Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 1 | // This file is part of Eigen, a lightweight C++ template library |
| 2 | // for linear algebra. |
| 3 | // |
| 4 | // Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr> |
| 5 | // |
| 6 | // This Source Code Form is subject to the terms of the Mozilla |
| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed |
| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. |
| 9 | |
| 10 | #ifndef EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H |
| 11 | #define EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H |
| 12 | |
| 13 | namespace Eigen { |
| 14 | |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 15 | template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjLhs, bool ConjRhs> |
| 16 | struct selfadjoint_rank1_update; |
| 17 | |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 18 | namespace internal { |
| 19 | |
| 20 | /********************************************************************** |
| 21 | * This file implements a general A * B product while |
| 22 | * evaluating only one triangular part of the product. |
| 23 | * This is more general version of self adjoint product (C += A A^T) |
| 24 | * as the level 3 SYRK Blas routine. |
| 25 | **********************************************************************/ |
| 26 | |
| 27 | // forward declarations (defined at the end of this file) |
| 28 | template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo> |
| 29 | struct tribb_kernel; |
| 30 | |
| 31 | /* Optimized matrix-matrix product evaluating only one triangular half */ |
| 32 | template <typename Index, |
| 33 | typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs, |
| 34 | typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, |
| 35 | int ResStorageOrder, int UpLo, int Version = Specialized> |
| 36 | struct general_matrix_matrix_triangular_product; |
| 37 | |
| 38 | // as usual if the result is row major => we transpose the product |
| 39 | template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs, |
| 40 | typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int UpLo, int Version> |
| 41 | struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor,UpLo,Version> |
| 42 | { |
| 43 | typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar; |
| 44 | static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* lhs, Index lhsStride, |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 45 | const RhsScalar* rhs, Index rhsStride, ResScalar* res, Index resStride, const ResScalar& alpha) |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 46 | { |
| 47 | general_matrix_matrix_triangular_product<Index, |
| 48 | RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs, |
| 49 | LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs, |
| 50 | ColMajor, UpLo==Lower?Upper:Lower> |
| 51 | ::run(size,depth,rhs,rhsStride,lhs,lhsStride,res,resStride,alpha); |
| 52 | } |
| 53 | }; |
| 54 | |
| 55 | template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs, |
| 56 | typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int UpLo, int Version> |
| 57 | struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor,UpLo,Version> |
| 58 | { |
| 59 | typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar; |
| 60 | static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* _lhs, Index lhsStride, |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 61 | const RhsScalar* _rhs, Index rhsStride, ResScalar* res, Index resStride, const ResScalar& alpha) |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 62 | { |
| 63 | const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride); |
| 64 | const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride); |
| 65 | |
| 66 | typedef gebp_traits<LhsScalar,RhsScalar> Traits; |
| 67 | |
| 68 | Index kc = depth; // cache block size along the K direction |
| 69 | Index mc = size; // cache block size along the M direction |
| 70 | Index nc = size; // cache block size along the N direction |
| 71 | computeProductBlockingSizes<LhsScalar,RhsScalar>(kc, mc, nc); |
| 72 | // !!! mc must be a multiple of nr: |
| 73 | if(mc > Traits::nr) |
| 74 | mc = (mc/Traits::nr)*Traits::nr; |
| 75 | |
| 76 | std::size_t sizeW = kc*Traits::WorkSpaceFactor; |
| 77 | std::size_t sizeB = sizeW + kc*size; |
| 78 | ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, kc*mc, 0); |
| 79 | ei_declare_aligned_stack_constructed_variable(RhsScalar, allocatedBlockB, sizeB, 0); |
| 80 | RhsScalar* blockB = allocatedBlockB + sizeW; |
| 81 | |
| 82 | gemm_pack_lhs<LhsScalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs; |
| 83 | gemm_pack_rhs<RhsScalar, Index, Traits::nr, RhsStorageOrder> pack_rhs; |
| 84 | gebp_kernel <LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp; |
| 85 | tribb_kernel<LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs, UpLo> sybb; |
| 86 | |
| 87 | for(Index k2=0; k2<depth; k2+=kc) |
| 88 | { |
