| // This file is part of Eigen, a lightweight C++ template library |
| // for linear algebra. |
| // |
| // Copyright (C) 2009-2010 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_GENERAL_MATRIX_MATRIX_TRIANGULAR_H |
| #define EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H |
| |
| namespace Eigen { |
| |
| template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjLhs, bool ConjRhs> |
| struct selfadjoint_rank1_update; |
| |
| namespace internal { |
| |
| /********************************************************************** |
| * This file implements a general A * B product while |
| * evaluating only one triangular part of the product. |
| * This is a more general version of self adjoint product (C += A A^T) |
| * as the level 3 SYRK Blas routine. |
| **********************************************************************/ |
| |
| // forward declarations (defined at the end of this file) |
| template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo> |
| struct tribb_kernel; |
| |
| /* Optimized matrix-matrix product evaluating only one triangular half */ |
| template <typename Index, |
| typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs, |
| typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, |
| int ResStorageOrder, int UpLo, int Version = Specialized> |
| struct general_matrix_matrix_triangular_product; |
| |
| // as usual if the result is row major => we transpose the product |
| template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs, |
| typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int UpLo, int Version> |
| struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor,UpLo,Version> |
| { |
| typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar; |
| static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* lhs, Index lhsStride, |
| const RhsScalar* rhs, Index rhsStride, ResScalar* res, Index resStride, |
| const ResScalar& alpha, level3_blocking<RhsScalar,LhsScalar>& blocking) |
| { |
| general_matrix_matrix_triangular_product<Index, |
| RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs, |
| LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs, |
| ColMajor, UpLo==Lower?Upper:Lower> |
| ::run(size,depth,rhs,rhsStride,lhs,lhsStride,res,resStride,alpha,blocking); |
| } |
| }; |
| |
| template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs, |
| typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int UpLo, int Version> |
| struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor,UpLo,Version> |
| { |
| typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar; |
| static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* _lhs, Index lhsStride, |
| const RhsScalar* _rhs, Index rhsStride, ResScalar* _res, Index resStride, |
| const ResScalar& alpha, level3_blocking<LhsScalar,RhsScalar>& blocking) |
| { |
| typedef gebp_traits<LhsScalar,RhsScalar> Traits; |
| |
| typedef const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> LhsMapper; |
| typedef const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> RhsMapper; |
| typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor> ResMapper; |
| LhsMapper lhs(_lhs,lhsStride); |
| RhsMapper rhs(_rhs,rhsStride); |
| ResMapper res(_res, resStride); |
| |
| Index kc = blocking.kc(); |
| Index mc = (std::min)(size,blocking.mc()); |
| |
| // !!! mc must be a multiple of nr: |
| if(mc > Traits::nr) |
| mc = (mc/Traits::nr)*Traits::nr; |
| |
| std::size_t sizeA = kc*mc; |
| std::size_t sizeB = kc*size; |
| |
| ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, blocking.blockA()); |
| ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, blocking.blockB()); |
| |
| gemm_pack_lhs<LhsScalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs; |
| gemm_pack_rhs<RhsScalar, Index, RhsMapper, Traits::nr, RhsStorageOrder> pack_rhs; |
| gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp; |
| tribb_kernel<LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs, UpLo> sybb; |
| |
| for(Index k2=0; k2<depth; k2+=kc) |
| { |
| const Index actual_kc = (std::min)(k2+kc,depth)-k2; |
| |
| // note that the actual rhs is the transpose/adjoint of mat |
| pack_rhs(blockB, rhs.getSubMapper(k2,0), actual_kc, size); |
| |
| for(Index i2=0; i2<size; i2+=mc) |
| { |
| const Index actual_mc = (std::min)(i2+mc,size)-i2; |
| |
| pack_lhs(blockA, lhs.getSubMapper(i2, k2), actual_kc, actual_mc); |
| |
| // the selected actual_mc * size panel of res is split into three different part: |
| // 1 - before the diagonal => processed with gebp or skipped |
