Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 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@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 | { |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 21 | static void run( |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 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, |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 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, |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 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 | } |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 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, |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 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, |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 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 | } |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 324 | |
| 325 | } // end namespace internal |
| 326 | |
| 327 | } // end namespace Eigen |
| 328 | |
| 329 | #endif // EIGEN_TRIANGULAR_SOLVER_MATRIX_H |