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 (at) 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 15 template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjLhs, bool ConjRhs> 16 struct selfadjoint_rank1_update; 17 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 a 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 ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar; 44 static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* lhs, Index lhsStride, 45 const RhsScalar* rhs, Index rhsStride, ResScalar* res, Index resStride, 46 const ResScalar& alpha, level3_blocking<RhsScalar,LhsScalar>& blocking) 47 { 48 general_matrix_matrix_triangular_product<Index, 49 RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs, 50 LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs, 51 ColMajor, UpLo==Lower?Upper:Lower> 52 ::run(size,depth,rhs,rhsStride,lhs,lhsStride,res,resStride,alpha,blocking); 53 } 54 }; 55 56 template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs, 57 typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int UpLo, int Version> 58 struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor,UpLo,Version> 59 { 60 typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar; 61 static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* _lhs, Index lhsStride, 62 const RhsScalar* _rhs, Index rhsStride, ResScalar* _res, Index resStride, 63 const ResScalar& alpha, level3_blocking<LhsScalar,RhsScalar>& blocking) 64 { 65 typedef gebp_traits<LhsScalar,RhsScalar> Traits; 66 67 typedef const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> LhsMapper; 68 typedef const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> RhsMapper; 69 typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor> ResMapper; 70 LhsMapper lhs(_lhs,lhsStride); 71 RhsMapper rhs(_rhs,rhsStride); 72 ResMapper res(_res, resStride); 73 74 Index kc = blocking.kc(); 75 Index mc = (std::min)(size,blocking.mc()); 76 77 // !!! mc must be a multiple of nr: 78 if(mc > Traits::nr) 79 mc = (mc/Traits::nr)*Traits::nr; 80 81 std::size_t sizeA = kc*mc; 82 std::size_t sizeB = kc*size; 83 84 ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, blocking.blockA()); 85 ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, blocking.blockB()); 86 87 gemm_pack_lhs<LhsScalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs; 88 gemm_pack_rhs<RhsScalar, Index, RhsMapper, Traits::nr, RhsStorageOrder> pack_rhs; 89 gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp; 90 tribb_kernel<LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs, UpLo> sybb; 91 92 for(Index k2=0; k2<depth; k2+=kc) 93 { 94 const Index actual_kc = (std::min)(k2+kc,depth)-k2; 95 96 // note that the actual rhs is the transpose/adjoint of mat 97 pack_rhs(blockB, rhs.getSubMapper(k2,0), actual_kc, size); 98 99 for(Index i2=0; i2<size; i2+=mc) 100 { 101 const Index actual_mc = (std::min)(i2+mc,size)-i2; 102 103 pack_lhs(blockA, lhs.getSubMapper(i2, k2), actual_kc, actual_mc); 104 105 // the selected actual_mc * size panel of res is split into three different part: 106 // 1 - before the diagonal => processed with gebp or skipped 107 // 2 - the actual_mc x actual_mc symmetric block => processed with a special kernel 108 // 3 - after the diagonal => processed with gebp or skipped 109 if (UpLo==Lower) 110 gebp(res.getSubMapper(i2, 0), blockA, blockB, actual_mc, actual_kc, 111 (std::min)(size,i2), alpha, -1, -1, 0, 0); 112 113 114 sybb(_res+resStride*i2 + i2, resStride, blockA, blockB + actual_kc*i2, actual_mc, actual_kc, alpha); 115 116 if (UpLo==Upper) 117 { 118 Index j2 = i2+actual_mc; 119 gebp(res.getSubMapper(i2, j2), blockA, blockB+actual_kc*j2, actual_mc, 120 actual_kc, (std::max)(Index(0), size-j2), alpha, -1, -1, 0, 0); 121 } 122 } 123 } 124 } 125 }; 126 127 // Optimized packed Block * packed Block product kernel evaluating only one given triangular part 128 // This kernel is built on top of the gebp kernel: 129 // - the current destination block is processed per panel of actual_mc x BlockSize 130 // where BlockSize is set to the minimal value allowing gebp to be as fast as possible 131 // - then, as usual, each panel is split into three parts along the diagonal, 132 // the sub blocks above and below the diagonal are processed as usual, 133 // while the triangular block overlapping the diagonal is evaluated into a 134 // small temporary buffer which is then accumulated into the result using a 135 // triangular traversal. 