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 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 template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder> 48 EIGEN_DONT_INLINE void triangular_solve_matrix<Scalar,Index,OnTheLeft,Mode,Conjugate,TriStorageOrder,ColMajor>::run( 49 Index size, Index otherSize, 50 const Scalar* _tri, Index triStride, 51 Scalar* _other, Index otherStride, 52 level3_blocking<Scalar,Scalar>& blocking) 53 { 54 Index cols = otherSize; 55 const_blas_data_mapper<Scalar, Index, TriStorageOrder> tri(_tri,triStride); 56 blas_data_mapper<Scalar, Index, ColMajor> other(_other,otherStride); 57 58 typedef gebp_traits<Scalar,Scalar> Traits; 59 enum { 60 SmallPanelWidth = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr), 61 IsLower = (Mode&Lower) == Lower 62 }; 63 64 Index kc = blocking.kc(); // cache block size along the K direction 65 Index mc = (std::min)(size,blocking.mc()); // cache block size along the M direction 66 67 std::size_t sizeA = kc*mc; 68 std::size_t sizeB = kc*cols; 69 std::size_t sizeW = kc*Traits::WorkSpaceFactor; 70 71 ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA()); 72 ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB()); 73 ei_declare_aligned_stack_constructed_variable(Scalar, blockW, sizeW, blocking.blockW()); 74 75 conj_if<Conjugate> conj; 76 gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, Conjugate, false> gebp_kernel; 77 gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, TriStorageOrder> pack_lhs; 78 gemm_pack_rhs<Scalar, Index, Traits::nr, ColMajor, false, true> pack_rhs; 79 80 // the goal here is to subdivise the Rhs panels such that we keep some cache 81 // coherence when accessing the rhs elements 82 std::ptrdiff_t l1, l2; 83 manage_caching_sizes(GetAction, &l1, &l2); 84 Index subcols = cols>0 ? l2/(4 * sizeof(Scalar) * otherStride) : 0; 85 subcols = std::max<Index>((subcols/Traits::nr)*Traits::nr, Traits::nr); 86 87 for(Index k2=IsLower ? 0 : size; 88 IsLower ? k2<size : k2>0; 89 IsLower ? k2+=kc : k2-=kc) 90 { 91 const Index actual_kc = (std::min)(IsLower ? size-k2 : k2, kc); 92 93 // We have selected and packed a big horizontal panel R1 of rhs. Let B be the packed copy of this panel, 94 // and R2 the remaining part of rhs. The corresponding vertical panel of lhs is split into 95 // A11 (the triangular part) and A21 the remaining rectangular part. 96 // Then the high level algorithm is: 97 // - B = R1 => general block copy (done during the next step) 98 // - R1 = A11^-1 B => tricky part 99 // - update B from the new R1 => actually this has to be performed continuously during the above step 100 // - R2 -= A21 * B => GEPP 101 102 // The tricky part: compute R1 = A11^-1 B while updating B from R1 103 // The idea is to split A11 into multiple small vertical panels. 104 // Each panel can be split into a small triangular part T1k which is processed without optimization, 105 // and the remaining small part T2k which is processed using gebp with appropriate block strides 106 for(Index j2=0; j2<cols; j2+=subcols) 107 { 108 Index actual_cols = (std::min)(cols-j2,subcols); 109 // for each small vertical panels [T1k^T, T2k^T]^T of lhs 110 for (Index k1=0; k1<actual_kc; k1+=SmallPanelWidth) 111 { 112 Index actualPanelWidth = std::min<Index>(actual_kc-k1, SmallPanelWidth); 113 // tr solve 114 for (Index k=0; k<actualPanelWidth; ++k) 115 { 116 // TODO write a small kernel handling this (can be shared with trsv) 117 Index i = IsLower ? k2+k1+k : k2-k1-k-1; 118 Index s = IsLower ? k2+k1 : i+1; 119 Index rs = actualPanelWidth - k - 