1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2009-2010 Gael Guennebaud <[email protected]> 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 ResInnerStride, 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 ResInnerStride, 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, 41 int ResInnerStride, int UpLo, int Version> 42 struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor,ResInnerStride,UpLo,Version> 43 { 44 typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar; 45 static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* lhs, Index lhsStride, 46 const RhsScalar* rhs, Index rhsStride, ResScalar* res, Index resIncr, Index resStride, 47 const ResScalar& alpha, level3_blocking<RhsScalar,LhsScalar>& blocking) 48 { 49 general_matrix_matrix_triangular_product<Index, 50 RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs, 51 LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs, 52 ColMajor, ResInnerStride, UpLo==Lower?Upper:Lower> 53 ::run(size,depth,rhs,rhsStride,lhs,lhsStride,res,resIncr,resStride,alpha,blocking); 54 } 55 }; 56 57 template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs, 58 typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, 59 int ResInnerStride, int UpLo, int Version> 60 struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor,ResInnerStride,UpLo,Version> 61 { 62 typedef typename ScalarBinaryOpTraits<LhsScalar, RhsScalar>::ReturnType ResScalar; 63 static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* _lhs, Index lhsStride, 64 const RhsScalar* _rhs, Index rhsStride, 65 ResScalar* _res, Index resIncr, Index resStride, 66 const ResScalar& alpha, level3_blocking<LhsScalar,RhsScalar>& blocking) 67 { 68 typedef gebp_traits<LhsScalar,RhsScalar> Traits; 69 70 typedef const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> LhsMapper; 71 typedef const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> RhsMapper; 72 typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor, Unaligned, ResInnerStride> ResMapper; 73 LhsMapper lhs(_lhs,lhsStride); 74 RhsMapper rhs(_rhs,rhsStride); 75 ResMapper res(_res, resStride, resIncr); 76 77 Index kc = blocking.kc(); 78 Index mc = (std::min)(size,blocking.mc()); 79 80 // !!! mc must be a multiple of nr: 81 if(mc > Traits::nr) 82 mc = (mc/Traits::nr)*Traits::nr; 83 84 std::size_t sizeA = kc*mc; 85 std::size_t sizeB = kc*size; 86 87 ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, blocking.blockA()); 88 ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, blocking.blockB()); 89 90 gemm_pack_lhs<LhsScalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, typename Traits::LhsPacket4Packing, LhsStorageOrder> pack_lhs; 91 gemm_pack_rhs<RhsScalar, Index, RhsMapper, Traits::nr, RhsStorageOrder> pack_rhs; 92 gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp; 93 tribb_kernel<LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs, ResInnerStride, UpLo> sybb; 94 95 for(Index k2=0; k2<depth; k2+=kc) 96 { 97 const Index actual_kc = (std::min)(k2+kc,depth)-k2; 98 99 // note that the actual rhs is the transpose/adjoint of mat 100 pack_rhs(blockB, rhs.getSubMapper(k2,0), actual_kc, size); 101 102 for(Index i2=0; i2<size; i2+=mc) 103 { 104 const Index actual_mc = (std::min)(i2+mc,size)-i2; 105 106 pack_lhs(blockA, lhs.getSubMapper(i2, k2), actual_kc, actual_mc); 107 108 // the selected actual_mc * size panel of res is split into three different part: 109 // 1 - before the diagonal => processed with gebp or skipped 110 // 2 - the actual_mc x actual_mc symmetric block => processed with a special kernel 111 // 3 - after the diagonal => processed with gebp or skipped 112 if (UpLo==Lower) 113 gebp(res.getSubMapper(i2, 0), blockA, blockB, actual_mc, actual_kc, 114 (std::min)(size,i2), alpha, -1, -1, 0, 0); 115 116 sybb(_res+resStride*i2 + resIncr*i2, resIncr, resStride, blockA, blockB + actual_kc*i2, actual_mc, actual_kc, alpha); 117 118 if (UpLo==Upper) 119 { 120 Index j2 = i2+actual_mc; 121 gebp(res.getSubMapper(i2, j2), blockA, blockB+actual_kc*j2, actual_mc, 122 actual_kc, (std::max)(Index(0), size-j2), alpha, -1, -1, 0, 0); 123 } 124 } 125 } 126 } 127 }; 128 129 // Optimized packed Block * packed Block product kernel evaluating only one given triangular part 130 // This kernel is built on top of the gebp kernel: 131 // - the current destination block is processed per panel of actual_mc x BlockSize 132 // where BlockSize is set to the minimal value allowing gebp to be as fast as possible 133 // - then, as usual, each panel is split into three parts along the diagonal, 134 // the sub blocks above and below the diagonal are processed as usual, 135 // while the triangular block overlapping the diagonal is evaluated into a 136 // small temporary buffer which is then accumulated into the result using a 137 // triangular traversal. 