136 template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo> 137 struct tribb_kernel 138 { 139 typedef gebp_traits<LhsScalar,RhsScalar,ConjLhs,ConjRhs> Traits; 140 typedef typename Traits::ResScalar ResScalar; 141 142 enum { 143 BlockSize = meta_least_common_multiple<EIGEN_PLAIN_ENUM_MAX(mr,nr),EIGEN_PLAIN_ENUM_MIN(mr,nr)>::ret 144 }; 145 void operator()(ResScalar* _res, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index size, Index depth, const ResScalar& alpha) 146 { 147 typedef blas_data_mapper<ResScalar, Index, ColMajor> ResMapper; 148 ResMapper res(_res, resStride); 149 gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, mr, nr, ConjLhs, ConjRhs> gebp_kernel; 150 151 Matrix<ResScalar,BlockSize,BlockSize,ColMajor> buffer((internal::constructor_without_unaligned_array_assert())); 152 153 // let's process the block per panel of actual_mc x BlockSize, 154 // again, each is split into three parts, etc. 155 for (Index j=0; j<size; j+=BlockSize) 156 { 157 Index actualBlockSize = std::min<Index>(BlockSize,size - j); 158 const RhsScalar* actual_b = blockB+j*depth; 159 160 if(UpLo==Upper) 161 gebp_kernel(res.getSubMapper(0, j), blockA, actual_b, j, depth, actualBlockSize, alpha, 162 -1, -1, 0, 0); 163 164 // selfadjoint micro block 165 { 166 Index i = j; 167 buffer.setZero(); 168 // 1 - apply the kernel on the temporary buffer 169 gebp_kernel(ResMapper(buffer.data(), BlockSize), blockA+depth*i, actual_b, actualBlockSize, depth, actualBlockSize, alpha, 170 -1, -1, 0, 0); 171 // 2 - triangular accumulation 172 for(Index j1=0; j1<actualBlockSize; ++j1) 173 { 174 ResScalar* r = &res(i, j + j1); 175 for(Index i1=UpLo==Lower ? j1 : 0; 176 UpLo==Lower ? i1<actualBlockSize : i1<=j1; ++i1) 177 r[i1] += buffer(i1,j1); 178 } 179 } 180 181 if(UpLo==Lower) 182 { 183 Index i = j+actualBlockSize; 184 gebp_kernel(res.getSubMapper(i, j), blockA+depth*i, actual_b, size-i, 185 depth, actualBlockSize, alpha, -1, -1, 0, 0); 186 } 187 } 188 } 189 }; 190 191 } // end namespace internal 192 193 // high level API 194 195 template<typename MatrixType, typename ProductType, int UpLo, bool IsOuterProduct> 196 struct general_product_to_triangular_selector; 197 198 199 template<typename MatrixType, typename ProductType, int UpLo> 200 struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,true> 201 { 202 static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha, bool beta) 203 { 204 typedef typename MatrixType::Scalar Scalar; 205 206 typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs; 207 typedef internal::blas_traits<Lhs> LhsBlasTraits; 208 typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs; 209 typedef typename internal::remove_all<ActualLhs>::type _ActualLhs; 210 typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs()); 211 212 typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs; 213 typedef internal::blas_traits<Rhs> RhsBlasTraits; 214 typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs; 215 typedef typename internal::remove_all<ActualRhs>::type _ActualRhs; 216 typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs()); 217 218 Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived()); 219 220 if(!beta) 221 mat.template triangularView<UpLo>().setZero(); 222 223 enum { 224 StorageOrder = (internal::traits<MatrixType>::Flags&RowMajorBit) ? RowMajor : ColMajor, 225 UseLhsDirectly = _ActualLhs::InnerStrideAtCompileTime==1, 226 UseRhsDirectly = _ActualRhs::InnerStrideAtCompileTime==1 227 }; 228 229 internal::gemv_static_vector_if<Scalar,Lhs::SizeAtCompileTime,Lhs::MaxSizeAtCompileTime,!UseLhsDirectly> static_lhs; 230 ei_declare_aligned_stack_constructed_variable(Scalar, actualLhsPtr, actualLhs.size(), 