blob: 93e97877954a6cb0a640b6806bc5f52e047f8ce1 [file] [log] [blame]
// 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 Gael Guennebaud <g.gael@free.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifndef EIGEN_PRODUCT_H
#define EIGEN_PRODUCT_H
/** \class GeneralProduct
*
* \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 = ei_product_type<Lhs,Rhs>::value>
class GeneralProduct;
template<int Rows, int Cols, int Depth> struct ei_product_type_selector;
enum {
Large = 2,
Small = 3
};
template<typename Lhs, typename Rhs> struct ei_product_type
{
typedef typename ei_cleantype<Lhs>::type _Lhs;
typedef typename ei_cleantype<Rhs>::type _Rhs;
enum {
Rows = _Lhs::MaxRowsAtCompileTime,
Cols = _Rhs::MaxColsAtCompileTime,
Depth = EIGEN_ENUM_MIN(_Lhs::MaxColsAtCompileTime,_Rhs::MaxRowsAtCompileTime)
};
// 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 = Rows >=EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD ? Large : (Rows==1 ? 1 : Small),
cols_select = Cols >=EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD ? Large : (Cols==1 ? 1 : Small),
depth_select = Depth>=EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD ? Large : (Depth==1 ? 1 : Small)
};
typedef ei_product_type_selector<rows_select, cols_select, depth_select> product_type_selector;
public:
enum {
value = product_type_selector::ret
};
};
/* 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 ei_product_type_selector<M,N,1> { enum { ret = OuterProduct }; };
template<int Depth> struct ei_product_type_selector<1, 1, Depth> { enum { ret = InnerProduct }; };
template<> struct ei_product_type_selector<1, 1, 1> { enum { ret = InnerProduct }; };
template<> struct ei_product_type_selector<Small,1, Small> { enum { ret = CoeffBasedProductMode }; };
template<> struct ei_product_type_selector<1, Small,Small> { enum { ret = CoeffBasedProductMode }; };
template<> struct ei_product_type_selector<Small,Small,Small> { enum { ret = CoeffBasedProductMode }; };
template<> struct ei_product_type_selector<Small, Small, 1> { enum { ret = LazyCoeffBasedProductMode }; };
template<> struct ei_product_type_selector<Small, Large, 1> { enum { ret = LazyCoeffBasedProductMode }; };
template<> struct ei_product_type_selector<Large, Small, 1> { enum { ret = LazyCoeffBasedProductMode }; };
template<> struct ei_product_type_selector<1, Large,Small> { enum { ret = CoeffBasedProductMode }; };
template<> struct ei_product_type_selector<1, Large,Large> { enum { ret = GemvProduct }; };
template<> struct ei_product_type_selector<1, Small,Large> { enum { ret = CoeffBasedProductMode }; };
template<> struct ei_product_type_selector<Large,1, Small> { enum { ret = CoeffBasedProductMode }; };
template<> struct ei_product_type_selector<Large,1, Large> { enum { ret = GemvProduct }; };
template<> struct ei_product_type_selector<Small,1, Large> { enum { ret = CoeffBasedProductMode }; };
template<> struct ei_product_type_selector<Small,Small,Large> { enum { ret = GemmProduct }; };
template<> struct ei_product_type_selector<Large,Small,Large> { enum { ret = GemmProduct }; };
template<> struct ei_product_type_selector<Small,Large,Large> { enum { ret = GemmProduct }; };
template<> struct ei_product_type_selector<Large,Large,Large> { enum { ret = GemmProduct }; };
template<> struct ei_product_type_selector<Large,Small,Small> { enum { ret = GemmProduct }; };
template<> struct ei_product_type_selector<Small,Large,Small> { enum { ret = GemmProduct }; };
template<> struct ei_product_type_selector<Large,Large,Small> { enum { ret = GemmProduct }; };
/** \class ProductReturnType
*
* \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 ei_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 ei_nested<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;
// typedef typename ei_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 ei_nested<Lhs, Rhs::ColsAtCompileTime, typename ei_plain_matrix_type<Lhs>::type >::type LhsNested;
typedef typename ei_nested<Rhs, Lhs::RowsAtCompileTime, typename ei_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 ei_nested<Lhs, Rhs::ColsAtCompileTime, typename ei_plain_matrix_type<Lhs>::type >::type LhsNested;