| 89 | const Index actual_kc = (std::min)(k2+kc,depth)-k2; |
| 90 | |
| 91 | // note that the actual rhs is the transpose/adjoint of mat |
| 92 | pack_rhs(blockB, &rhs(k2,0), rhsStride, actual_kc, size); |
| 93 | |
| 94 | for(Index i2=0; i2<size; i2+=mc) |
| 95 | { |
| 96 | const Index actual_mc = (std::min)(i2+mc,size)-i2; |
| 97 | |
| 98 | pack_lhs(blockA, &lhs(i2, k2), lhsStride, actual_kc, actual_mc); |
| 99 | |
| 100 | // the selected actual_mc * size panel of res is split into three different part: |
| 101 | // 1 - before the diagonal => processed with gebp or skipped |
| 102 | // 2 - the actual_mc x actual_mc symmetric block => processed with a special kernel |
| 103 | // 3 - after the diagonal => processed with gebp or skipped |
| 104 | if (UpLo==Lower) |
| 105 | gebp(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, (std::min)(size,i2), alpha, |
| 106 | -1, -1, 0, 0, allocatedBlockB); |
| 107 | |
| 108 | sybb(res+resStride*i2 + i2, resStride, blockA, blockB + actual_kc*i2, actual_mc, actual_kc, alpha, allocatedBlockB); |
| 109 | |
| 110 | if (UpLo==Upper) |
| 111 | { |
| 112 | Index j2 = i2+actual_mc; |
| 113 | gebp(res+resStride*j2+i2, resStride, blockA, blockB+actual_kc*j2, actual_mc, actual_kc, (std::max)(Index(0), size-j2), alpha, |
| 114 | -1, -1, 0, 0, allocatedBlockB); |
| 115 | } |
| 116 | } |
| 117 | } |
| 118 | } |
| 119 | }; |
| 120 | |
| 121 | // Optimized packed Block * packed Block product kernel evaluating only one given triangular part |
| 122 | // This kernel is built on top of the gebp kernel: |
| 123 | // - the current destination block is processed per panel of actual_mc x BlockSize |
| 124 | // where BlockSize is set to the minimal value allowing gebp to be as fast as possible |
| 125 | // - then, as usual, each panel is split into three parts along the diagonal, |
| 126 | // the sub blocks above and below the diagonal are processed as usual, |
| 127 | // while the triangular block overlapping the diagonal is evaluated into a |
| 128 | // small temporary buffer which is then accumulated into the result using a |
| 129 | // triangular traversal. |
| 130 | template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo> |
| 131 | struct tribb_kernel |
| 132 | { |
| 133 | typedef gebp_traits<LhsScalar,RhsScalar,ConjLhs,ConjRhs> Traits; |
| 134 | typedef typename Traits::ResScalar ResScalar; |
| 135 | |
| 136 | enum { |
| 137 | BlockSize = EIGEN_PLAIN_ENUM_MAX(mr,nr) |
| 138 | }; |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 139 | void operator()(ResScalar* res, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index size, Index depth, const ResScalar& alpha, RhsScalar* workspace) |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 140 | { |
| 141 | gebp_kernel<LhsScalar, RhsScalar, Index, mr, nr, ConjLhs, ConjRhs> gebp_kernel; |
| 142 | Matrix<ResScalar,BlockSize,BlockSize,ColMajor> buffer; |
| 143 | |
| 144 | // let's process the block per panel of actual_mc x BlockSize, |
| 145 | // again, each is split into three parts, etc. |
| 146 | for (Index j=0; j<size; j+=BlockSize) |
| 147 | { |
| 148 | Index actualBlockSize = std::min<Index>(BlockSize,size - j); |
| 149 | const RhsScalar* actual_b = blockB+j*depth; |
| 150 | |
| 151 | if(UpLo==Upper) |
| 152 | gebp_kernel(res+j*resStride, resStride, blockA, actual_b, j, depth, actualBlockSize, alpha, |
| 153 | -1, -1, 0, 0, workspace); |
| 154 | |
| 155 | // selfadjoint micro block |
| 156 | { |
| 157 | Index i = j; |
| 158 | buffer.setZero(); |
| 159 | // 1 - apply the kernel on the temporary buffer |
| 160 | gebp_kernel(buffer.data(), BlockSize, blockA+depth*i, actual_b, actualBlockSize, depth, actualBlockSize, alpha, |
| 161 | -1, -1, 0, 0, workspace); |
| 162 | // 2 - triangular accumulation |
| 163 | for(Index j1=0; j1<actualBlockSize; ++j1) |
| 164 | { |
| 165 | ResScalar* r = res + (j+j1)*resStride + i; |
| 166 | for(Index i1=UpLo==Lower ? j1 : 0; |
| 167 | UpLo==Lower ? i1<actualBlockSize : i1<=j1; ++i1) |
| 168 | r[i1] += buffer(i1,j1); |
| 169 | } |
| 170 | } |
| 171 | |
| 172 | if(UpLo==Lower) |
| 173 | { |
| 174 | Index i = j+actualBlockSize; |
| 175 | gebp_kernel(res+j*resStride+i, resStride, blockA+depth*i, actual_b, size-i, depth, actualBlockSize, alpha, |
| 176 | -1, -1, 0, 0, workspace); |
| 177 | } |
| 178 | } |
| 179 | } |
| 180 | }; |
| 181 | |
| 182 | } // end namespace internal |
| 183 | |
| 184 | // high level API |
| 185 | |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 186 | template<typename MatrixType, typename ProductType, int UpLo, bool IsOuterProduct> |
| 187 | struct general_product_to_triangular_selector; |
| 188 | |
| 189 | |
| 190 | template<typename MatrixType, typename ProductType, int UpLo> |
| 191 | struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,true> |
| 192 | { |
| 193 | static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha) |
| 194 | { |
| 195 | typedef typename MatrixType::Scalar Scalar; |