231 (UseLhsDirectly ? const_cast<Scalar*>(actualLhs.data()) : static_lhs.data())); 232 if(!UseLhsDirectly) Map<typename _ActualLhs::PlainObject>(actualLhsPtr, actualLhs.size()) = actualLhs; 233 234 internal::gemv_static_vector_if<Scalar,Rhs::SizeAtCompileTime,Rhs::MaxSizeAtCompileTime,!UseRhsDirectly> static_rhs; 235 ei_declare_aligned_stack_constructed_variable(Scalar, actualRhsPtr, actualRhs.size(), 236 (UseRhsDirectly ? const_cast<Scalar*>(actualRhs.data()) : static_rhs.data())); 237 if(!UseRhsDirectly) Map<typename _ActualRhs::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs; 238 239 240 selfadjoint_rank1_update<Scalar,Index,StorageOrder,UpLo, 241 LhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex, 242 RhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex> 243 ::run(actualLhs.size(), mat.data(), mat.outerStride(), actualLhsPtr, actualRhsPtr, actualAlpha); 244 } 245 }; 246 247 template<typename MatrixType, typename ProductType, int UpLo> 248 struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,false> 249 { 250 static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha, bool beta) 251 { 252 typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs; 253 typedef internal::blas_traits<Lhs> LhsBlasTraits; 254 typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs; 255 typedef typename internal::remove_all<ActualLhs>::type _ActualLhs; 256 typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs()); 257 258 typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs; 259 typedef internal::blas_traits<Rhs> RhsBlasTraits; 260 typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs; 261 typedef typename internal::remove_all<ActualRhs>::type _ActualRhs; 262 typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs()); 263 264 typename ProductType::Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived()); 265 266 if(!beta) 267 mat.template triangularView<UpLo>().setZero(); 268 269 enum { 270 IsRowMajor = (internal::traits<MatrixType>::Flags&RowMajorBit) ? 1 : 0, 271 LhsIsRowMajor = _ActualLhs::Flags&RowMajorBit ? 1 : 0, 272 RhsIsRowMajor = _ActualRhs::Flags&RowMajorBit ? 1 : 0, 273 SkipDiag = (UpLo&(UnitDiag|ZeroDiag))!=0 274 }; 275 276 Index size = mat.cols(); 277 if(SkipDiag) 278 size--; 279 Index depth = actualLhs.cols(); 280 281 typedef internal::gemm_blocking_space<IsRowMajor ? RowMajor : ColMajor,typename Lhs::Scalar,typename Rhs::Scalar, 282 MatrixType::MaxColsAtCompileTime, MatrixType::MaxColsAtCompileTime, _ActualRhs::MaxColsAtCompileTime> BlockingType; 283 284 BlockingType blocking(size, size, depth, 1, false); 285 286 internal::general_matrix_matrix_triangular_product<Index, 287 typename Lhs::Scalar, LhsIsRowMajor ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate, 288 typename Rhs::Scalar, RhsIsRowMajor ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate, 289 IsRowMajor ? RowMajor : ColMajor, UpLo&(Lower|Upper)> 290 ::run(size, depth, 291 &actualLhs.coeffRef(SkipDiag&&(UpLo&Lower)==Lower ? 1 : 0,0), actualLhs.outerStride(), 292 &actualRhs.coeffRef(0,SkipDiag&&(UpLo&Upper)==Upper ? 1 : 0), actualRhs.outerStride(), 293 mat.data() + (SkipDiag ? (bool(IsRowMajor) != ((UpLo&Lower)==Lower) ? 1 : mat.outerStride() ) : 0), mat.outerStride(), actualAlpha, blocking); 294 } 295 }; 296 297 template<typename MatrixType, unsigned int UpLo> 298 template<typename ProductType> 299 TriangularView<MatrixType,UpLo>& TriangularViewImpl<MatrixType,UpLo,Dense>::_assignProduct(const ProductType& prod, const Scalar& alpha, bool beta) 300 { 301 EIGEN_STATIC_ASSERT((UpLo&UnitDiag)==0, WRITING_TO_TRIANGULAR_PART_WITH_UNIT_DIAGONAL_IS_NOT_SUPPORTED); 302 eigen_assert(derived().nestedExpression().rows() == prod.rows() && derived().cols() == prod.cols()); 303 304 general_product_to_triangular_selector<MatrixType, ProductType, UpLo, internal::traits<ProductType>::InnerSize==1>::run(derived().nestedExpression().const_cast_derived(), prod, alpha, beta); 305 306 return derived(); 307 } 308 309 } // end namespace Eigen 310 311 #endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H 312
