
operator*(const typename Derived::RealScalar& x,const ProductBase<Derived,Lhs,Rhs>& prod)
{ return ScaledProduct<Derived>(prod.derived(), x); }

namespace internal {
template<typename NestedProduct>
struct traits<ScaledProduct<NestedProduct> >
 : traits<ProductBase<ScaledProduct<NestedProduct>,
                         typename NestedProduct::_LhsNested,
                         typename NestedProduct::_RhsNested> >
{
  typedef typename traits<NestedProduct>::StorageKind StorageKind;
};
}

template<typename NestedProduct>
class ScaledProduct
  : public ProductBase<ScaledProduct<NestedProduct>,
                       typename NestedProduct::_LhsNested,
                       typename NestedProduct::_RhsNested>
{
  public:
    typedef ProductBase<ScaledProduct<NestedProduct>,
                       typename NestedProduct::_LhsNested,
                       typename NestedProduct::_RhsNested> Base;
    typedef typename Base::Scalar Scalar;
    typedef typename Base::PlainObject PlainObject;
//     EIGEN_PRODUCT_PUBLIC_INTERFACE(ScaledProduct)

    ScaledProduct(const NestedProduct& prod, const Scalar& x)
    : Base(prod.lhs(),prod.rhs()), m_prod(prod), m_alpha(x) {}

    template<typename Dest>
    inline void evalTo(Dest& dst) const { dst.setZero(); scaleAndAddTo(dst, Scalar(1)); }

    template<typename Dest>
    inline void addTo(Dest& dst) const { scaleAndAddTo(dst, Scalar(1)); }

    template<typename Dest>
    inline void subTo(Dest& dst) const { scaleAndAddTo(dst, Scalar(-1)); }

    template<typename Dest>
    inline void scaleAndAddTo(Dest& dst, const Scalar& a_alpha) const { m_prod.derived().scaleAndAddTo(dst,a_alpha * m_alpha); }

    const Scalar& alpha() const { return m_alpha; }
    
  protected:
    const NestedProduct& m_prod;
    Scalar m_alpha;
};

/** \internal
  * Overloaded to perform an efficient C = (A*B).lazy() */
template<typename Derived>
template<typename ProductDerived, typename Lhs, typename Rhs>
EIGEN_DEVICE_FUNC
Derived& MatrixBase<Derived>::lazyAssign(const ProductBase<ProductDerived, Lhs,Rhs>& other)
{
  other.derived().evalTo(derived());
  return derived();
}

} // end namespace Eigen

#endif // EIGEN_PRODUCTBASE_H