| // 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 |
| |
| // IWYU pragma: private |
| #include "../InternalHeaderCheck.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 ResInnerStride, 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 ResInnerStride, 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 ResInnerStride, int UpLo, int Version> |
| struct general_matrix_matrix_triangular_product<Index, LhsScalar, LhsStorageOrder, ConjugateLhs, RhsScalar, |
| RhsStorageOrder, ConjugateRhs, RowMajor, ResInnerStride, 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 resIncr, |
| 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, ResInnerStride, |
| UpLo == Lower ? Upper : Lower>::run(size, depth, rhs, rhsStride, lhs, |
| lhsStride, res, resIncr, resStride, |
| alpha, blocking); |
| } |
| }; |
| |
| template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs, typename RhsScalar, |
| int RhsStorageOrder, bool ConjugateRhs, int ResInnerStride, int UpLo, int Version> |
| struct general_matrix_matrix_triangular_product<Index, LhsScalar, LhsStorageOrder, ConjugateLhs, RhsScalar, |
| RhsStorageOrder, ConjugateRhs, ColMajor, ResInnerStride, 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 resIncr, |
| 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, Unaligned, ResInnerStride> ResMapper; |
| LhsMapper lhs(lhs_, lhsStride); |
| RhsMapper rhs(rhs_, rhsStride); |
| ResMapper res(res_, resStride, resIncr); |
| |
| Index kc = blocking.kc(); |
| // Ensure that mc >= nr and <= size |
| Index mc = (std::min)(size, (std::max)(static_cast<decltype(blocking.mc())>(Traits::nr), blocking.mc())); |
| |
| // !!! mc must be a multiple of nr |
| if (mc > Traits::nr) { |
| using UnsignedIndex = typename make_unsigned<Index>::type; |
| mc = (UnsignedIndex(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, typename Traits::LhsPacket4Packing, |
| 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, ResInnerStride, 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 + resIncr * i2, resIncr, 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 ResInnerStride, int UpLo> |
| struct tribb_kernel { |
| typedef gebp_traits<LhsScalar, RhsScalar, ConjLhs, ConjRhs> Traits; |
| typedef typename Traits::ResScalar ResScalar; |
| |
| enum { BlockSize = meta_least_common_multiple<plain_enum_max(mr, nr), plain_enum_min(mr, nr)>::ret }; |
| void operator()(ResScalar* res_, Index resIncr, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, |
| Index size, Index depth, const ResScalar& alpha) { |
| typedef blas_data_mapper<ResScalar, Index, ColMajor, Unaligned, ResInnerStride> ResMapper; |
| typedef blas_data_mapper<ResScalar, Index, ColMajor, Unaligned> BufferMapper; |
| ResMapper res(res_, resStride, resIncr); |
| gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, mr, nr, ConjLhs, ConjRhs> gebp_kernel1; |
| gebp_kernel<LhsScalar, RhsScalar, Index, BufferMapper, mr, nr, ConjLhs, ConjRhs> gebp_kernel2; |
| |
| 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_kernel1(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_kernel2(BufferMapper(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) { |
| typename ResMapper::LinearMapper r = res.getLinearMapper(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_kernel1(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 internal::remove_all_t<typename ProductType::LhsNested> Lhs; |
| typedef internal::blas_traits<Lhs> LhsBlasTraits; |
| typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs; |
| typedef internal::remove_all_t<ActualLhs> ActualLhs_; |
| internal::add_const_on_value_type_t<ActualLhs> actualLhs = LhsBlasTraits::extract(prod.lhs()); |
| |
| typedef internal::remove_all_t<typename ProductType::RhsNested> Rhs; |
| typedef internal::blas_traits<Rhs> RhsBlasTraits; |
| typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs; |
| typedef internal::remove_all_t<ActualRhs> ActualRhs_; |
| internal::add_const_on_value_type_t<ActualRhs> 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 internal::remove_all_t<typename ProductType::LhsNested> Lhs; |
| typedef internal::blas_traits<Lhs> LhsBlasTraits; |
| typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs; |
| typedef internal::remove_all_t<ActualLhs> ActualLhs_; |
| internal::add_const_on_value_type_t<ActualLhs> actualLhs = LhsBlasTraits::extract(prod.lhs()); |
| |
| typedef internal::remove_all_t<typename ProductType::RhsNested> Rhs; |
| typedef internal::blas_traits<Rhs> RhsBlasTraits; |
| typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs; |
| typedef internal::remove_all_t<ActualRhs> ActualRhs_; |
| internal::add_const_on_value_type_t<ActualRhs> 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, MatrixType::InnerStrideAtCompileTime, |
| 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) ? mat.innerStride() |
| : mat.outerStride()) |
| : 0), |
| mat.innerStride(), mat.outerStride(), actualAlpha, blocking); |
| } |
| }; |
| |
| template <typename MatrixType, unsigned int UpLo> |
| template <typename ProductType> |
| EIGEN_DEVICE_FUNC 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 |
