| // 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 |
| |
| // IWYU pragma: private |
| #include "../InternalHeaderCheck.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 && logical_xor(ConjugateLhs, IsRowMajor), ConjugateRhs> cj0; |
| conj_helper<Scalar, Scalar, NumTraits<Scalar>::IsComplex && logical_xor(ConjugateLhs, !IsRowMajor), ConjugateRhs> cj1; |
| conj_helper<RealScalar, Scalar, false, ConjugateRhs> cjd; |
| |
| conj_helper<Packet, Packet, NumTraits<Scalar>::IsComplex && logical_xor(ConjugateLhs, IsRowMajor), ConjugateRhs> pcj0; |
| conj_helper<Packet, Packet, NumTraits<Scalar>::IsComplex && 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 internal::remove_all_t<ActualLhsType> ActualLhsTypeCleaned; |
| |
| typedef internal::blas_traits<Rhs> RhsBlasTraits; |
| typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType; |
| typedef internal::remove_all_t<ActualRhsType> 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>, plain_enum_min(AlignedMax, internal::packet_traits<ResScalar>::size)> |
| MappedDest; |
| |
| eigen_assert(dest.rows() == a_lhs.rows() && dest.cols() == a_rhs.cols()); |
| |
| add_const_on_value_type_t<ActualLhsType> lhs = LhsBlasTraits::extract(a_lhs); |
| add_const_on_value_type_t<ActualRhsType> 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 |
