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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 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_SELFADJOINT_MATRIX_VECTOR_H
#define EIGEN_SELFADJOINT_MATRIX_VECTOR_H
namespace Eigen {
namespace internal {
/* Optimized selfadjoint matrix * vector product:
* This algorithm processes 2 columns at onces that allows to both reduce
* the number of load/stores of the result by a factor 2 and to reduce
* the instruction dependency.
*/
template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs, int Version=Specialized>
struct selfadjoint_matrix_vector_product;
template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs, int Version>
struct selfadjoint_matrix_vector_product
{
static EIGEN_DONT_INLINE void run(
Index size,
const Scalar* lhs, Index lhsStride,
const Scalar* rhs,
Scalar* res,
Scalar alpha);
};
template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs, int Version>
EIGEN_DONT_INLINE void selfadjoint_matrix_vector_product<Scalar,Index,StorageOrder,UpLo,ConjugateLhs,ConjugateRhs,Version>::run(
Index size,
const Scalar* lhs, Index lhsStride,
const Scalar* rhs,
Scalar* res,
Scalar alpha)
{
typedef typename packet_traits<Scalar>::type Packet;
typedef typename NumTraits<Scalar>::Real RealScalar;
const Index PacketSize = sizeof(Packet)/sizeof(Scalar);
enum {
IsRowMajor = StorageOrder==RowMajor ? 1 : 0,
IsLower = UpLo == Lower ? 1 : 0,
FirstTriangular = IsRowMajor == IsLower
};
conj_helper<Scalar,Scalar,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs, IsRowMajor), ConjugateRhs> cj0;
conj_helper<Scalar,Scalar,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs, !IsRowMajor), ConjugateRhs> cj1;
conj_helper<RealScalar,Scalar,false, ConjugateRhs> cjd;
conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs, IsRowMajor), ConjugateRhs> pcj0;
conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs, !IsRowMajor), ConjugateRhs> pcj1;
Scalar cjAlpha = ConjugateRhs ? numext::conj(alpha) : alpha;
Index bound = (std::max)(Index(0),size-8) & 0xfffffffe;
if (FirstTriangular)
bound = size - bound;
for (Index j=FirstTriangular ? bound : 0;
j<(FirstTriangular ? size : bound);j+=2)
{
const Scalar* EIGEN_RESTRICT A0 = lhs + j*lhsStride;
const Scalar* EIGEN_RESTRICT A1 = lhs + (j+1)*lhsStride;
Scalar t0 = cjAlpha * rhs[j];
Packet ptmp0 = pset1<Packet>(t0);
Scalar t1 = cjAlpha * rhs[j+1];
Packet ptmp1 = pset1<Packet>(t1);
Scalar t2(0);
Packet ptmp2 = pset1<Packet>(t2);
Scalar t3(0);
Packet ptmp3 = pset1<Packet>(t3);
Index starti = FirstTriangular ? 0 : j+2;
Index endi = FirstTriangular ? j : size;
Index alignedStart = (starti) + internal::first_default_aligned(&res[starti], endi-starti);
Index alignedEnd = alignedStart + ((endi-alignedStart)/(PacketSize))*(PacketSize);
res[j] += cjd.pmul(numext::real(A0[j]), t0);
res[j+1] += cjd.pmul(numext::real(A1[j+1]), t1);
if(FirstTriangular)
{
res[j] += cj0.pmul(A1[j], t1);
t3 += cj1.pmul(A1[j], rhs[j]);
}
else
{
res[j+1] += cj0.pmul(A0[j+1],t0);
t2 += cj1.pmul(A0[j+1], rhs[j+1]);
}
for (Index i=starti; i<alignedStart; ++i)
{
res[i] += cj0.pmul(A0[i], t0) + cj0.pmul(A1[i],t1);
t2 += cj1.pmul(A0[i], rhs[i]);
t3 += cj1.pmul(A1[i], rhs[i]);
}
// Yes this an optimization for gcc 4.3 and 4.4 (=> huge speed up)
// gcc 4.2 does this optimization automatically.
