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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>
//
// 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_SELFADJOINT_MATRIX_VECTOR_H
#define EIGEN_SELFADJOINT_MATRIX_VECTOR_H
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>
static EIGEN_DONT_INLINE void product_selfadjoint_vector(
Index size,
const Scalar* lhs, Index lhsStride,
const Scalar* _rhs, Index rhsIncr,
Scalar* res, Scalar alpha)
{
typedef typename packet_traits<Scalar>::type Packet;
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<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 ? conj(alpha) : alpha;
// if the rhs is not sequentially stored in memory we copy it to a temporary buffer,
// this is because we need to extract packets
const Scalar* EIGEN_RESTRICT rhs = _rhs;
if (rhsIncr!=1)
{
Scalar* r = ei_aligned_stack_new(Scalar, size);
const Scalar* it = _rhs;
for (Index i=0; i<size; ++i, it+=rhsIncr)
r[i] = *it;
rhs = r;
}
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)
{
register const Scalar* EIGEN_RESTRICT A0 = lhs + j*lhsStride;
register 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);
size_t starti = FirstTriangular ? 0 : j+2;
size_t endi = FirstTriangular ? j : size;
size_t alignedEnd = starti;
size_t alignedStart = (starti) + first_aligned(&res[starti], endi-starti);
alignedEnd = alignedStart + ((endi-alignedStart)/(PacketSize))*(PacketSize);
res[j] += cj0.pmul(A0[j], t0);
if(FirstTriangular)
{
res[j+1] += cj0.pmul(A1[j+1], t1);
res[j] += cj0.pmul(A1[j], t1);
t3 += cj1.pmul(A1[j], rhs[j]);
}
else
{
res[j+1] += cj0.pmul(A0[j+1],t0) + cj0.pmul(A1[j+1],t1);
t2 += cj1.pmul(A0[j+1], rhs[j+1]);
}
for (size_t i=starti; i<alignedStart; ++i)
{
res[i] += t0 * A0[i] + t1 * A1[i];
t2 += conj(A0[i]) * rhs[i];
t3 += conj(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 (size_t 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 (size_t 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++)
{
register const Scalar* EIGEN_RESTRICT A0 = lhs + j*lhsStride;
Scalar t1 = cjAlpha * rhs[j];
Scalar t2 = 0;
res[j] += cj0.pmul(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;
}
if(rhsIncr!=1)
ei_aligned_stack_delete(Scalar, const_cast<Scalar*>(rhs), size);
}
} // end namespace internal
/***************************************************************************
* Wrapper to product_selfadjoint_vector
***************************************************************************/
namespace internal {
template<typename Lhs, int LhsMode, typename Rhs>
struct traits<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,0,true> >
: traits<ProductBase<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,0,true>, Lhs, Rhs> >
{};
}
template<typename Lhs, int LhsMode, typename Rhs>
struct SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,0,true>
: public ProductBase<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,0,true>, Lhs, Rhs >
{
EIGEN_PRODUCT_PUBLIC_INTERFACE(SelfadjointProductMatrix)
enum {
LhsUpLo = LhsMode&(Upper|Lower)
};
SelfadjointProductMatrix(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) {}
template<typename Dest> void scaleAndAddTo(Dest& dst, Scalar alpha) const
{
eigen_assert(dst.rows()==m_lhs.rows() && dst.cols()==m_rhs.cols());
const ActualLhsType lhs = LhsBlasTraits::extract(m_lhs);
const ActualRhsType rhs = RhsBlasTraits::extract(m_rhs);
Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs)
* RhsBlasTraits::extractScalarFactor(m_rhs);
eigen_assert(dst.innerStride()==1 && "not implemented yet");
internal::product_selfadjoint_vector<Scalar, Index, (internal::traits<_ActualLhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, int(LhsUpLo), bool(LhsBlasTraits::NeedToConjugate), bool(RhsBlasTraits::NeedToConjugate)>
(
lhs.rows(), // size
&lhs.coeff(0,0), lhs.outerStride(), // lhs info
&rhs.coeff(0), rhs.innerStride(), // rhs info
&dst.coeffRef(0), // result info
actualAlpha // scale factor
);
}
};
namespace internal {
template<typename Lhs, typename Rhs, int RhsMode>
struct traits<SelfadjointProductMatrix<Lhs,0,true,Rhs,RhsMode,false> >
: traits<ProductBase<SelfadjointProductMatrix<Lhs,0,true,Rhs,RhsMode,false>, Lhs, Rhs> >
{};
}
template<typename Lhs, typename Rhs, int RhsMode>
struct SelfadjointProductMatrix<Lhs,0,true,Rhs,RhsMode,false>
: public ProductBase<SelfadjointProductMatrix<Lhs,0,true,Rhs,RhsMode,false>, Lhs, Rhs >
{
EIGEN_PRODUCT_PUBLIC_INTERFACE(SelfadjointProductMatrix)
enum {
RhsUpLo = RhsMode&(Upper|Lower)
};
SelfadjointProductMatrix(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) {}
template<typename Dest> void scaleAndAddTo(Dest& dst, Scalar alpha) const
{
eigen_assert(dst.rows()==m_lhs.rows() && dst.cols()==m_rhs.cols());
const ActualLhsType lhs = LhsBlasTraits::extract(m_lhs);
const ActualRhsType rhs = RhsBlasTraits::extract(m_rhs);
Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs)
* RhsBlasTraits::extractScalarFactor(m_rhs);
eigen_assert(dst.innerStride()==1 && "not implemented yet");
// transpose the product
internal::product_selfadjoint_vector<Scalar, Index, (internal::traits<_ActualRhsType>::Flags&RowMajorBit) ? ColMajor : RowMajor, int(RhsUpLo)==Upper ? Lower : Upper,
bool(RhsBlasTraits::NeedToConjugate), bool(LhsBlasTraits::NeedToConjugate)>
(
rhs.rows(), // size
&rhs.coeff(0,0), rhs.outerStride(), // lhs info
&lhs.coeff(0), lhs.innerStride(), // rhs info
&dst.coeffRef(0), // result info
actualAlpha // scale factor
);
}
};
#endif // EIGEN_SELFADJOINT_MATRIX_VECTOR_H
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