| // This file is part of Eigen, a lightweight C++ template library |
| // for linear algebra. |
| // |
| // Copyright (C) 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_TRIANGULAR_MATRIX_MATRIX_H |
| #define EIGEN_TRIANGULAR_MATRIX_MATRIX_H |
| |
| namespace Eigen { |
| |
| namespace internal { |
| |
| // template<typename Scalar, int mr, int StorageOrder, bool Conjugate, int Mode> |
| // struct gemm_pack_lhs_triangular |
| // { |
| // Matrix<Scalar,mr,mr, |
| // void operator()(Scalar* blockA, const EIGEN_RESTRICT Scalar* _lhs, int lhsStride, int depth, int rows) |
| // { |
| // conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj; |
| // const_blas_data_mapper<Scalar, StorageOrder> lhs(_lhs,lhsStride); |
| // int count = 0; |
| // const int peeled_mc = (rows/mr)*mr; |
| // for(int i=0; i<peeled_mc; i+=mr) |
| // { |
| // for(int k=0; k<depth; k++) |
| // for(int w=0; w<mr; w++) |
| // blockA[count++] = cj(lhs(i+w, k)); |
| // } |
| // for(int i=peeled_mc; i<rows; i++) |
| // { |
| // for(int k=0; k<depth; k++) |
| // blockA[count++] = cj(lhs(i, k)); |
| // } |
| // } |
| // }; |
| |
| /* Optimized triangular matrix * matrix (_TRMM++) product built on top of |
| * the general matrix matrix product. |
| */ |
| template <typename Scalar, typename Index, |
| int Mode, bool LhsIsTriangular, |
| int LhsStorageOrder, bool ConjugateLhs, |
| int RhsStorageOrder, bool ConjugateRhs, |
| int ResStorageOrder, int Version = Specialized> |
| struct product_triangular_matrix_matrix; |
| |
| template <typename Scalar, typename Index, |
| int Mode, bool LhsIsTriangular, |
| int LhsStorageOrder, bool ConjugateLhs, |
| int RhsStorageOrder, bool ConjugateRhs, int Version> |
| struct product_triangular_matrix_matrix<Scalar,Index,Mode,LhsIsTriangular, |
| LhsStorageOrder,ConjugateLhs, |
| RhsStorageOrder,ConjugateRhs,RowMajor,Version> |
| { |
| static EIGEN_STRONG_INLINE void run( |
| Index rows, Index cols, Index depth, |
| const Scalar* lhs, Index lhsStride, |
| const Scalar* rhs, Index rhsStride, |
| Scalar* res, Index resStride, |
| const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking) |
| { |
| product_triangular_matrix_matrix<Scalar, Index, |
| (Mode&(UnitDiag|ZeroDiag)) | ((Mode&Upper) ? Lower : Upper), |
| (!LhsIsTriangular), |
| RhsStorageOrder==RowMajor ? ColMajor : RowMajor, |
| ConjugateRhs, |
| LhsStorageOrder==RowMajor ? ColMajor : RowMajor, |
| ConjugateLhs, |
| ColMajor> |
| ::run(cols, rows, depth, rhs, rhsStride, lhs, lhsStride, res, resStride, alpha, blocking); |
| } |
| }; |
| |
| // implements col-major += alpha * op(triangular) * op(general) |
| template <typename Scalar, typename Index, int Mode, |
| int LhsStorageOrder, bool ConjugateLhs, |
| int RhsStorageOrder, bool ConjugateRhs, int Version> |
| struct product_triangular_matrix_matrix<Scalar,Index,Mode,true, |
| LhsStorageOrder,ConjugateLhs, |
| RhsStorageOrder,ConjugateRhs,ColMajor,Version> |
| { |
| |
| typedef gebp_traits<Scalar,Scalar> Traits; |
| enum { |
| SmallPanelWidth = 2 * EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr), |
| IsLower = (Mode&Lower) == Lower, |
| SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1 |
| }; |
| |
| static EIGEN_DONT_INLINE void run( |
| Index _rows, Index _cols, Index _depth, |
| const Scalar* _lhs, Index lhsStride, |
| const Scalar* _rhs, Index rhsStride, |
| Scalar* res, Index resStride, |
| const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking); |
| }; |
| |
| template <typename Scalar, typename Index, int Mode, |