const Scalar* EIGEN_RESTRICT a0It = A0 + alignedStart;
const Scalar* EIGEN_RESTRICT a1It = A1 + alignedStart;
const Scalar* EIGEN_RESTRICT rhsIt = rhs + alignedStart;
Scalar* EIGEN_RESTRICT resIt = res + alignedStart;
for (Index i=alignedStart; i<alignedEnd; i+=PacketSize)
{
Packet A0i = ploadu<Packet>(a0It); a0It += PacketSize;
Packet A1i = ploadu<Packet>(a1It); a1It += PacketSize;
Packet Bi = ploadu<Packet>(rhsIt); rhsIt += PacketSize; // FIXME should be aligned in most cases
Packet Xi = pload <Packet>(resIt);
Xi = pcj0.pmadd(A0i,ptmp0, pcj0.pmadd(A1i,ptmp1,Xi));
ptmp2 = pcj1.pmadd(A0i, Bi, ptmp2);
ptmp3 = pcj1.pmadd(A1i, Bi, ptmp3);
pstore(resIt,Xi); resIt += PacketSize;
}
for (Index i=alignedEnd; i<endi; i++)
{
res[i] += cj0.pmul(A0[i], t0) + cj0.pmul(A1[i],t1);
t2 += cj1.pmul(A0[i], rhs[i]);
t3 += cj1.pmul(A1[i], rhs[i]);
}
res[j] += alpha * (t2 + predux(ptmp2));
res[j+1] += alpha * (t3 + predux(ptmp3));
}
for (Index j=FirstTriangular ? 0 : bound;j<(FirstTriangular ? bound : size);j++)
{
const Scalar* EIGEN_RESTRICT A0 = lhs + j*lhsStride;
Scalar t1 = cjAlpha * rhs[j];
Scalar t2(0);
res[j] += cjd.pmul(numext::real(A0[j]), t1);
for (Index i=FirstTriangular ? 0 : j+1; i<(FirstTriangular ? j : size); i++)
{
res[i] += cj0.pmul(A0[i], t1);
t2 += cj1.pmul(A0[i], rhs[i]);
}
res[j] += alpha * t2;
}
}
} // end namespace internal
/***************************************************************************
* Wrapper to product_selfadjoint_vector
***************************************************************************/
namespace internal {
template<typename Lhs, int LhsMode, typename Rhs>
struct selfadjoint_product_impl<Lhs,LhsMode,false,Rhs,0,true>
{
typedef typename Product<Lhs,Rhs>::Scalar Scalar;
typedef internal::blas_traits<Lhs> LhsBlasTraits;
typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
typedef typename internal::remove_all<ActualLhsType>::type ActualLhsTypeCleaned;
typedef internal::blas_traits<Rhs> RhsBlasTraits;
typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
typedef typename internal::remove_all<ActualRhsType>::type ActualRhsTypeCleaned;
enum { LhsUpLo = LhsMode&(Upper|Lower) };
template<typename Dest>
static void run(Dest& dest, const Lhs &a_lhs, const Rhs &a_rhs, const Scalar& alpha)
{
typedef typename Dest::Scalar ResScalar;
typedef typename Rhs::Scalar RhsScalar;
typedef Map<Matrix<ResScalar,Dynamic,1>, EIGEN_PLAIN_ENUM_MIN(AlignedMax,internal::packet_traits<ResScalar>::size)> MappedDest;
eigen_assert(dest.rows()==a_lhs.rows() && dest.cols()==a_rhs.cols());
typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(a_lhs);
typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(a_rhs);
Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(a_lhs)
* RhsBlasTraits::extractScalarFactor(a_rhs);
enum {
EvalToDest = (Dest::InnerStrideAtCompileTime==1),
UseRhs = (ActualRhsTypeCleaned::InnerStrideAtCompileTime==1)
};
internal::gemv_static_vector_if<ResScalar,Dest::SizeAtCompileTime,Dest::MaxSizeAtCompileTime,!EvalToDest> static_dest;
internal::gemv_static_vector_if<RhsScalar,ActualRhsTypeCleaned::SizeAtCompileTime,ActualRhsTypeCleaned::MaxSizeAtCompileTime,!UseRhs> static_rhs;
ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),
EvalToDest ? dest.data() : static_dest.data());
ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,rhs.size(),
UseRhs ? const_cast<RhsScalar*>(rhs.data()) : static_rhs.data());
if(!EvalToDest)
{
#ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
Index size = dest.size();
EIGEN_DENSE_STORAGE_CTOR_PLUGIN
#endif
MappedDest(actualDestPtr, dest.size()) = dest;
}
if(!UseRhs)
{
#ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
Index size = rhs.size();
EIGEN_DENSE_STORAGE_CTOR_PLUGIN
#endif
Map<typename ActualRhsTypeCleaned::PlainObject>(actualRhsPtr, rhs.size()) = rhs;
}
internal::selfadjoint_matrix_vector_product<Scalar, Index, (internal::traits<ActualLhsTypeCleaned>::Flags&RowMajorBit) ? RowMajor : ColMajor,
int(LhsUpLo), bool(LhsBlasTraits::NeedToConjugate), bool(RhsBlasTraits::NeedToConjugate)>::run
(
lhs.rows(), // size
&lhs.coeffRef(0,0), lhs.outerStride(), // lhs info
actualRhsPtr, // rhs info
actualDestPtr, // result info
actualAlpha // scale factor
);
if(!EvalToDest)
dest = MappedDest(actualDestPtr, dest.size());
}
};
template<typename Lhs, typename Rhs, int RhsMode>
struct selfadjoint_product_impl<Lhs,0,true,Rhs,RhsMode,false>
{
typedef typename Product<Lhs,Rhs>::Scalar Scalar;
enum { RhsUpLo = RhsMode&(Upper|Lower) };
template<typename Dest>
static void run(Dest& dest, const Lhs &a_lhs, const Rhs &a_rhs, const Scalar& alpha)
{
// let's simply transpose the product
Transpose<Dest> destT(dest);
selfadjoint_product_impl<Transpose<const Rhs>, int(RhsUpLo)==Upper ? Lower : Upper, false,
Transpose<const Lhs>, 0, true>::run(destT, a_rhs.transpose(), a_lhs.transpose(), alpha);
}
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_SELFADJOINT_MATRIX_VECTOR_H
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