1; // remaining size 120 121 Scalar a = (Mode & UnitDiag) ? Scalar(1) : Scalar(1)/conj(tri(i,i)); 122 for (Index j=j2; j<j2+actual_cols; ++j) 123 { 124 if (TriStorageOrder==RowMajor) 125 { 126 Scalar b(0); 127 const Scalar* l = &tri(i,s); 128 Scalar* r = &other(s,j); 129 for (Index i3=0; i3<k; ++i3) 130 b += conj(l[i3]) * r[i3]; 131 132 other(i,j) = (other(i,j) - b)*a; 133 } 134 else 135 { 136 Index s = IsLower ? i+1 : i-rs; 137 Scalar b = (other(i,j) *= a); 138 Scalar* r = &other(s,j); 139 const Scalar* l = &tri(s,i); 140 for (Index i3=0;i3<rs;++i3) 141 r[i3] -= b * conj(l[i3]); 142 } 143 } 144 } 145 146 Index lengthTarget = actual_kc-k1-actualPanelWidth; 147 Index startBlock = IsLower ? k2+k1 : k2-k1-actualPanelWidth; 148 Index blockBOffset = IsLower ? k1 : lengthTarget; 149 150 // update the respective rows of B from other 151 pack_rhs(blockB+actual_kc*j2, &other(startBlock,j2), otherStride, actualPanelWidth, actual_cols, actual_kc, blockBOffset); 152 153 // GEBP 154 if (lengthTarget>0) 155 { 156 Index startTarget = IsLower ? k2+k1+actualPanelWidth : k2-actual_kc; 157 158 pack_lhs(blockA, &tri(startTarget,startBlock), triStride, actualPanelWidth, lengthTarget); 159 160 gebp_kernel(&other(startTarget,j2), otherStride, blockA, blockB+actual_kc*j2, lengthTarget, actualPanelWidth, actual_cols, Scalar(-1), 161 actualPanelWidth, actual_kc, 0, blockBOffset, blockW); 162 } 163 } 164 } 165 166 // R2 -= A21 * B => GEPP 167 { 168 Index start = IsLower ? k2+kc : 0; 169 Index end = IsLower ? size : k2-kc; 170 for(Index i2=start; i2<end; i2+=mc) 171 { 172 const Index actual_mc = (std::min)(mc,end-i2); 173 if (actual_mc>0) 174 { 175 pack_lhs(blockA, &tri(i2, IsLower ? k2 : k2-kc), triStride, actual_kc, actual_mc); 176 177 gebp_kernel(_other+i2, otherStride, blockA, blockB, actual_mc, actual_kc, cols, Scalar(-1), -1, -1, 0, 0, blockW); 178 } 179 } 180 } 181 } 182 } 183 184 /* Optimized triangular solver with multiple left hand sides and the trinagular matrix on the right 185 */ 186 template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder> 187 struct triangular_solve_matrix<Scalar,Index,OnTheRight,Mode,Conjugate,TriStorageOrder,ColMajor> 188 { 189 static EIGEN_DONT_INLINE void run( 190 Index size, Index otherSize, 191 const Scalar* _tri, Index triStride, 192 Scalar* _other, Index otherStride, 193 level3_blocking<Scalar,Scalar>& blocking); 194 }; 195 template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder> 196 EIGEN_DONT_INLINE void triangular_solve_matrix<Scalar,Index,OnTheRight,Mode,Conjugate,TriStorageOrder,ColMajor>::run( 197 Index size, Index otherSize, 198 const Scalar* _tri, Index triStride, 199 Scalar* _other, Index otherStride, 200 level3_blocking<Scalar,Scalar>& blocking) 201 { 202 Index rows = otherSize; 203 const_blas_data_mapper<Scalar, Index, TriStorageOrder> rhs(_tri,triStride); 204 blas_data_mapper<Scalar, Index, ColMajor> lhs(_other,otherStride); 205 206 typedef gebp_traits<Scalar,Scalar> Traits; 207 enum { 208 RhsStorageOrder = TriStorageOrder, 209 SmallPanelWidth = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr), 210 IsLower = (Mode&Lower) == Lower 211 }; 212 213 Index kc = blocking.kc(); // cache block size along the K direction 214 Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction 215 216 std::size_t sizeA = kc*mc; 217 std::size_t sizeB = kc*size; 218 std::size_t sizeW = kc*Traits::WorkSpaceFactor; 219 220 ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA()); 221 ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB()); 222 ei_declare_aligned_stack_constructed_variable(Scalar, blockW, sizeW, blocking.blockW()); 