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 namespace internal { 16 17 /********************************************************************** 18 * This file implements a general A * B product while 19 * evaluating only one triangular part of the product. 20 * This is more general version of self adjoint product (C += A A^T) 21 * as the level 3 SYRK Blas routine. 22 **********************************************************************/ 23 24 // forward declarations (defined at the end of this file) 25 template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo> 26 struct tribb_kernel; 27 28 /* Optimized matrix-matrix product evaluating only one triangular half */ 29 template <typename Index, 30 typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs, 31 typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, 32 int ResStorageOrder, int UpLo, int Version = Specialized> 33 struct general_matrix_matrix_triangular_product; 34 35 // as usual if the result is row major => we transpose the product 36 template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs, 37 typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int UpLo, int Version> 38 struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor,UpLo,Version> 39 { 40 typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar; 41 static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* lhs, Index lhsStride, 42 const RhsScalar* rhs, Index rhsStride, ResScalar* res, Index resStride, ResScalar alpha) 43 { 44 general_matrix_matrix_triangular_product<Index, 45 RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs, 46 LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs, 47 ColMajor, UpLo==Lower?Upper:Lower> 48 ::run(size,depth,rhs,rhsStride,lhs,lhsStride,res,resStride,alpha); 49 } 50 }; 51 52 template <typename Index, typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs, 53 typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs, int UpLo, int Version> 54 struct general_matrix_matrix_triangular_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor,UpLo,Version> 55 { 56 typedef typename scalar_product_traits<LhsScalar, RhsScalar>::ReturnType ResScalar; 57 static EIGEN_STRONG_INLINE void run(Index size, Index depth,const LhsScalar* _lhs, Index lhsStride, 58 const RhsScalar* _rhs, Index rhsStride, ResScalar* res, Index resStride, ResScalar alpha) 59 { 60 const_blas_data_mapper<LhsScalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride); 61 const_blas_data_mapper<RhsScalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride); 62 63 typedef gebp_traits<LhsScalar,RhsScalar> Traits; 64 65 Index kc = depth; // cache block size along the K direction 66 Index mc = size; // cache block size along the M direction 67 Index nc = size; // cache block size along the N direction 68 computeProductBlockingSizes<LhsScalar,RhsScalar>(kc, mc, nc); 69 // !!! mc must be a multiple of nr: 70 if(mc > Traits::nr) 71 mc = (mc/Traits::nr)*Traits::nr; 72 73 std::size_t sizeW = kc*Traits::WorkSpaceFactor; 74 std::size_t sizeB = sizeW + kc*size; 75 ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, kc*mc, 0); 76 ei_declare_aligned_stack_constructed_variable(RhsScalar, allocatedBlockB, sizeB, 0); 77 RhsScalar* blockB = allocatedBlockB + sizeW; 78 79 gemm_pack_lhs<LhsScalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs; 80 gemm_pack_rhs<RhsScalar, Index, Traits::nr, RhsStorageOrder> pack_rhs; 81 gebp_kernel <LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp; 82 tribb_kernel<LhsScalar, RhsScalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs, UpLo> sybb; 83 84 for(Index k2=0; k2<depth; k2+=kc) 85 { 86 const Index actual_kc = (std::min)(k2+kc,depth)-k2; 87 88 // note that the actual rhs is the transpose/adjoint of mat 89 pack_rhs(blockB, &rhs(k2,0), rhsStride, actual_kc, size); 90 91 for(Index i2=0; i2<size; i2+=mc) 92 { 93 const Index actual_mc = (std::min)(i2+mc,size)-i2; 94 95 pack_lhs(blockA, &lhs(i2, k2), lhsStride, actual_kc, actual_mc); 96 97 // the selected actual_mc * size panel of res is split into three different part: 98 // 1 - before the diagonal => processed with gebp or skipped 99 // 2 - the actual_mc x actual_mc symmetric block => processed with a special kernel 100 // 3 - after the diagonal => processed with gebp or skipped 101 if (UpLo==Lower) 102 gebp(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, (std::min)(size,i2), alpha, 103 -1, -1, 0, 0, allocatedBlockB); 104 105 sybb(res+resStride*i2 + i2, resStride, blockA, blockB + actual_kc*i2, actual_mc, actual_kc, alpha, allocatedBlockB); 106 107 if (UpLo==Upper) 108 { 109 Index j2 = i2+actual_mc; 110 