| // 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 once 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 EIGEN_DEVICE_FUNC |
| 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 EIGEN_DEVICE_FUNC |
| 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 = numext::maxi(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 EIGEN_DEVICE_FUNC |
| 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 |
