1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2009 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_TRIANGULAR_SOLVER_MATRIX_H 11 #define EIGEN_TRIANGULAR_SOLVER_MATRIX_H 12 13 namespace Eigen { 14 15 namespace internal { 16 17 // if the rhs is row major, let's transpose the product 18 template <typename Scalar, typename Index, int Side, int Mode, bool Conjugate, int TriStorageOrder> 19 struct triangular_solve_matrix<Scalar,Index,Side,Mode,Conjugate,TriStorageOrder,RowMajor> 20 { 21 static EIGEN_DONT_INLINE void run( 22 Index size, Index cols, 23 const Scalar* tri, Index triStride, 24 Scalar* _other, Index otherStride, 25 level3_blocking<Scalar,Scalar>& blocking) 26 { 27 triangular_solve_matrix< 28 Scalar, Index, Side==OnTheLeft?OnTheRight:OnTheLeft, 29 (Mode&UnitDiag) | ((Mode&Upper) ? Lower : Upper), 30 NumTraits<Scalar>::IsComplex && Conjugate, 31 TriStorageOrder==RowMajor ? ColMajor : RowMajor, ColMajor> 32 ::run(size, cols, tri, triStride, _other, otherStride, blocking); 33 } 34 }; 35 36 /* Optimized triangular solver with multiple right hand side and the triangular matrix on the left 37 */ 38 template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder> 39 struct triangular_solve_matrix<Scalar,Index,OnTheLeft,Mode,Conjugate,TriStorageOrder,ColMajor> 40 { 41 static EIGEN_DONT_INLINE void run( 42 Index size, Index otherSize, 43 const Scalar* _tri, Index triStride, 44 Scalar* _other, Index otherStride, 45 level3_blocking<Scalar,Scalar>& blocking) 46 { 47 Index cols = otherSize; 48 const_blas_data_mapper<Scalar, Index, TriStorageOrder> tri(_tri,triStride); 49 blas_data_mapper<Scalar, Index, ColMajor> other(_other,otherStride); 50 51 typedef gebp_traits<Scalar,Scalar> Traits; 52 enum { 53 SmallPanelWidth = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr), 54 IsLower = (Mode&Lower) == Lower 55 }; 56 57 Index kc = blocking.kc(); // cache block size along the K direction 58 Index mc = (std::min)(size,blocking.mc()); // cache block size along the M direction 59 60 std::size_t sizeA = kc*mc; 61 std::size_t sizeB = kc*cols; 62 std::size_t sizeW = kc*Traits::WorkSpaceFactor; 63 64 ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA()); 65 ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB()); 66 ei_declare_aligned_stack_constructed_variable(Scalar, blockW, sizeW, blocking.blockW()); 67 68 conj_if<Conjugate> conj; 69 gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, Conjugate, false> gebp_kernel; 70 gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, TriStorageOrder> pack_lhs; 71 gemm_pack_rhs<Scalar, Index, Traits::nr, ColMajor, false, true> pack_rhs; 72 73 // the goal here is to subdivise the Rhs panels such that we keep some cache 74 // coherence when accessing the rhs elements 75 std::ptrdiff_t l1, l2; 76 manage_caching_sizes(GetAction, &l1, &l2); 77 Index subcols = cols>0 ? l2/(4 * sizeof(Scalar) * otherStride) : 0; 78 subcols = std::max<Index>((subcols/Traits::nr)*Traits::nr, Traits::nr); 79 80 for(Index k2=IsLower ? 0 : size; 81 IsLower ? k2<size : k2>0; 82 IsLower ? k2+=kc : k2-=kc) 83 { 84 const Index actual_kc = (std::min)(IsLower ? size-k2 : k2, kc); 85 86 // We have selected and packed a big horizontal panel R1 of rhs. Let B be the packed copy of this panel, 87 // and R2 the remaining part of rhs. The corresponding vertical panel of lhs is split into 88 // A11 (the triangular part) and A21 the remaining rectangular part. 89 // Then the high level algorithm is: 90 // - B = R1 => general block copy (done during the next step) 91 // - R1 = A11^-1 B => tricky part 92 // - update B from the new R1 => actually this has to be performed continuously during the above step 93 // - R2 -= A21 * B => GEPP 94 95 // The tricky part: compute R1 = A11^-1 B while updating B from R1 96 // The idea is to split A11 into multiple small vertical panels. 