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|
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob@math.jussieu.fr>
// 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
template<int Index, int Size, typename Lhs, typename Rhs>
struct ei_product_unroller
{
static void run(int row, int col, const Lhs& lhs, const Rhs& rhs,
typename Lhs::Scalar &res)
{
ei_product_unroller<Index-1, Size, Lhs, Rhs>::run(row, col, lhs, rhs, res);
res += lhs.coeff(row, Index) * rhs.coeff(Index, col);
}
};
template<int Size, typename Lhs, typename Rhs>
struct ei_product_unroller<0, Size, Lhs, Rhs>
{
static void run(int row, int col, const Lhs& lhs, const Rhs& rhs,
typename Lhs::Scalar &res)
{
res = lhs.coeff(row, 0) * rhs.coeff(0, col);
}
};
template<int Index, typename Lhs, typename Rhs>
struct ei_product_unroller<Index, Dynamic, Lhs, Rhs>
{
static void run(int, int, const Lhs&, const Rhs&, typename Lhs::Scalar&) {}
};
// prevent buggy user code from causing an infinite recursion
template<int Index, typename Lhs, typename Rhs>
struct ei_product_unroller<Index, 0, Lhs, Rhs>
{
static void run(int, int, const Lhs&, const Rhs&, typename Lhs::Scalar&) {}
};
template<bool RowMajor, int Index, int Size, typename Lhs, typename Rhs, typename PacketScalar>
struct ei_packet_product_unroller
{
static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, PacketScalar &res)
{
ei_packet_product_unroller<RowMajor, Index-1, Size, Lhs, Rhs, PacketScalar>::run(row, col, lhs, rhs, res);
if (RowMajor)
res = ei_padd(res, ei_pmul(ei_pset1(lhs.coeff(row, Index)), rhs.packetCoeff(Index, col)));
else
res = ei_padd(res, ei_pmul(lhs.packetCoeff(row, Index), ei_pset1(rhs.coeff(Index, col))));
}
};
template<bool RowMajor, int Size, typename Lhs, typename Rhs, typename PacketScalar>
struct ei_packet_product_unroller<RowMajor, 0, Size, Lhs, Rhs, PacketScalar>
{
static void run(int row, int col, const Lhs& lhs, const Rhs& rhs, PacketScalar &res)
{
if (RowMajor)
res = ei_pmul(ei_pset1(lhs.coeff(row, 0)),rhs.packetCoeff(0, col));
else
res = ei_pmul(lhs.packetCoeff(row, 0), ei_pset1(rhs.coeff(0, col)));
}
};
template<bool RowMajor, int Index, typename Lhs, typename Rhs, typename PacketScalar>
struct ei_packet_product_unroller<RowMajor, Index, Dynamic, Lhs, Rhs, PacketScalar>
{
static void run(int, int, const Lhs&, const Rhs&, PacketScalar&) {}
};
/** \class Product
*
* \brief Expression of the product of two matrices
*
* \param Lhs the type of the left-hand side
* \param Rhs the type of the right-hand side
* \param EvalMode internal use only
*
* This class represents an expression of the product of two matrices.
* It is the return type of the operator* between matrices, and most of the time
* this is the only way it is used.