gebp(res+resStride*j2+i2, resStride, blockA, blockB+actual_kc*j2, actual_mc, actual_kc, (std::max)(Index(0), size-j2), alpha, 111 -1, -1, 0, 0, allocatedBlockB); 112 } 113 } 114 } 115 } 116 }; 117 118 // Optimized packed Block * packed Block product kernel evaluating only one given triangular part 119 // This kernel is built on top of the gebp kernel: 120 // - the current destination block is processed per panel of actual_mc x BlockSize 121 // where BlockSize is set to the minimal value allowing gebp to be as fast as possible 122 // - then, as usual, each panel is split into three parts along the diagonal, 123 // the sub blocks above and below the diagonal are processed as usual, 124 // while the triangular block overlapping the diagonal is evaluated into a 125 // small temporary buffer which is then accumulated into the result using a 126 // triangular traversal. 127 template<typename LhsScalar, typename RhsScalar, typename Index, int mr, int nr, bool ConjLhs, bool ConjRhs, int UpLo> 128 struct tribb_kernel 129 { 130 typedef gebp_traits<LhsScalar,RhsScalar,ConjLhs,ConjRhs> Traits; 131 typedef typename Traits::ResScalar ResScalar; 132 133 enum { 134 BlockSize = EIGEN_PLAIN_ENUM_MAX(mr,nr) 135 }; 136 void operator()(ResScalar* res, Index resStride, const LhsScalar* blockA, const RhsScalar* blockB, Index size, Index depth, ResScalar alpha, RhsScalar* workspace) 137 { 138 gebp_kernel<LhsScalar, RhsScalar, Index, mr, nr, ConjLhs, ConjRhs> gebp_kernel; 139 Matrix<ResScalar,BlockSize,BlockSize,ColMajor> buffer; 140 141 // let's process the block per panel of actual_mc x BlockSize, 142 // again, each is split into three parts, etc. 143 for (Index j=0; j<size; j+=BlockSize) 144 { 145 Index actualBlockSize = std::min<Index>(BlockSize,size - j); 146 const RhsScalar* actual_b = blockB+j*depth; 147 148 if(UpLo==Upper) 149 gebp_kernel(res+j*resStride, resStride, blockA, actual_b, j, depth, actualBlockSize, alpha, 150 -1, -1, 0, 0, workspace); 151 152 // selfadjoint micro block 153 { 154 Index i = j; 155 buffer.setZero(); 156 // 1 - apply the kernel on the temporary buffer 157 gebp_kernel(buffer.data(), BlockSize, blockA+depth*i, actual_b, actualBlockSize, depth, actualBlockSize, alpha, 158 -1, -1, 0, 0, workspace); 159 // 2 - triangular accumulation 160 for(Index j1=0; j1<actualBlockSize; ++j1) 161 { 162 ResScalar* r = res + (j+j1)*resStride + i; 163 for(Index i1=UpLo==Lower ? j1 : 0; 164 UpLo==Lower ? i1<actualBlockSize : i1<=j1; ++i1) 165 r[i1] += buffer(i1,j1); 166 } 167 } 168 169 if(UpLo==Lower) 170 { 171 Index i = j+actualBlockSize; 172 gebp_kernel(res+j*resStride+i, resStride, blockA+depth*i, actual_b, size-i, depth, actualBlockSize, alpha, 173 -1, -1, 0, 0, workspace); 174 } 175 } 176 } 177 }; 178 179 } // end namespace internal 180 181 // high level API 182 183 template<typename MatrixType, unsigned int UpLo> 184 template<typename ProductDerived, typename _Lhs, typename _Rhs> 185 TriangularView<MatrixType,UpLo>& TriangularView<MatrixType,UpLo>::assignProduct(const ProductBase<ProductDerived, _Lhs,_Rhs>& prod, const Scalar& alpha) 186 { 187 typedef typename internal::remove_all<typename ProductDerived::LhsNested>::type Lhs; 188 typedef internal::blas_traits<Lhs> LhsBlasTraits; 189 typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhs; 190 typedef typename internal::remove_all<ActualLhs>::type _ActualLhs; 191 typename internal::add_const_on_value_type<ActualLhs>::type actualLhs = LhsBlasTraits::extract(prod.lhs()); 192 193 typedef typename internal::remove_all<typename ProductDerived::RhsNested>::type Rhs; 194 typedef internal::blas_traits<Rhs> RhsBlasTraits; 195 typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhs; 196 typedef typename internal::remove_all<ActualRhs>::type _ActualRhs; 197 typename internal::add_const_on_value_type<ActualRhs>::type actualRhs = RhsBlasTraits::extract(prod.rhs()); 198 199 typename ProductDerived::Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs().derived()) * RhsBlasTraits::extractScalarFactor(prod.rhs().derived()); 200 201 internal::general_matrix_matrix_triangular_product<Index, 202 typename Lhs::Scalar, _ActualLhs::Flags&RowMajorBit ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate, 203 typename Rhs::Scalar, _ActualRhs::Flags&RowMajorBit ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate, 204 MatrixType::Flags&RowMajorBit ? RowMajor : ColMajor, UpLo> 205 ::run(m_matrix.cols(), actualLhs.cols(), 206 &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &actualRhs.coeffRef(0,0), actualRhs.outerStride(), 207 const_cast<Scalar*>(m_matrix.data()), m_matrix.outerStride(), actualAlpha); 208 209 return *this; 210 } 211 212 } // end namespace Eigen 213 214 #endif // EIGEN_GENERAL_MATRIX_MATRIX_TRIANGULAR_H 215