typedef typename ei_nested<Rhs, Lhs::RowsAtCompileTime, typename ei_plain_matrix_type<Rhs>::type >::type RhsNested;
typedef CoeffBasedProduct<LhsNested, RhsNested, NestByRefBit> Type;
};
/***********************************************************************
* 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);
template<typename Lhs, typename Rhs>
struct ei_traits<GeneralProduct<Lhs,Rhs,InnerProduct> >
: ei_traits<Matrix<typename ei_scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType,1,1> >
{};
template<typename Lhs, typename Rhs>
class GeneralProduct<Lhs, Rhs, InnerProduct>
: ei_no_assignment_operator,
public Matrix<typename ei_scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType,1,1>
{
typedef Matrix<typename ei_scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType,1,1> Base;
public:
GeneralProduct(const Lhs& lhs, const Rhs& rhs)
{
EIGEN_STATIC_ASSERT((ei_is_same_type<typename Lhs::RealScalar, typename Rhs::RealScalar>::ret),
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();
}
typename Base::Scalar value() const { return Base::coeff(0,0); }
};
/***********************************************************************
* Implementation of Outer Vector Vector Product
***********************************************************************/
template<int StorageOrder> struct ei_outer_product_selector;
template<typename Lhs, typename Rhs>
struct ei_traits<GeneralProduct<Lhs,Rhs,OuterProduct> >
: ei_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>
{
public:
EIGEN_PRODUCT_PUBLIC_INTERFACE(GeneralProduct)
GeneralProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
{
EIGEN_STATIC_ASSERT((ei_is_same_type<typename Lhs::RealScalar, typename Rhs::RealScalar>::ret),
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
}
template<typename Dest> void scaleAndAddTo(Dest& dest, Scalar alpha) const
{
ei_outer_product_selector<(int(Dest::Flags)&RowMajorBit) ? RowMajor : ColMajor>::run(*this, dest, alpha);
}
};
template<> struct ei_outer_product_selector<ColMajor> {
template<typename ProductType, typename Dest>
EIGEN_DONT_INLINE static void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha) {
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)
dest.col(j) += (alpha * prod.rhs().coeff(j)) * prod.lhs();
}
};
template<> struct ei_outer_product_selector<RowMajor> {
template<typename ProductType, typename Dest>
EIGEN_DONT_INLINE static void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha) {
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)
dest.row(i) += (alpha * prod.lhs().coeff(i)) * prod.rhs();
}
};
/***********************************************************************
* 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.
*/
template<typename Lhs, typename Rhs>
struct ei_traits<GeneralProduct<Lhs,Rhs,GemvProduct> >
: ei_traits<ProductBase<GeneralProduct<Lhs,Rhs,GemvProduct>, Lhs, Rhs> >
{};
template<int Side, int StorageOrder, bool BlasCompatible>
struct ei_gemv_selector;
template<typename Lhs, typename Rhs>
class GeneralProduct<Lhs, Rhs, GemvProduct>
: public ProductBase<GeneralProduct<Lhs,Rhs,GemvProduct>, Lhs, Rhs>
{
public:
EIGEN_PRODUCT_PUBLIC_INTERFACE(GeneralProduct)
GeneralProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
{
EIGEN_STATIC_ASSERT((ei_is_same_type<typename Lhs::Scalar, typename Rhs::Scalar>::ret),
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 ei_meta_if<int(Side)==OnTheRight,_LhsNested,_RhsNested>::ret MatrixType;
template<typename Dest> void scaleAndAddTo(Dest& dst, Scalar alpha) const
{
ei_assert(m_lhs.rows() == dst.rows() && m_rhs.cols() == dst.cols());
ei_gemv_selector<Side,(int(MatrixType::Flags)&RowMajorBit) ? RowMajor : ColMajor,
bool(ei_blas_traits<MatrixType>::HasUsableDirectAccess)>::run(*this, dst, alpha);
}
};
// The vector is on the left => transposition
template<int StorageOrder, bool BlasCompatible>
struct ei_gemv_selector<OnTheLeft,StorageOrder,BlasCompatible>
{
template<typename ProductType, typename Dest>