*
* \sa class Sum, class Difference
*/
template<typename Lhs, typename Rhs> struct ei_product_eval_mode
{
enum{ value = Lhs::MaxRowsAtCompileTime >= 16 && Rhs::MaxColsAtCompileTime >= 16
? CacheOptimalProduct : NormalProduct };
};
template<typename Lhs, typename Rhs, int EvalMode>
struct ei_traits<Product<Lhs, Rhs, EvalMode> >
{
typedef typename Lhs::Scalar Scalar;
typedef typename ei_nested<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;
typedef typename ei_nested<Rhs,Lhs::RowsAtCompileTime>::type RhsNested;
typedef typename ei_unref<LhsNested>::type _LhsNested;
typedef typename ei_unref<RhsNested>::type _RhsNested;
enum {
LhsCoeffReadCost = _LhsNested::CoeffReadCost,
RhsCoeffReadCost = _RhsNested::CoeffReadCost,
LhsFlags = _LhsNested::Flags,
RhsFlags = _RhsNested::Flags,
RowsAtCompileTime = Lhs::RowsAtCompileTime,
ColsAtCompileTime = Rhs::ColsAtCompileTime,
MaxRowsAtCompileTime = Lhs::MaxRowsAtCompileTime,
MaxColsAtCompileTime = Rhs::MaxColsAtCompileTime,
Flags = (( (RowsAtCompileTime == Dynamic || ColsAtCompileTime == Dynamic)
? (unsigned int)(LhsFlags | RhsFlags)
: (unsigned int)(LhsFlags | RhsFlags) & ~LargeBit )
| EvalBeforeAssigningBit
| (ei_product_eval_mode<Lhs, Rhs>::value == (int)CacheOptimalProduct ? EvalBeforeNestingBit : 0))
& (
~(RowMajorBit | VectorizableBit)
| (
(
!(Lhs::Flags & RowMajorBit) && (Lhs::Flags & VectorizableBit)
)
? VectorizableBit
: (
(
(Rhs::Flags & RowMajorBit) && (Rhs::Flags & VectorizableBit)
)
? RowMajorBit | VectorizableBit
: 0
)
)
),
CoeffReadCost
= Lhs::ColsAtCompileTime == Dynamic
? Dynamic
: Lhs::ColsAtCompileTime
* (NumTraits<Scalar>::MulCost + LhsCoeffReadCost + RhsCoeffReadCost)
+ (Lhs::ColsAtCompileTime - 1) * NumTraits<Scalar>::AddCost
};
};
template<typename Lhs, typename Rhs, int EvalMode> class Product : ei_no_assignment_operator,
public MatrixBase<Product<Lhs, Rhs, EvalMode> >
{
public:
EIGEN_GENERIC_PUBLIC_INTERFACE(Product)
typedef typename ei_traits<Product>::LhsNested LhsNested;
typedef typename ei_traits<Product>::RhsNested RhsNested;
typedef typename ei_traits<Product>::_LhsNested _LhsNested;
typedef typename ei_traits<Product>::_RhsNested _RhsNested;
Product(const Lhs& lhs, const Rhs& rhs)
: m_lhs(lhs), m_rhs(rhs)
{
ei_assert(lhs.cols() == rhs.rows());
}
/** \internal */
template<typename DestDerived>
void _cacheOptimalEval(DestDerived& res) const;
private:
int _rows() const { return m_lhs.rows(); }
int _cols() const { return m_rhs.cols(); }
const Scalar _coeff(int row, int col) const
{
Scalar res;
const bool unroll = CoeffReadCost <= EIGEN_UNROLLING_LIMIT;
if(unroll)
{
ei_product_unroller<Lhs::ColsAtCompileTime-1,
unroll ? Lhs::ColsAtCompileTime : Dynamic,
_LhsNested, _RhsNested>
::run(row, col, m_lhs, m_rhs, res);
}
else
{
res = m_lhs.coeff(row, 0) * m_rhs.coeff(0, col);
for(int i = 1; i < m_lhs.cols(); i++)
res += m_lhs.coeff(row, i) * m_rhs.coeff(i, col);
}
return res;
}
PacketScalar _packetCoeff(int row, int col) const EIGEN_ALWAYS_INLINE
{
PacketScalar res;
if(Lhs::ColsAtCompileTime <= EIGEN_UNROLLING_LIMIT)
{
ei_packet_product_unroller<Flags&RowMajorBit, Lhs::ColsAtCompileTime-1,
Lhs::ColsAtCompileTime <= EIGEN_UNROLLING_LIMIT
? Lhs::ColsAtCompileTime : Dynamic,
Lhs, Rhs, PacketScalar>
::run(row, col, m_lhs, m_rhs, res);
}
else
{
if (Flags&RowMajorBit)
{
res = ei_pmul(ei_pset1(m_lhs.coeff(row, 0)),m_rhs.packetCoeff(0, col));
for(int i = 1; i < m_lhs.cols(); i++)
res = ei_padd(res, ei_pmul(ei_pset1(m_lhs.coeff(row, i)), m_rhs.packetCoeff(i, col)));
}
else
{
res = ei_pmul(m_lhs.packetCoeff(row, 0), ei_pset1(m_rhs.coeff(0, col)));
for(int i = 1; i < m_lhs.cols(); i++)
res = ei_padd(res, ei_pmul(m_lhs.packetCoeff(row, i), ei_pset1(m_rhs.coeff(i, col))));
}
}
return res;
}
protected:
const LhsNested m_lhs;
const RhsNested m_rhs;
};
/** \returns the matrix product of \c *this and \a other.
*
* \note This function causes an immediate evaluation. If you want to perform a matrix product
* without immediate evaluation, call .lazy() on one of the matrices before taking the product.