| // 2 - the actual_mc x actual_mc symmetric block => processed with a special kernel |
| // 3 - after the diagonal => processed with gebp or skipped |
| if (UpLo==Lower) |
| gebp(res.getSubMapper(i2, 0), blockA, blockB, actual_mc, actual_kc, |
| (std::min)(size,i2), alpha, -1, -1, 0, 0); |
| |
| |
| sybb(_res+resStride*i2 + i2, resStride, blockA, blockB + actual_kc*i2, actual_mc, actual_kc, alpha); |
| |
| if (UpLo==Upper) |
| { |
| Index j2 = i2+actual_mc; |
| gebp(res.getSubMapper(i2, j2), blockA, blockB+actual_kc*j2, actual_mc, |
| actual_kc, (std::max)(Index(0), size-j2), alpha, -1, -1, 0, 0); |
| } |
| } |
| } |
| } |
| }; |
| |
| // Optimized packed Block * packed Block product kernel evaluating only one given triangular part |
| // This kernel is built on top of the gebp kernel: |
| // - the current destination block is processed per panel of actual_mc x BlockSize |
| // where BlockSize is set to the minimal value allowing gebp to be as fast as possible |
| // - then, as usual, each panel is split into three parts along the diagonal, |
| // the sub blocks above and below the diagonal are processed as usual, |
| // while the triangular block overlapping the diagonal is evaluated into a |
| // small temporary buffer which is then accumulated into the result using a |
| // triangular traversal. |
| template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo> |
| struct tribb_kernel |
| { |
| typedef gebp_traits<LhsScalar,RhsScalar,ConjLhs,ConjRhs> Traits; |
| typedef typename Traits::ResScalar ResScalar; |
| |
| enum { |
| BlockSize = meta_least_common_multiple<EIGEN_PLAIN_ENUM_MAX(mr,nr),EIGEN_PLAIN_ENUM_MIN(mr,nr)>::ret |
| }; |
| void operator()(ResScalar* _res, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index size, Index depth, const ResScalar& alpha) |
| { |
| typedef blas_data_mapper<ResScalar, Index, ColMajor> ResMapper; |
| ResMapper res(_res, resStride); |
| gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, mr, nr, ConjLhs, ConjRhs> gebp_kernel; |
| |
| Matrix<ResScalar,BlockSize,BlockSize,ColMajor> buffer((internal::constructor_without_unaligned_array_assert())); |
| |
| // let's process the block per panel of actual_mc x BlockSize, |
| // again, each is split into three parts, etc. |
| for (Index j=0; j<size; j+=BlockSize) |
| { |
| Index actualBlockSize = std::min<Index>(BlockSize,size - j); |
| const RhsScalar* actual_b = blockB+j*depth; |
| |
| if(UpLo==Upper) |
| gebp_kernel(res.getSubMapper(0, j), blockA, actual_b, j, depth, actualBlockSize, alpha, |
| -1, -1, 0, 0); |
| |
| // selfadjoint micro block |
| { |
| Index i = j; |
| buffer.setZero(); |
| // 1 - apply the kernel on the temporary buffer |
| gebp_kernel(ResMapper(buffer.data(), BlockSize), blockA+depth*i, actual_b, actualBlockSize, depth, actualBlockSize, alpha, |
| -1, -1, 0, 0); |
| // 2 - triangular accumulation |
| for(Index j1=0; j1<actualBlockSize; ++j1) |
| { |
| ResScalar* r = &res(i, j + j1); |
| for(Index i1=UpLo==Lower ? j1 : 0; |
| UpLo==Lower ? i1<actualBlockSize : i1<=j1; ++i1) |
| r[i1] += buffer(i1,j1); |
| } |
| } |
| |
| if(UpLo==Lower) |
| { |
| Index i = j+actualBlockSize; |
| gebp_kernel(res.getSubMapper(i, j), blockA+depth*i, actual_b, size-i, |
| depth, actualBlockSize, alpha, -1, -1, 0, 0); |
| } |
| } |
| } |
| }; |
| |
| } // end namespace internal |
| |
| // high level API |
| |
| template<typename MatrixType, typename ProductType, int UpLo, bool IsOuterProduct> |
| struct general_product_to_triangular_selector; |
| |
| |
| template<typename MatrixType, typename ProductType, int UpLo> |
| struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,true> |
| { |
| static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha, bool beta) |
| { |
| typedef typename MatrixType::Scalar Scalar; |
| |
| typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs; |
| typedef internal::blas_traits<Lhs> LhsBlasTraits; |
| typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs; |
| typedef typename internal::remove_all<ActualLhs>::type _ActualLhs; |
| typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs()); |
| |
| typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs; |
| typedef internal::blas_traits<Rhs> RhsBlasTraits; |
| typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs; |
| typedef typename internal::remove_all<ActualRhs>::type _ActualRhs; |
| typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs()); |
| |
| Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived()); |
| |
| if(!beta) |
| mat.template triangularView<UpLo>().setZero(); |