| int LhsStorageOrder, bool ConjugateLhs, |
| int RhsStorageOrder, bool ConjugateRhs, int Version> |
| EIGEN_DONT_INLINE void product_triangular_matrix_matrix<Scalar,Index,Mode,true, |
| LhsStorageOrder,ConjugateLhs, |
| RhsStorageOrder,ConjugateRhs,ColMajor,Version>::run( |
| Index _rows, Index _cols, Index _depth, |
| const Scalar* _lhs, Index lhsStride, |
| const Scalar* _rhs, Index rhsStride, |
| Scalar* _res, Index resStride, |
| const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking) |
| { |
| // strip zeros |
| Index diagSize = (std::min)(_rows,_depth); |
| Index rows = IsLower ? _rows : diagSize; |
| Index depth = IsLower ? diagSize : _depth; |
| Index cols = _cols; |
| |
| typedef const_blas_data_mapper<Scalar, Index, LhsStorageOrder> LhsMapper; |
| typedef const_blas_data_mapper<Scalar, 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(); // cache block size along the K direction |
| Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction |
| // The small panel size must not be larger than blocking size. |
| // Usually this should never be the case because SmallPanelWidth^2 is very small |
| // compared to L2 cache size, but let's be safe: |
| Index panelWidth = (std::min)(Index(SmallPanelWidth),(std::min)(kc,mc)); |
| |
| std::size_t sizeA = kc*mc; |
| std::size_t sizeB = kc*cols; |
| |
| ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA()); |
| ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB()); |
| |
| // To work around an "error: member reference base type 'Matrix<...> |
| // (Eigen::internal::constructor_without_unaligned_array_assert (*)())' is |
| // not a structure or union" compilation error in nvcc (tested V8.0.61), |
| // create a dummy internal::constructor_without_unaligned_array_assert |
| // object to pass to the Matrix constructor. |
| internal::constructor_without_unaligned_array_assert a; |
| Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,LhsStorageOrder> triangularBuffer(a); |
| triangularBuffer.setZero(); |
| if((Mode&ZeroDiag)==ZeroDiag) |
| triangularBuffer.diagonal().setZero(); |
| else |
| triangularBuffer.diagonal().setOnes(); |
| |
| gebp_kernel<Scalar, Scalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel; |
| gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs; |
| gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr,RhsStorageOrder> pack_rhs; |
| |
| for(Index k2=IsLower ? depth : 0; |
| IsLower ? k2>0 : k2<depth; |
| IsLower ? k2-=kc : k2+=kc) |
| { |
| Index actual_kc = (std::min)(IsLower ? k2 : depth-k2, kc); |
| Index actual_k2 = IsLower ? k2-actual_kc : k2; |
| |
| // align blocks with the end of the triangular part for trapezoidal lhs |
| if((!IsLower)&&(k2<rows)&&(k2+actual_kc>rows)) |
| { |
| actual_kc = rows-k2; |
| k2 = k2+actual_kc-kc; |
| } |
| |
| pack_rhs(blockB, rhs.getSubMapper(actual_k2,0), actual_kc, cols); |
| |
| // the selected lhs's panel has to be split in three different parts: |
| // 1 - the part which is zero => skip it |
| // 2 - the diagonal block => special kernel |
| // 3 - the dense panel below (lower case) or above (upper case) the diagonal block => GEPP |
| |
| // the block diagonal, if any: |
| if(IsLower || actual_k2<rows) |
| { |
| // for each small vertical panels of lhs |
| for (Index k1=0; k1<actual_kc; k1+=panelWidth) |
| { |
| Index actualPanelWidth = std::min<Index>(actual_kc-k1, panelWidth); |
| Index lengthTarget = IsLower ? actual_kc-k1-actualPanelWidth : k1; |
| Index startBlock = actual_k2+k1; |
| Index blockBOffset = k1; |
| |