97 // Each panel can be split into a small triangular part T1k which is processed without optimization, 98 // and the remaining small part T2k which is processed using gebp with appropriate block strides 99 for(Index j2=0; j2<cols; j2+=subcols) 100 { 101 Index actual_cols = (std::min)(cols-j2,subcols); 102 // for each small vertical panels [T1k^T, T2k^T]^T of lhs 103 for (Index k1=0; k1<actual_kc; k1+=SmallPanelWidth) 104 { 105 Index actualPanelWidth = std::min<Index>(actual_kc-k1, SmallPanelWidth); 106 // tr solve 107 for (Index k=0; k<actualPanelWidth; ++k) 108 { 109 // TODO write a small kernel handling this (can be shared with trsv) 110 Index i = IsLower ? k2+k1+k : k2-k1-k-1; 111 Index s = IsLower ? k2+k1 : i+1; 112 Index rs = actualPanelWidth - k - 1; // remaining size 113 114 Scalar a = (Mode & UnitDiag) ? Scalar(1) : Scalar(1)/conj(tri(i,i)); 115 for (Index j=j2; j<j2+actual_cols; ++j) 116 { 117 if (TriStorageOrder==RowMajor) 118 { 119 Scalar b(0); 120 const Scalar* l = &tri(i,s); 121 Scalar* r = &other(s,j); 122 for (Index i3=0; i3<k; ++i3) 123 b += conj(l[i3]) * r[i3]; 124 125 other(i,j) = (other(i,j) - b)*a; 126 } 127 else 128 { 129 Index s = IsLower ? i+1 : i-rs; 130 Scalar b = (other(i,j) *= a); 131 Scalar* r = &other(s,j); 132 const Scalar* l = &tri(s,i); 133 for (Index i3=0;i3<rs;++i3) 134 r[i3] -= b * conj(l[i3]); 135 } 136 } 137 } 138 139 Index lengthTarget = actual_kc-k1-actualPanelWidth; 140 Index startBlock = IsLower ? k2+k1 : k2-k1-actualPanelWidth; 141 Index blockBOffset = IsLower ? k1 : lengthTarget; 142 143 // update the respective rows of B from other 144 pack_rhs(blockB+actual_kc*j2, &other(startBlock,j2), otherStride, actualPanelWidth, actual_cols, actual_kc, blockBOffset); 145 146 // GEBP 147 if (lengthTarget>0) 148 { 149 Index startTarget = IsLower ? k2+k1+actualPanelWidth : k2-actual_kc; 150 151 pack_lhs(blockA, &tri(startTarget,startBlock), triStride, actualPanelWidth, lengthTarget); 152 153 gebp_kernel(&other(startTarget,j2), otherStride, blockA, blockB+actual_kc*j2, lengthTarget, actualPanelWidth, actual_cols, Scalar(-1), 154 actualPanelWidth, actual_kc, 0, blockBOffset, blockW); 155 } 156 } 157 } 158 159 // R2 -= A21 * B => GEPP 160 { 161 Index start = IsLower ? k2+kc : 0; 162 Index end = IsLower ? size : k2-kc; 163 for(Index i2=start; i2<end; i2+=mc) 164 { 165 const Index actual_mc = (std::min)(mc,end-i2); 166 if (actual_mc>0) 167 { 168 pack_lhs(blockA, &tri(i2, IsLower ? k2 : k2-kc), triStride, actual_kc, actual_mc); 169 170 gebp_kernel(_other+i2, otherStride, blockA, blockB, actual_mc, actual_kc, cols, Scalar(-1), -1, -1, 0, 0, blockW); 171 } 172 } 173 } 174 } 175 } 176 }; 177 178 /* Optimized triangular solver with multiple left hand sides and the trinagular matrix on the right 179 */ 180 template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder> 181 struct triangular_solve_matrix<Scalar,Index,OnTheRight,Mode,Conjugate,TriStorageOrder,ColMajor> 182 { 183 static EIGEN_DONT_INLINE void run( 184 Index size, Index otherSize, 185 const Scalar* _tri, Index triStride, 186 Scalar* _other, Index otherStride, 187 level3_blocking<Scalar,Scalar>& blocking) 188 { 189 Index rows = otherSize; 190 const_blas_data_mapper<Scalar, Index, TriStorageOrder> rhs(_tri,triStride); 191 blas_data_mapper<Scalar, Index, ColMajor> lhs(_other,otherStride); 192 193 typedef gebp_traits<Scalar,Scalar> Traits; 194 enum { 195 RhsStorageOrder = TriStorageOrder, 196 SmallPanelWidth = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr), 197 IsLower = (Mode&Lower) == Lower 198 }; 199 200 Index kc = blocking.kc(); // cache block size along the K direction 201 Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction 202 203 std::size_t sizeA = kc*mc; 204 std::size_t sizeB = kc*size; 205 std::size_t