| 196 | typedef typename MatrixType::Index Index; |
| 197 | |
| 198 | typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs; |
| 199 | typedef internal::blas_traits<Lhs> LhsBlasTraits; |
| 200 | typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs; |
| 201 | typedef typename internal::remove_all<ActualLhs>::type _ActualLhs; |
| 202 | typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs()); |
| 203 | |
| 204 | typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs; |
| 205 | typedef internal::blas_traits<Rhs> RhsBlasTraits; |
| 206 | typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs; |
| 207 | typedef typename internal::remove_all<ActualRhs>::type _ActualRhs; |
| 208 | typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs()); |
| 209 | |
| 210 | Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived()); |
| 211 | |
| 212 | enum { |
| 213 | StorageOrder = (internal::traits<MatrixType>::Flags&RowMajorBit) ? RowMajor : ColMajor, |
| 214 | UseLhsDirectly = _ActualLhs::InnerStrideAtCompileTime==1, |
| 215 | UseRhsDirectly = _ActualRhs::InnerStrideAtCompileTime==1 |
| 216 | }; |
| 217 | |
| 218 | internal::gemv_static_vector_if<Scalar,Lhs::SizeAtCompileTime,Lhs::MaxSizeAtCompileTime,!UseLhsDirectly> static_lhs; |
| 219 | ei_declare_aligned_stack_constructed_variable(Scalar, actualLhsPtr, actualLhs.size(), |
| 220 | (UseLhsDirectly ? const_cast<Scalar*>(actualLhs.data()) : static_lhs.data())); |
| 221 | if(!UseLhsDirectly) Map<typename _ActualLhs::PlainObject>(actualLhsPtr, actualLhs.size()) = actualLhs; |
| 222 | |
| 223 | internal::gemv_static_vector_if<Scalar,Rhs::SizeAtCompileTime,Rhs::MaxSizeAtCompileTime,!UseRhsDirectly> static_rhs; |
| 224 | ei_declare_aligned_stack_constructed_variable(Scalar, actualRhsPtr, actualRhs.size(), |
| 225 | (UseRhsDirectly ? const_cast<Scalar*>(actualRhs.data()) : static_rhs.data())); |
| 226 | if(!UseRhsDirectly) Map<typename _ActualRhs::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs; |
| 227 | |
| 228 | |
| 229 | selfadjoint_rank1_update<Scalar,Index,StorageOrder,UpLo, |
| 230 | LhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex, |
| 231 | RhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex> |
| 232 | ::run(actualLhs.size(), mat.data(), mat.outerStride(), actualLhsPtr, actualRhsPtr, actualAlpha); |
| 233 | } |
| 234 | }; |
| 235 | |
| 236 | template<typename MatrixType, typename ProductType, int UpLo> |
| 237 | struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,false> |
| 238 | { |
| 239 | static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha) |
| 240 | { |
| 241 | typedef typename MatrixType::Index Index; |
| 242 | |
| 243 | typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs; |
| 244 | typedef internal::blas_traits<Lhs> LhsBlasTraits; |
| 245 | typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs; |
| 246 | typedef typename internal::remove_all<ActualLhs>::type _ActualLhs; |
| 247 | typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs()); |
| 248 | |
| 249 | typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs; |
| 250 | typedef internal::blas_traits<Rhs> RhsBlasTraits; |
| 251 | typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs; |
| 252 | typedef typename internal::remove_all<ActualRhs>::type _ActualRhs; |
| 253 | typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs()); |
| 254 | |
| 255 | typename ProductType::Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived()); |
| 256 | |
| 257 | internal::general_matrix_matrix_triangular_product<Index, |
| 258 | typename Lhs::Scalar, _ActualLhs::Flags&RowMajorBit ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate, |
| 259 | typename Rhs::Scalar, _ActualRhs::Flags&RowMajorBit ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate, |
| 260 | MatrixType::Flags&RowMajorBit ? RowMajor : ColMajor, UpLo> |
| 261 | ::run(mat.cols(), actualLhs.cols(), |
| 262 | &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &actualRhs.coeffRef(0,0), actualRhs.outerStride(), |
| 263 | mat.data(), mat.outerStride(), actualAlpha); |
| 264 | } |
| 265 | }; |
| 266 | |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 267 | template<typename MatrixType, unsigned int UpLo> |
| 268 | template<typename ProductDerived, typename _Lhs, typename _Rhs> |
| 269 | TriangularView<MatrixType,UpLo>& TriangularView<MatrixType,UpLo>::assignProduct(const ProductBase<ProductDerived, _Lhs,_Rhs>& prod, const Scalar& alpha) |
| 270 | { |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 271 | general_product_to_triangular_selector<MatrixType, ProductDerived, UpLo, (_Lhs::ColsAtCompileTime==1) || (_Rhs::RowsAtCompileTime==1)>::run(m_matrix.const_cast_derived(), prod.derived(), alpha); |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 272 | |
| 273 | return *this; |
| 274 | } |
| 275 | |
| 276 | } // end namespace Eigen |
| 277 | |
| 278 | #endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H |