| // => GEBP with the micro triangular block |
| // The trick is to pack this micro block while filling the opposite triangular part with zeros. |
| // To this end we do an extra triangular copy to a small temporary buffer |
| for (Index k=0;k<actualPanelWidth;++k) |
| { |
| if (SetDiag) |
| triangularBuffer.coeffRef(k,k) = lhs(startBlock+k,startBlock+k); |
| for (Index i=IsLower ? k+1 : 0; IsLower ? i<actualPanelWidth : i<k; ++i) |
| triangularBuffer.coeffRef(i,k) = lhs(startBlock+i,startBlock+k); |
| } |
| pack_lhs(blockA, LhsMapper(triangularBuffer.data(), triangularBuffer.outerStride()), actualPanelWidth, actualPanelWidth); |
| |
| gebp_kernel(res.getSubMapper(startBlock, 0), blockA, blockB, |
| actualPanelWidth, actualPanelWidth, cols, alpha, |
| actualPanelWidth, actual_kc, 0, blockBOffset); |
| |
| // GEBP with remaining micro panel |
| if (lengthTarget>0) |
| { |
| Index startTarget = IsLower ? actual_k2+k1+actualPanelWidth : actual_k2; |
| |
| pack_lhs(blockA, lhs.getSubMapper(startTarget,startBlock), actualPanelWidth, lengthTarget); |
| |
| gebp_kernel(res.getSubMapper(startTarget, 0), blockA, blockB, |
| lengthTarget, actualPanelWidth, cols, alpha, |
| actualPanelWidth, actual_kc, 0, blockBOffset); |
| } |
| } |
| } |
| // the part below (lower case) or above (upper case) the diagonal => GEPP |
| { |
| Index start = IsLower ? k2 : 0; |
| Index end = IsLower ? rows : (std::min)(actual_k2,rows); |
| for(Index i2=start; i2<end; i2+=mc) |
| { |
| const Index actual_mc = (std::min)(i2+mc,end)-i2; |
| gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr,Traits::LhsProgress, LhsStorageOrder,false>() |
| (blockA, lhs.getSubMapper(i2, actual_k2), actual_kc, actual_mc); |
| |
| gebp_kernel(res.getSubMapper(i2, 0), blockA, blockB, actual_mc, |
| actual_kc, cols, alpha, -1, -1, 0, 0); |
| } |
| } |
| } |
| } |
| |
| // implements col-major += alpha * op(general) * op(triangular) |
| template <typename Scalar, typename Index, int Mode, |
| int LhsStorageOrder, bool ConjugateLhs, |
| int RhsStorageOrder, bool ConjugateRhs, int Version> |
| struct product_triangular_matrix_matrix<Scalar,Index,Mode,false, |
| LhsStorageOrder,ConjugateLhs, |
| RhsStorageOrder,ConjugateRhs,ColMajor,Version> |
| { |
| typedef gebp_traits<Scalar,Scalar> Traits; |
| enum { |
| SmallPanelWidth = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr), |
| IsLower = (Mode&Lower) == Lower, |
| SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1 |
| }; |
| |
| static EIGEN_DONT_INLINE void run( |
| Index _rows, Index _cols, Index _depth, |
| const Scalar* _lhs, Index lhsStride, |
| const Scalar* _rhs, Index rhsStride, |
| Scalar* res, Index resStride, |
| const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking); |
| }; |
| |
| template <typename Scalar, typename Index, int Mode, |
| int LhsStorageOrder, bool ConjugateLhs, |
| int RhsStorageOrder, bool ConjugateRhs, int Version> |
| EIGEN_DONT_INLINE void product_triangular_matrix_matrix<Scalar,Index,Mode,false, |
| LhsStorageOrder,ConjugateLhs, |
| RhsStorageOrder,ConjugateRhs,ColMajor,Version>::run( |
| Index _rows, Index _cols, Index _depth, |
| const Scalar* _lhs, Index lhsStride, |
| const Scalar* _rhs, Index rhsStride, |
| Scalar* _res, Index resStride, |
| const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking) |
| { |
| const Index PacketBytes = packet_traits<Scalar>::size*sizeof(Scalar); |
| // strip zeros |
| Index diagSize = (std::min)(_cols,_depth); |
| Index rows = _rows; |
| Index depth = IsLower ? _depth : diagSize; |