sizeW = kc*Traits::WorkSpaceFactor; 206 207 ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA()); 208 ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB()); 209 ei_declare_aligned_stack_constructed_variable(Scalar, blockW, sizeW, blocking.blockW()); 210 211 conj_if<Conjugate> conj; 212 gebp_kernel<Scalar,Scalar, Index, Traits::mr, Traits::nr, false, Conjugate> gebp_kernel; 213 gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs; 214 gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder,false,true> pack_rhs_panel; 215 gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, ColMajor, false, true> pack_lhs_panel; 216 217 for(Index k2=IsLower ? size : 0; 218 IsLower ? k2>0 : k2<size; 219 IsLower ? k2-=kc : k2+=kc) 220 { 221 const Index actual_kc = (std::min)(IsLower ? k2 : size-k2, kc); 222 Index actual_k2 = IsLower ? k2-actual_kc : k2 ; 223 224 Index startPanel = IsLower ? 0 : k2+actual_kc; 225 Index rs = IsLower ? actual_k2 : size - actual_k2 - actual_kc; 226 Scalar* geb = blockB+actual_kc*actual_kc; 227 228 if (rs>0) pack_rhs(geb, &rhs(actual_k2,startPanel), triStride, actual_kc, rs); 229 230 // triangular packing (we only pack the panels off the diagonal, 231 // neglecting the blocks overlapping the diagonal 232 { 233 for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth) 234 { 235 Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth); 236 Index actual_j2 = actual_k2 + j2; 237 Index panelOffset = IsLower ? j2+actualPanelWidth : 0; 238 Index panelLength = IsLower ? actual_kc-j2-actualPanelWidth : j2; 239 240 if (panelLength>0) 241 pack_rhs_panel(blockB+j2*actual_kc, 242 &rhs(actual_k2+panelOffset, actual_j2), triStride, 243 panelLength, actualPanelWidth, 244 actual_kc, panelOffset); 245 } 246 } 247 248 for(Index i2=0; i2<rows; i2+=mc) 249 { 250 const Index actual_mc = (std::min)(mc,rows-i2); 251 252 // triangular solver kernel 253 { 254 // for each small block of the diagonal (=> vertical panels of rhs) 255 for (Index j2 = IsLower 256 ? (actual_kc - ((actual_kc%SmallPanelWidth) ? Index(actual_kc%SmallPanelWidth) 257 : Index(SmallPanelWidth))) 258 : 0; 259 IsLower ? j2>=0 : j2<actual_kc; 260 IsLower ? j2-=SmallPanelWidth : j2+=SmallPanelWidth) 261 { 262 Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth); 263 Index absolute_j2 = actual_k2 + j2; 264 Index panelOffset = IsLower ? j2+actualPanelWidth : 0; 265 Index panelLength = IsLower ? actual_kc - j2 - actualPanelWidth : j2; 266 267 // GEBP 268 if(panelLength>0) 269 { 270 gebp_kernel(&lhs(i2,absolute_j2), otherStride, 271 blockA, blockB+j2*actual_kc, 272 actual_mc, panelLength, actualPanelWidth, 273 Scalar(-1), 274 actual_kc, actual_kc, // strides 275 panelOffset, panelOffset, // offsets 276 blockW); // workspace 277 } 278 279 // unblocked triangular solve 280 for (Index k=0; k<actualPanelWidth; ++k) 281 { 282 Index j = IsLower ? absolute_j2+actualPanelWidth-k-1 : absolute_j2+k; 283 284 Scalar* r = &lhs(i2,j); 285 for (Index k3=0; k3<k; ++k3) 286 { 287 Scalar b = conj(rhs(IsLower ? j+1+k3 : absolute_j2+k3,j)); 288 Scalar* a = &lhs(i2,IsLower ? j+1+k3 : absolute_j2+k3); 289 for (Index i=0; i<actual_mc; ++i) 290 r[i] -= a[i] * b; 291 } 292 Scalar b = (Mode & UnitDiag) ? Scalar(1) : Scalar(1)/conj(rhs(j,j)); 293 for (Index i=0; i<actual_mc; ++i) 294 r[i] *= b; 295 } 296 297 // pack the just computed part of lhs to A 298 pack_lhs_panel(blockA, _other+absolute_j2*otherStride+i2, otherStride, 299 actualPanelWidth, actual_mc, 300 actual_kc, j2); 301 } 302 } 303 304 if (rs>0) 305 gebp_kernel(_other+i2+startPanel*otherStride, otherStride, blockA, geb, 306 actual_mc, actual_kc, rs, Scalar(-1), 307 -1, -1, 0, 0, blockW); 308 } 309 } 310 } 311 }; 312 313 } // end namespace internal 314 315 } // end namespace Eigen 316 317 #endif // EIGEN_TRIANGULAR_SOLVER_MATRIX_H 318
