TriangularSolverMatrix.h
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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 {
21  static void run(
22  Index size, Index cols,
23  const Scalar* tri, Index triStride,
24  Scalar* _other, Index otherStride,
26  {
28  Scalar, Index, Side==OnTheLeft?OnTheRight:OnTheLeft,
29  (Mode&UnitDiag) | ((Mode&Upper) ? Lower : Upper),
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,
46 };
47 template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder>
49  Index size, Index otherSize,
50  const Scalar* _tri, Index triStride,
51  Scalar* _other, Index otherStride,
53  {
54  Index cols = otherSize;
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 
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;
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,
194 };
195 template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder>
197  Index size, Index otherSize,
198  const Scalar* _tri, Index triStride,
199  Scalar* _other, Index otherStride,
201  {
202  Index rows = otherSize;
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 
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
const AutoDiffScalar< DerType > & conj(const AutoDiffScalar< DerType > &x)
#define ei_declare_aligned_stack_constructed_variable(TYPE, NAME, SIZE, BUFFER)
iterative scaling algorithm to equilibrate rows and column norms in matrices
Definition: matrix.hpp:471
void manage_caching_sizes(Action action, std::ptrdiff_t *l1=0, std::ptrdiff_t *l2=0)
Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...
Definition: NumTraits.h:88
static void run(Index size, Index cols, const Scalar *tri, Index triStride, Scalar *_other, Index otherStride, level3_blocking< Scalar, Scalar > &blocking)
void rhs(const real_t *x, real_t *f)
#define EIGEN_DONT_INLINE
#define EIGEN_PLAIN_ENUM_MAX(a, b)


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Author(s): Milan Vukov, Rien Quirynen
autogenerated on Mon Jun 10 2019 12:35:14