138 template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int ResInnerStride, int UpLo> 139 struct tribb_kernel 140 { 141 typedef gebp_traits<LhsScalar,RhsScalar,ConjLhs,ConjRhs> Traits; 142 typedef typename Traits::ResScalar ResScalar; 143 144 enum { 145 BlockSize = meta_least_common_multiple<EIGEN_PLAIN_ENUM_MAX(mr,nr),EIGEN_PLAIN_ENUM_MIN(mr,nr)>::ret 146 }; 147 void operator()(ResScalar* _res, Index resIncr, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index size, Index depth, const ResScalar& alpha) 148 { 149 typedef blas_data_mapper<ResScalar, Index, ColMajor, Unaligned, ResInnerStride> ResMapper; 150 typedef blas_data_mapper<ResScalar, Index, ColMajor, Unaligned> BufferMapper; 151 ResMapper res(_res, resStride, resIncr); 152 gebp_kernel<LhsScalar, RhsScalar, Index, ResMapper, mr, nr, ConjLhs, ConjRhs> gebp_kernel1; 153 gebp_kernel<LhsScalar, RhsScalar, Index, BufferMapper, mr, nr, ConjLhs, ConjRhs> gebp_kernel2; 154 155 Matrix<ResScalar,BlockSize,BlockSize,ColMajor> buffer((internal::constructor_without_unaligned_array_assert())); 156 157 // let's process the block per panel of actual_mc x BlockSize, 158 // again, each is split into three parts, etc. 159 for (Index j=0; j<size; j+=BlockSize) 160 { 161 Index actualBlockSize = std::min<Index>(BlockSize,size - j); 162 const RhsScalar* actual_b = blockB+j*depth; 163 164 if(UpLo==Upper) 165 gebp_kernel1(res.getSubMapper(0, j), blockA, actual_b, j, depth, actualBlockSize, alpha, 166 -1, -1, 0, 0); 167 168 // selfadjoint micro block 169 { 170 Index i = j; 171 buffer.setZero(); 172 // 1 - apply the kernel on the temporary buffer 173 gebp_kernel2(BufferMapper(buffer.data(), BlockSize), blockA+depth*i, actual_b, actualBlockSize, depth, actualBlockSize, alpha, 174 -1, -1, 0, 0); 175 176 // 2 - triangular accumulation 177 for(Index j1=0; j1<actualBlockSize; ++j1) 178 { 179 typename ResMapper::LinearMapper r = res.getLinearMapper(i,j+j1); 180 for(Index i1=UpLo==Lower ? j1 : 0; 181 UpLo==Lower ? i1<actualBlockSize : i1<=j1; ++i1) 182 r(i1) += buffer(i1,j1); 183 } 184 } 185 186 if(UpLo==Lower) 187 { 188 Index i = j+actualBlockSize; 189 gebp_kernel1(res.getSubMapper(i, j), blockA+depth*i, actual_b, size-i, 190 depth, actualBlockSize, alpha, -1, -1, 0, 0); 191 } 192 } 193 } 194 }; 195 196 } // end namespace internal 197 198 // high level API 199 200 template<typename MatrixType, typename ProductType, int UpLo, bool IsOuterProduct> 201 struct general_product_to_triangular_selector; 202 203 204 template<typename MatrixType, typename ProductType, int UpLo> 205 struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,true> 206 { 207 static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha, bool beta) 208 { 209 typedef typename MatrixType::Scalar Scalar; 210 211 typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs; 212 typedef internal::blas_traits<Lhs> LhsBlasTraits; 213 typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs; 214 typedef typename internal::remove_all<ActualLhs>::type _ActualLhs; 215 typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs()); 216 217 typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs; 218 typedef internal::blas_traits<Rhs> RhsBlasTraits; 219 typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs; 220 typedef typename internal::remove_all<ActualRhs>::type _ActualRhs; 221 typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs()); 222 223 Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived()); 224 225 if(!beta) 226 mat.template triangularView<UpLo>().setZero(); 227 228 enum { 229 StorageOrder = (internal::traits<MatrixType>::Flags&RowMajorBit) ? RowMajor : ColMajor, 230 UseLhsDirectly = _ActualLhs::InnerStrideAtCompileTime==1, 231 UseRhsDirectly = _ActualRhs::InnerStrideAtCompileTime==1 232 }; 233 234 internal::gemv_static_vector_if<Scalar,Lhs::SizeAtCompileTime,Lhs::MaxSizeAtCompileTime,!UseLhsDirectly> static_lhs; 