| |
| enum { |
| StorageOrder = (internal::traits<MatrixType>::Flags&RowMajorBit) ? RowMajor : ColMajor, |
| UseLhsDirectly = _ActualLhs::InnerStrideAtCompileTime==1, |
| UseRhsDirectly = _ActualRhs::InnerStrideAtCompileTime==1 |
| }; |
| |
| internal::gemv_static_vector_if<Scalar,Lhs::SizeAtCompileTime,Lhs::MaxSizeAtCompileTime,!UseLhsDirectly> static_lhs; |
| ei_declare_aligned_stack_constructed_variable(Scalar, actualLhsPtr, actualLhs.size(), |
| (UseLhsDirectly ? const_cast<Scalar*>(actualLhs.data()) : static_lhs.data())); |
| if(!UseLhsDirectly) Map<typename _ActualLhs::PlainObject>(actualLhsPtr, actualLhs.size()) = actualLhs; |
| |
| internal::gemv_static_vector_if<Scalar,Rhs::SizeAtCompileTime,Rhs::MaxSizeAtCompileTime,!UseRhsDirectly> static_rhs; |
| ei_declare_aligned_stack_constructed_variable(Scalar, actualRhsPtr, actualRhs.size(), |
| (UseRhsDirectly ? const_cast<Scalar*>(actualRhs.data()) : static_rhs.data())); |
| if(!UseRhsDirectly) Map<typename _ActualRhs::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs; |
| |
| |
| selfadjoint_rank1_update<Scalar,Index,StorageOrder,UpLo, |
| LhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex, |
| RhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex> |
| ::run(actualLhs.size(), mat.data(), mat.outerStride(), actualLhsPtr, actualRhsPtr, actualAlpha); |
| } |
| }; |
| |
| template<typename MatrixType, typename ProductType, int UpLo> |
| struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,false> |
| { |
| static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha, bool beta) |
| { |
| typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs; |
| typedef internal::blas_traits<Lhs> LhsBlasTraits; |
| typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs; |
| typedef typename internal::remove_all<ActualLhs>::type _ActualLhs; |
| typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs()); |
| |
| typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs; |
| typedef internal::blas_traits<Rhs> RhsBlasTraits; |
| typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs; |
| typedef typename internal::remove_all<ActualRhs>::type _ActualRhs; |
| typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs()); |
| |
| typename ProductType::Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived()); |
| |
| if(!beta) |
| mat.template triangularView<UpLo>().setZero(); |
| |
| enum { |
| IsRowMajor = (internal::traits<MatrixType>::Flags&RowMajorBit) ? 1 : 0, |
| LhsIsRowMajor = _ActualLhs::Flags&RowMajorBit ? 1 : 0, |
| RhsIsRowMajor = _ActualRhs::Flags&RowMajorBit ? 1 : 0, |
| SkipDiag = (UpLo&(UnitDiag|ZeroDiag))!=0 |
| }; |
| |
| Index size = mat.cols(); |
| if(SkipDiag) |
| size--; |
| Index depth = actualLhs.cols(); |
| |
| typedef internal::gemm_blocking_space<IsRowMajor ? RowMajor : ColMajor,typename Lhs::Scalar,typename Rhs::Scalar, |
| MatrixType::MaxColsAtCompileTime, MatrixType::MaxColsAtCompileTime, _ActualRhs::MaxColsAtCompileTime> BlockingType; |
| |
| BlockingType blocking(size, size, depth, 1, false); |
| |
| internal::general_matrix_matrix_triangular_product<Index, |
| typename Lhs::Scalar, LhsIsRowMajor ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate, |
| typename Rhs::Scalar, RhsIsRowMajor ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate, |
| IsRowMajor ? RowMajor : ColMajor, UpLo&(Lower|Upper)> |
| ::run(size, depth, |
| &actualLhs.coeffRef(SkipDiag&&(UpLo&Lower)==Lower ? 1 : 0,0), actualLhs.outerStride(), |
| &actualRhs.coeffRef(0,SkipDiag&&(UpLo&Upper)==Upper ? 1 : 0), actualRhs.outerStride(), |
| mat.data() + (SkipDiag ? (bool(IsRowMajor) != ((UpLo&Lower)==Lower) ? 1 : mat.outerStride() ) : 0), mat.outerStride(), actualAlpha, blocking); |
| } |
| }; |
| |
| template<typename MatrixType, unsigned int UpLo> |
| template<typename ProductType> |
| TriangularView<MatrixType,UpLo>& TriangularViewImpl<MatrixType,UpLo,Dense>::_assignProduct(const ProductType& prod, const Scalar& alpha, bool beta) |
| { |
| EIGEN_STATIC_ASSERT((UpLo&UnitDiag)==0, WRITING_TO_TRIANGULAR_PART_WITH_UNIT_DIAGONAL_IS_NOT_SUPPORTED); |
| eigen_assert(derived().nestedExpression().rows() == prod.rows() && derived().cols() == prod.cols()); |
| |
| general_product_to_triangular_selector<MatrixType, ProductType, UpLo, internal::traits<ProductType>::InnerSize==1>::run(derived().nestedExpression().const_cast_derived(), prod, alpha, beta); |
| |
| return derived(); |
| } |
| |
| } // end namespace Eigen |
| |
| #endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H |
