| // 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 { |
| |
| namespace internal { |
| |
| /********************************************************************** |
| * This file implements a general A * B product while |
| * evaluating only one triangular part of the product. |
| * This is 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 scalar_product_traits<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, ResScalar alpha) |
| { |
| 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); |
| } |
| }; |
| |
| 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 scalar_product_traits<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, ResScalar alpha) |
| { |
| const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride); |
| const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride); |
| |
| typedef gebp_traits<LhsScalar,RhsScalar> Traits; |
| |
| Index kc = depth; // cache block size along the K direction |
| Index mc = size; // cache block size along the M direction |
| Index nc = size; // cache block size along the N direction |
| computeProductBlockingSizes<LhsScalar,RhsScalar>(kc, mc, nc); |
| // !!! mc must be a multiple of nr: |
| if(mc > Traits::nr) |
| mc = (mc/Traits::nr)*Traits::nr; |
| |
| std::size_t sizeW = kc*Traits::WorkSpaceFactor; |
| std::size_t sizeB = sizeW + kc*size; |
| ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, kc*mc, 0); |
| ei_declare_aligned_stack_constructed_variable(RhsScalar, allocatedBlockB, sizeB, 0); |
| RhsScalar* blockB = allocatedBlockB + sizeW; |
| |
| gemm_pack_lhs<LhsScalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs; |
| gemm_pack_rhs<RhsScalar, Index, Traits::nr, RhsStorageOrder> pack_rhs; |
| gebp_kernel <LhsScalar, RhsScalar, Index, 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(k2,0), rhsStride, 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(i2, k2), lhsStride, 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+i2, resStride, blockA, blockB, actual_mc, actual_kc, (std::min)(size,i2), alpha, |
| -1, -1, 0, 0, allocatedBlockB); |
| |
| sybb(res+resStride*i2 + i2, resStride, blockA, blockB + actual_kc*i2, actual_mc, actual_kc, alpha, allocatedBlockB); |
| |
| if (UpLo==Upper) |
| { |
| Index j2 = i2+actual_mc; |
| gebp(res+resStride*j2+i2, resStride, blockA, blockB+actual_kc*j2, actual_mc, actual_kc, (std::max)(Index(0), size-j2), alpha, |
| -1, -1, 0, 0, allocatedBlockB); |
| } |
| } |
| } |
| } |
| }; |
| |
| // 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 = EIGEN_PLAIN_ENUM_MAX(mr,nr) |
| }; |
| void operator()(ResScalar* res, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index size, Index depth, ResScalar alpha, RhsScalar* workspace) |
| { |
| gebp_kernel<LhsScalar, RhsScalar, Index, mr, nr, ConjLhs, ConjRhs> gebp_kernel; |
| Matrix<ResScalar,BlockSize,BlockSize,ColMajor> buffer; |
| |
| // 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+j*resStride, resStride, blockA, actual_b, j, depth, actualBlockSize, alpha, |
| -1, -1, 0, 0, workspace); |
| |
| // selfadjoint micro block |
| { |
| Index i = j; |
| buffer.setZero(); |
| // 1 - apply the kernel on the temporary buffer |
| gebp_kernel(buffer.data(), BlockSize, blockA+depth*i, actual_b, actualBlockSize, depth, actualBlockSize, alpha, |
| -1, -1, 0, 0, workspace); |
| // 2 - triangular accumulation |
| for(Index j1=0; j1<actualBlockSize; ++j1) |
| { |
| ResScalar* r = res + (j+j1)*resStride + i; |
| 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+j*resStride+i, resStride, blockA+depth*i, actual_b, size-i, depth, actualBlockSize, alpha, |
| -1, -1, 0, 0, workspace); |
| } |
| } |
| } |
| }; |
| |
| } // end namespace internal |
| |
| // high level API |
| |
| template<typename MatrixType, unsigned int UpLo> |
| template<typename ProductDerived, typename _Lhs, typename _Rhs> |
| TriangularView<MatrixType,UpLo>& TriangularView<MatrixType,UpLo>::assignProduct(const ProductBase<ProductDerived, _Lhs,_Rhs>& prod, const Scalar& alpha) |
| { |
| typedef typename internal::remove_all<typename ProductDerived::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 ProductDerived::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 ProductDerived::Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived()); |
| |
| internal::general_matrix_matrix_triangular_product<Index, |
| typename Lhs::Scalar, _ActualLhs::Flags&RowMajorBit ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate, |
| typename Rhs::Scalar, _ActualRhs::Flags&RowMajorBit ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate, |
| MatrixType::Flags&RowMajorBit ? RowMajor : ColMajor, UpLo> |
| ::run(m_matrix.cols(), actualLhs.cols(), |
| &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &actualRhs.coeffRef(0,0), actualRhs.outerStride(), |
| const_cast<Scalar*>(m_matrix.data()), m_matrix.outerStride(), actualAlpha); |
| |
| return *this; |
| } |
| |
| } // end namespace Eigen |
| |
| #endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H |
