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 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 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, 45 const RhsScalar* rhs, Index rhsStride, ResScalar* res, Index resStride, const ResScalar& alpha) 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, 61 const RhsScalar* _rhs, Index rhsStride, ResScalar* res, Index resStride, const ResScalar& alpha) 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 }; 139 void operator()(ResScalar* res, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index size, Index depth, const ResScalar& alpha, RhsScalar* workspace) 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 185 186 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 }; 266 267 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 { 271 general_product_to_triangular_selector<MatrixType, ProductDerived, UpLo, (_Lhs::ColsAtCompileTime==1) || (_Rhs::RowsAtCompileTime==1)>::run(m_matrix.const_cast_derived(), prod.derived(), alpha); 272 273 return *this; 274 } 275 276 } // end namespace Eigen 277 278 #endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H 279