*
* \sa lazy(), operator*=(const MatrixBase&)
*/
template<typename Derived>
template<typename OtherDerived>
const Product<Derived,OtherDerived>
MatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const
{
return Product<Derived,OtherDerived>(derived(), other.derived());
}
/** replaces \c *this by \c *this * \a other.
*
* \returns a reference to \c *this
*/
template<typename Derived>
template<typename OtherDerived>
Derived &
MatrixBase<Derived>::operator*=(const MatrixBase<OtherDerived> &other)
{
return *this = *this * other;
}
template<typename Derived>
template<typename Derived1, typename Derived2>
Derived& MatrixBase<Derived>::lazyAssign(const Product<Derived1,Derived2,CacheOptimalProduct>& product)
{
product._cacheOptimalEval(*this);
return derived();
}
template<typename Lhs, typename Rhs, int EvalMode>
template<typename DestDerived>
void Product<Lhs,Rhs,EvalMode>::_cacheOptimalEval(DestDerived& res) const
{
res.setZero();
const int cols4 = m_lhs.cols() & 0xfffffffC;
const bool should_parallelize = (Flags & DestDerived::Flags & LargeBit)
&& res.size() >= EIGEN_PARALLELIZATION_TRESHOLD;
#ifdef EIGEN_VECTORIZE
if( (Flags & VectorizableBit) && (!(Lhs::Flags & RowMajorBit)) )
{
#define EIGEN_THE_PARALLELIZABLE_LOOP \
for(int k=0; k<this->cols(); k++) \
{ \
int j=0; \
for(; j<cols4; j+=4) \
{ \
const typename ei_packet_traits<Scalar>::type tmp0 = ei_pset1(m_rhs.coeff(j+0,k)); \
const typename ei_packet_traits<Scalar>::type tmp1 = ei_pset1(m_rhs.coeff(j+1,k)); \
const typename ei_packet_traits<Scalar>::type tmp2 = ei_pset1(m_rhs.coeff(j+2,k)); \
const typename ei_packet_traits<Scalar>::type tmp3 = ei_pset1(m_rhs.coeff(j+3,k)); \
for (int i=0; i<this->rows(); i+=ei_packet_traits<Scalar>::size) \
{ \
res.writePacketCoeff(i,k,\
ei_padd( \
res.packetCoeff(i,k), \
ei_padd( \
ei_padd( \
ei_pmul(tmp0, m_lhs.packetCoeff(i,j)), \
ei_pmul(tmp1, m_lhs.packetCoeff(i,j+1))), \
ei_padd( \
ei_pmul(tmp2, m_lhs.packetCoeff(i,j+2)), \
ei_pmul(tmp3, m_lhs.packetCoeff(i,j+3)) \
) \
) \
) \
); \
} \
} \
for(; j<m_lhs.cols(); ++j) \
{ \
const typename ei_packet_traits<Scalar>::type tmp = ei_pset1(m_rhs.coeff(j,k)); \
for (int i=0; i<this->rows(); ++i) \
res.writePacketCoeff(i,k,ei_pmul(tmp, m_lhs.packetCoeff(i,j))); \
} \
}
EIGEN_RUN_PARALLELIZABLE_LOOP(should_parallelize)
#undef EIGEN_THE_PARALLELIZABLE_LOOP
}
else
#endif // EIGEN_VECTORIZE
{
#define EIGEN_THE_PARALLELIZABLE_LOOP \
for(int k=0; k<this->cols(); ++k) \
{ \
int j=0; \
for(; j<cols4; j+=4) \
{ \
const Scalar tmp0 = m_rhs.coeff(j ,k); \
const Scalar tmp1 = m_rhs.coeff(j+1,k); \
const Scalar tmp2 = m_rhs.coeff(j+2,k); \
const Scalar tmp3 = m_rhs.coeff(j+3,k); \
for (int i=0; i<this->rows(); ++i) \
res.coeffRef(i,k) += tmp0 * m_lhs.coeff(i,j) + tmp1 * m_lhs.coeff(i,j+1) \
+ tmp2 * m_lhs.coeff(i,j+2) + tmp3 * m_lhs.coeff(i,j+3); \
} \
for(; j<m_lhs.cols(); ++j) \
{ \
const Scalar tmp = m_rhs.coeff(j,k); \
for (int i=0; i<this->rows(); ++i) \
res.coeffRef(i,k) += tmp * m_lhs.coeff(i,j); \
} \
}
EIGEN_RUN_PARALLELIZABLE_LOOP(should_parallelize)
#undef EIGEN_THE_PARALLELIZABLE_LOOP
}
}
#endif // EIGEN_PRODUCT_H
|