static void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha)
{
Transpose<Dest> destT(dest);
enum { OtherStorageOrder = StorageOrder == RowMajor ? ColMajor : RowMajor };
ei_gemv_selector<OnTheRight,OtherStorageOrder,BlasCompatible>
::run(GeneralProduct<Transpose<typename ProductType::_RhsNested>,Transpose<typename ProductType::_LhsNested>, GemvProduct>
(prod.rhs().transpose(), prod.lhs().transpose()), destT, alpha);
}
};
template<> struct ei_gemv_selector<OnTheRight,ColMajor,true>
{
template<typename ProductType, typename Dest>
static void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha)
{
typedef typename ProductType::Scalar Scalar;
typedef typename ProductType::ActualLhsType ActualLhsType;
typedef typename ProductType::ActualRhsType ActualRhsType;
typedef typename ProductType::LhsBlasTraits LhsBlasTraits;
typedef typename ProductType::RhsBlasTraits RhsBlasTraits;
ActualLhsType actualLhs = LhsBlasTraits::extract(prod.lhs());
ActualRhsType actualRhs = RhsBlasTraits::extract(prod.rhs());
Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs())
* RhsBlasTraits::extractScalarFactor(prod.rhs());
enum {
EvalToDest = (ei_packet_traits<Scalar>::size==1)
||((Dest::Flags&ActualPacketAccessBit) && (!(Dest::Flags & RowMajorBit)))
};
Scalar* EIGEN_RESTRICT actualDest;
if (EvalToDest)
actualDest = &dest.coeffRef(0);
else
{
actualDest = ei_aligned_stack_new(Scalar,dest.size());
Map<typename Dest::PlainObject>(actualDest, dest.size()) = dest;
}
ei_cache_friendly_product_colmajor_times_vector
<LhsBlasTraits::NeedToConjugate,RhsBlasTraits::NeedToConjugate>(
dest.size(),
&actualLhs.const_cast_derived().coeffRef(0,0), actualLhs.outerStride(),
actualRhs, actualDest, actualAlpha);
if (!EvalToDest)
{
dest = Map<typename Dest::PlainObject>(actualDest, dest.size());
ei_aligned_stack_delete(Scalar, actualDest, dest.size());
}
}
};
template<> struct ei_gemv_selector<OnTheRight,RowMajor,true>
{
template<typename ProductType, typename Dest>
static void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha)
{
typedef typename ProductType::Scalar Scalar;
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;
ActualLhsType actualLhs = LhsBlasTraits::extract(prod.lhs());
ActualRhsType actualRhs = RhsBlasTraits::extract(prod.rhs());
Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs())
* RhsBlasTraits::extractScalarFactor(prod.rhs());
enum {
DirectlyUseRhs = ((ei_packet_traits<Scalar>::size==1) || (_ActualRhsType::Flags&ActualPacketAccessBit))
&& (!(_ActualRhsType::Flags & RowMajorBit))
};
Scalar* EIGEN_RESTRICT rhs_data;
if (DirectlyUseRhs)
rhs_data = &actualRhs.const_cast_derived().coeffRef(0);
else
{
rhs_data = ei_aligned_stack_new(Scalar, actualRhs.size());
Map<typename _ActualRhsType::PlainObject>(rhs_data, actualRhs.size()) = actualRhs;
}
ei_cache_friendly_product_rowmajor_times_vector
<LhsBlasTraits::NeedToConjugate,RhsBlasTraits::NeedToConjugate>(
&actualLhs.const_cast_derived().coeffRef(0,0), actualLhs.outerStride(),
rhs_data, prod.rhs().size(), dest, actualAlpha);
if (!DirectlyUseRhs) ei_aligned_stack_delete(Scalar, rhs_data, prod.rhs().size());
}
};
template<> struct ei_gemv_selector<OnTheRight,ColMajor,false>
{
template<typename ProductType, typename Dest>
static void run(const ProductType& prod, Dest& dest, 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 ei_gemv_selector<OnTheRight,RowMajor,false>
{
template<typename ProductType, typename Dest>
static void run(const ProductType& prod, Dest& dest, 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();
}
};
/***************************************************************************
* 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 ei_matrix_storage 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)
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 ProductReturnType<Derived,OtherDerived,LazyCoeffBasedProductMode>::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 ProductReturnType<Derived,OtherDerived,LazyCoeffBasedProductMode>::Type(derived(), other.derived());
}
#endif // EIGEN_PRODUCT_H