223 224 conj_if<Conjugate> conj; 225 gebp_kernel<Scalar,Scalar, Index, Traits::mr, Traits::nr, false, Conjugate> gebp_kernel; 226 gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs; 227 gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder,false,true> pack_rhs_panel; 228 gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, ColMajor, false, true> pack_lhs_panel; 229 230 for(Index k2=IsLower ? size : 0; 231 IsLower ? k2>0 : k2<size; 232 IsLower ? k2-=kc : k2+=kc) 233 { 234 const Index actual_kc = (std::min)(IsLower ? k2 : size-k2, kc); 235 Index actual_k2 = IsLower ? k2-actual_kc : k2 ; 236 237 Index startPanel = IsLower ? 0 : k2+actual_kc; 238 Index rs = IsLower ? actual_k2 : size - actual_k2 - actual_kc; 239 Scalar* geb = blockB+actual_kc*actual_kc; 240 241 if (rs>0) pack_rhs(geb, &rhs(actual_k2,startPanel), triStride, actual_kc, rs); 242 243 // triangular packing (we only pack the panels off the diagonal, 244 // neglecting the blocks overlapping the diagonal 245 { 246 for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth) 247 { 248 Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth); 249 Index actual_j2 = actual_k2 + j2; 250 Index panelOffset = IsLower ? j2+actualPanelWidth : 0; 251 Index panelLength = IsLower ? actual_kc-j2-actualPanelWidth : j2; 252 253 if (panelLength>0) 254 pack_rhs_panel(blockB+j2*actual_kc, 255 &rhs(actual_k2+panelOffset, actual_j2), triStride, 256 panelLength, actualPanelWidth, 257 actual_kc, panelOffset); 258 } 259 } 260 261 for(Index i2=0; i2<rows; i2+=mc) 262 { 263 const Index actual_mc = (std::min)(mc,rows-i2); 264 265 // triangular solver kernel 266 { 267 // for each small block of the diagonal (=> vertical panels of rhs) 268 for (Index j2 = IsLower 269 ? (actual_kc - ((actual_kc%SmallPanelWidth) ? Index(actual_kc%SmallPanelWidth) 270 : Index(SmallPanelWidth))) 271 : 0; 272 IsLower ? j2>=0 : j2<actual_kc; 273 IsLower ? j2-=SmallPanelWidth : j2+=SmallPanelWidth) 274 { 275 Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth); 276 Index absolute_j2 = actual_k2 + j2; 277 Index panelOffset = IsLower ? j2+actualPanelWidth : 0; 278 Index panelLength = IsLower ? actual_kc - j2 - actualPanelWidth : j2; 279 280 // GEBP 281 if(panelLength>0) 282 { 283 gebp_kernel(&lhs(i2,absolute_j2), otherStride, 284 blockA, blockB+j2*actual_kc, 285 actual_mc, panelLength, actualPanelWidth, 286 Scalar(-1), 287 actual_kc, actual_kc, // strides 288 panelOffset, panelOffset, // offsets 289 blockW); // workspace 290 } 291 292 // unblocked triangular solve 293 for (Index k=0; k<actualPanelWidth; ++k) 294 { 295 Index j = IsLower ? absolute_j2+actualPanelWidth-k-1 : absolute_j2+k; 296 297 Scalar* r = &lhs(i2,j); 298 for (Index k3=0; k3<k; ++k3) 299 { 300 Scalar b = conj(rhs(IsLower ? j+1+k3 : absolute_j2+k3,j)); 301 Scalar* a = &lhs(i2,IsLower ? j+1+k3 : absolute_j2+k3); 302 for (Index i=0; i<actual_mc; ++i) 303 r[i] -= a[i] * b; 304 } 305 Scalar b = (Mode & UnitDiag) ? Scalar(1) : Scalar(1)/conj(rhs(j,j)); 306 for (Index i=0; i<actual_mc; ++i) 307 r[i] *= b; 308 } 309 310 // pack the just computed part of lhs to A 311 pack_lhs_panel(blockA, _other+absolute_j2*otherStride+i2, otherStride, 312 actualPanelWidth, actual_mc, 313 actual_kc, j2); 314 } 315 } 316 317 if (rs>0) 318 gebp_kernel(_other+i2+startPanel*otherStride, otherStride, blockA, geb, 319 actual_mc, actual_kc, rs, Scalar(-1), 320 -1, -1, 0, 0, blockW); 321 } 322 } 323 } 324 325 } // end namespace internal 326 327 } // end namespace Eigen 328 329 #endif // EIGEN_TRIANGULAR_SOLVER_MATRIX_H 330