| Index cols = IsLower ? diagSize : _cols; |
| |
| typedef const_blas_data_mapper<Scalar, Index, LhsStorageOrder> LhsMapper; |
| typedef const_blas_data_mapper<Scalar, 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(); // cache block size along the K direction |
| Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction |
| |
| std::size_t sizeA = kc*mc; |
| std::size_t sizeB = kc*cols+EIGEN_MAX_ALIGN_BYTES/sizeof(Scalar); |
| |
| ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA()); |
| ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB()); |
| |
| internal::constructor_without_unaligned_array_assert a; |
| Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,RhsStorageOrder> triangularBuffer(a); |
| triangularBuffer.setZero(); |
| if((Mode&ZeroDiag)==ZeroDiag) |
| triangularBuffer.diagonal().setZero(); |
| else |
| triangularBuffer.diagonal().setOnes(); |
| |
| gebp_kernel<Scalar, Scalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel; |
| gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs; |
| gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr,RhsStorageOrder> pack_rhs; |
| gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr,RhsStorageOrder,false,true> pack_rhs_panel; |
| |
| for(Index k2=IsLower ? 0 : depth; |
| IsLower ? k2<depth : k2>0; |
| IsLower ? k2+=kc : k2-=kc) |
| { |
| Index actual_kc = (std::min)(IsLower ? depth-k2 : k2, kc); |
| Index actual_k2 = IsLower ? k2 : k2-actual_kc; |
| |
| // align blocks with the end of the triangular part for trapezoidal rhs |
| if(IsLower && (k2<cols) && (actual_k2+actual_kc>cols)) |
| { |
| actual_kc = cols-k2; |
| k2 = actual_k2 + actual_kc - kc; |
| } |
| |
| // remaining size |
| Index rs = IsLower ? (std::min)(cols,actual_k2) : cols - k2; |
| // size of the triangular part |
| Index ts = (IsLower && actual_k2>=cols) ? 0 : actual_kc; |
| |
| Scalar* geb = blockB+ts*ts; |
| geb = geb + internal::first_aligned<PacketBytes>(geb,PacketBytes/sizeof(Scalar)); |
| |
| pack_rhs(geb, rhs.getSubMapper(actual_k2,IsLower ? 0 : k2), actual_kc, rs); |
| |
| // pack the triangular part of the rhs padding the unrolled blocks with zeros |
| if(ts>0) |
| { |
| for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth) |
| { |
| Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth); |
| Index actual_j2 = actual_k2 + j2; |
| Index panelOffset = IsLower ? j2+actualPanelWidth : 0; |
| Index panelLength = IsLower ? actual_kc-j2-actualPanelWidth : j2; |
| // general part |
| pack_rhs_panel(blockB+j2*actual_kc, |
| rhs.getSubMapper(actual_k2+panelOffset, actual_j2), |
| panelLength, actualPanelWidth, |
| actual_kc, panelOffset); |
| |
| // append the triangular part via a temporary buffer |
| for (Index j=0;j<actualPanelWidth;++j) |
| { |
| if (SetDiag) |
| triangularBuffer.coeffRef(j,j) = rhs(actual_j2+j,actual_j2+j); |
| for (Index k=IsLower ? j+1 : 0; IsLower ? k<actualPanelWidth : k<j; ++k) |
| triangularBuffer.coeffRef(k,j) = rhs(actual_j2+k,actual_j2+j); |
| } |
| |
| pack_rhs_panel(blockB+j2*actual_kc, |
| RhsMapper(triangularBuffer.data(), triangularBuffer.outerStride()), |
| actualPanelWidth, actualPanelWidth, |
| actual_kc, j2); |
| } |
| } |
| |
| for (Index i2=0; i2<rows; i2+=mc) |
| { |
| const Index actual_mc = (std::min)(mc,rows-i2); |
| pack_lhs(blockA, lhs.getSubMapper(i2, actual_k2), actual_kc, actual_mc); |
| |
| // triangular kernel |
| if(ts>0) |
| { |
| for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth) |
| { |
| Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth); |