235 ei_declare_aligned_stack_constructed_variable(Scalar, actualLhsPtr, actualLhs.size(), 236 (UseLhsDirectly ? const_cast<Scalar*>(actualLhs.data()) : static_lhs.data())); 237 if(!UseLhsDirectly) Map<typename _ActualLhs::PlainObject>(actualLhsPtr, actualLhs.size()) = actualLhs; 238 239 internal::gemv_static_vector_if<Scalar,Rhs::SizeAtCompileTime,Rhs::MaxSizeAtCompileTime,!UseRhsDirectly> static_rhs; 240 ei_declare_aligned_stack_constructed_variable(Scalar, actualRhsPtr, actualRhs.size(), 241 (UseRhsDirectly ? const_cast<Scalar*>(actualRhs.data()) : static_rhs.data())); 242 if(!UseRhsDirectly) Map<typename _ActualRhs::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs; 243 244 245 selfadjoint_rank1_update<Scalar,Index,StorageOrder,UpLo, 246 LhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex, 247 RhsBlasTraits::NeedToConjugate && NumTraits<Scalar>::IsComplex> 248 ::run(actualLhs.size(), mat.data(), mat.outerStride(), actualLhsPtr, actualRhsPtr, actualAlpha); 249 } 250 }; 251 252 template<typename MatrixType, typename ProductType, int UpLo> 253 struct general_product_to_triangular_selector<MatrixType,ProductType,UpLo,false> 254 { 255 static void run(MatrixType& mat, const ProductType& prod, const typename MatrixType::Scalar& alpha, bool beta) 256 { 257 typedef typename internal::remove_all<typename ProductType::LhsNested>::type Lhs; 258 typedef internal::blas_traits<Lhs> LhsBlasTraits; 259 typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs; 260 typedef typename internal::remove_all<ActualLhs>::type _ActualLhs; 261 typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs()); 262 263 typedef typename internal::remove_all<typename ProductType::RhsNested>::type Rhs; 264 typedef internal::blas_traits<Rhs> RhsBlasTraits; 265 typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs; 266 typedef typename internal::remove_all<ActualRhs>::type _ActualRhs; 267 typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs()); 268 269 typename ProductType::Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived()); 270 271 if(!beta) 272 mat.template triangularView<UpLo>().setZero(); 273 274 enum { 275 IsRowMajor = (internal::traits<MatrixType>::Flags&RowMajorBit) ? 1 : 0, 276 LhsIsRowMajor = _ActualLhs::Flags&RowMajorBit ? 1 : 0, 277 RhsIsRowMajor = _ActualRhs::Flags&RowMajorBit ? 1 : 0, 278 SkipDiag = (UpLo&(UnitDiag|ZeroDiag))!=0 279 }; 280 281 Index size = mat.cols(); 282 if(SkipDiag) 283 size--; 284 Index depth = actualLhs.cols(); 285 286 typedef internal::gemm_blocking_space<IsRowMajor ? RowMajor : ColMajor,typename Lhs::Scalar,typename Rhs::Scalar, 287 MatrixType::MaxColsAtCompileTime, MatrixType::MaxColsAtCompileTime, _ActualRhs::MaxColsAtCompileTime> BlockingType; 288 289 BlockingType blocking(size, size, depth, 1, false); 290 291 internal::general_matrix_matrix_triangular_product<Index, 292 typename Lhs::Scalar, LhsIsRowMajor ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate, 293 typename Rhs::Scalar, RhsIsRowMajor ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate, 294 IsRowMajor ? RowMajor : ColMajor, MatrixType::InnerStrideAtCompileTime, UpLo&(Lower|Upper)> 295 ::run(size, depth, 296 &actualLhs.coeffRef(SkipDiag&&(UpLo&Lower)==Lower ? 1 : 0,0), actualLhs.outerStride(), 297 &actualRhs.coeffRef(0,SkipDiag&&(UpLo&Upper)==Upper ? 1 : 0), actualRhs.outerStride(), 298 mat.data() + (SkipDiag ? (bool(IsRowMajor) != ((UpLo&Lower)==Lower) ? mat.innerStride() : mat.outerStride() ) : 0), 299 mat.innerStride(), mat.outerStride(), actualAlpha, blocking); 300 } 301 }; 302 303 template<typename MatrixType, unsigned int UpLo> 304 template<typename ProductType> 305 EIGEN_DEVICE_FUNC TriangularView<MatrixType,UpLo>& TriangularViewImpl<MatrixType,UpLo,Dense>::_assignProduct(const ProductType& prod, const Scalar& alpha, bool beta) 306 { 307 EIGEN_STATIC_ASSERT((UpLo&UnitDiag)==0, WRITING_TO_TRIANGULAR_PART_WITH_UNIT_DIAGONAL_IS_NOT_SUPPORTED); 308 eigen_assert(derived().nestedExpression().rows() == prod.rows() && derived().cols() == prod.cols()); 309 310 general_product_to_triangular_selector<MatrixType, ProductType, UpLo, internal::traits<ProductType>::InnerSize==1>::run(derived().nestedExpression().const_cast_derived(), prod, alpha, beta); 311 312 return derived(); 313 } 314 315 } // end namespace Eigen 316 317 #endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H 318