| Index panelLength = IsLower ? actual_kc-j2 : j2+actualPanelWidth; |
| Index blockOffset = IsLower ? j2 : 0; |
| |
| gebp_kernel(res.getSubMapper(i2, actual_k2 + j2), |
| blockA, blockB+j2*actual_kc, |
| actual_mc, panelLength, actualPanelWidth, |
| alpha, |
| actual_kc, actual_kc, // strides |
| blockOffset, blockOffset);// offsets |
| } |
| } |
| gebp_kernel(res.getSubMapper(i2, IsLower ? 0 : k2), |
| blockA, geb, actual_mc, actual_kc, rs, |
| alpha, |
| -1, -1, 0, 0); |
| } |
| } |
| } |
| |
| /*************************************************************************** |
| * Wrapper to product_triangular_matrix_matrix |
| ***************************************************************************/ |
| |
| } // end namespace internal |
| |
| namespace internal { |
| template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs> |
| struct triangular_product_impl<Mode,LhsIsTriangular,Lhs,false,Rhs,false> |
| { |
| template<typename Dest> static void run(Dest& dst, const Lhs &a_lhs, const Rhs &a_rhs, const typename Dest::Scalar& alpha) |
| { |
| typedef typename Lhs::Scalar LhsScalar; |
| typedef typename Rhs::Scalar RhsScalar; |
| typedef typename Dest::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; |
| |
| 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); |
| |
| LhsScalar lhs_alpha = LhsBlasTraits::extractScalarFactor(a_lhs); |
| RhsScalar rhs_alpha = RhsBlasTraits::extractScalarFactor(a_rhs); |
| Scalar actualAlpha = alpha * lhs_alpha * rhs_alpha; |
| |
| typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar, |
| Lhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxColsAtCompileTime,4> BlockingType; |
| |
| enum { IsLower = (Mode&Lower) == Lower }; |
| Index stripedRows = ((!LhsIsTriangular) || (IsLower)) ? lhs.rows() : (std::min)(lhs.rows(),lhs.cols()); |
| Index stripedCols = ((LhsIsTriangular) || (!IsLower)) ? rhs.cols() : (std::min)(rhs.cols(),rhs.rows()); |
| Index stripedDepth = LhsIsTriangular ? ((!IsLower) ? lhs.cols() : (std::min)(lhs.cols(),lhs.rows())) |
| : ((IsLower) ? rhs.rows() : (std::min)(rhs.rows(),rhs.cols())); |
| |
| BlockingType blocking(stripedRows, stripedCols, stripedDepth, 1, false); |
| |
| internal::product_triangular_matrix_matrix<Scalar, Index, |
| Mode, LhsIsTriangular, |
| (internal::traits<ActualLhsTypeCleaned>::Flags&RowMajorBit) ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate, |
| (internal::traits<ActualRhsTypeCleaned>::Flags&RowMajorBit) ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate, |
| (internal::traits<Dest >::Flags&RowMajorBit) ? RowMajor : ColMajor> |
| ::run( |
| stripedRows, stripedCols, stripedDepth, // sizes |
| &lhs.coeffRef(0,0), lhs.outerStride(), // lhs info |
| &rhs.coeffRef(0,0), rhs.outerStride(), // rhs info |
| &dst.coeffRef(0,0), dst.outerStride(), // result info |
| actualAlpha, blocking |
| ); |
| |
| // Apply correction if the diagonal is unit and a scalar factor was nested: |
| if ((Mode&UnitDiag)==UnitDiag) |
| { |
| if (LhsIsTriangular && lhs_alpha!=LhsScalar(1)) |
| { |
| Index diagSize = (std::min)(lhs.rows(),lhs.cols()); |
| dst.topRows(diagSize) -= ((lhs_alpha-LhsScalar(1))*a_rhs).topRows(diagSize); |
| } |
| else if ((!LhsIsTriangular) && rhs_alpha!=RhsScalar(1)) |
| { |
| Index diagSize = (std::min)(rhs.rows(),rhs.cols()); |
| dst.leftCols(diagSize) -= (rhs_alpha-RhsScalar(1))*a_lhs.leftCols(diagSize); |
| } |
| } |
| } |
| }; |
| |
| } // end namespace internal |
| |
| } // end namespace Eigen |
| |
| #endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_H |
