Eigen  3.3.0
 
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TriangularMatrixMatrix.h
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_MATRIX_MATRIX_H
11#define EIGEN_TRIANGULAR_MATRIX_MATRIX_H
12
13namespace Eigen {
14
15namespace internal {
16
17// template<typename Scalar, int mr, int StorageOrder, bool Conjugate, int Mode>
18// struct gemm_pack_lhs_triangular
19// {
20// Matrix<Scalar,mr,mr,
21// void operator()(Scalar* blockA, const EIGEN_RESTRICT Scalar* _lhs, int lhsStride, int depth, int rows)
22// {
23// conj_if<NumTraits<Scalar>::IsComplex && Conjugate> cj;
24// const_blas_data_mapper<Scalar, StorageOrder> lhs(_lhs,lhsStride);
25// int count = 0;
26// const int peeled_mc = (rows/mr)*mr;
27// for(int i=0; i<peeled_mc; i+=mr)
28// {
29// for(int k=0; k<depth; k++)
30// for(int w=0; w<mr; w++)
31// blockA[count++] = cj(lhs(i+w, k));
32// }
33// for(int i=peeled_mc; i<rows; i++)
34// {
35// for(int k=0; k<depth; k++)
36// blockA[count++] = cj(lhs(i, k));
37// }
38// }
39// };
40
41/* Optimized triangular matrix * matrix (_TRMM++) product built on top of
42 * the general matrix matrix product.
43 */
44template <typename Scalar, typename Index,
45 int Mode, bool LhsIsTriangular,
46 int LhsStorageOrder, bool ConjugateLhs,
47 int RhsStorageOrder, bool ConjugateRhs,
48 int ResStorageOrder, int Version = Specialized>
49struct product_triangular_matrix_matrix;
50
51template <typename Scalar, typename Index,
52 int Mode, bool LhsIsTriangular,
53 int LhsStorageOrder, bool ConjugateLhs,
54 int RhsStorageOrder, bool ConjugateRhs, int Version>
55struct product_triangular_matrix_matrix<Scalar,Index,Mode,LhsIsTriangular,
56 LhsStorageOrder,ConjugateLhs,
57 RhsStorageOrder,ConjugateRhs,RowMajor,Version>
58{
59 static EIGEN_STRONG_INLINE void run(
60 Index rows, Index cols, Index depth,
61 const Scalar* lhs, Index lhsStride,
62 const Scalar* rhs, Index rhsStride,
63 Scalar* res, Index resStride,
64 const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)
65 {
66 product_triangular_matrix_matrix<Scalar, Index,
67 (Mode&(UnitDiag|ZeroDiag)) | ((Mode&Upper) ? Lower : Upper),
68 (!LhsIsTriangular),
69 RhsStorageOrder==RowMajor ? ColMajor : RowMajor,
70 ConjugateRhs,
71 LhsStorageOrder==RowMajor ? ColMajor : RowMajor,
72 ConjugateLhs,
74 ::run(cols, rows, depth, rhs, rhsStride, lhs, lhsStride, res, resStride, alpha, blocking);
75 }
76};
77
78// implements col-major += alpha * op(triangular) * op(general)
79template <typename Scalar, typename Index, int Mode,
80 int LhsStorageOrder, bool ConjugateLhs,
81 int RhsStorageOrder, bool ConjugateRhs, int Version>
82struct product_triangular_matrix_matrix<Scalar,Index,Mode,true,
83 LhsStorageOrder,ConjugateLhs,
84 RhsStorageOrder,ConjugateRhs,ColMajor,Version>
85{
86
87 typedef gebp_traits<Scalar,Scalar> Traits;
88 enum {
89 SmallPanelWidth = 2 * EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),
90 IsLower = (Mode&Lower) == Lower,
91 SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1
92 };
93
94 static EIGEN_DONT_INLINE void run(
95 Index _rows, Index _cols, Index _depth,
96 const Scalar* _lhs, Index lhsStride,
97 const Scalar* _rhs, Index rhsStride,
98 Scalar* res, Index resStride,
99 const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking);
100};
101
102template <typename Scalar, typename Index, int Mode,
103 int LhsStorageOrder, bool ConjugateLhs,
104 int RhsStorageOrder, bool ConjugateRhs, int Version>
105EIGEN_DONT_INLINE void product_triangular_matrix_matrix<Scalar,Index,Mode,true,
106 LhsStorageOrder,ConjugateLhs,
107 RhsStorageOrder,ConjugateRhs,ColMajor,Version>::run(
108 Index _rows, Index _cols, Index _depth,
109 const Scalar* _lhs, Index lhsStride,
110 const Scalar* _rhs, Index rhsStride,
111 Scalar* _res, Index resStride,
112 const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)
113 {
114 // strip zeros
115 Index diagSize = (std::min)(_rows,_depth);
116 Index rows = IsLower ? _rows : diagSize;
117 Index depth = IsLower ? diagSize : _depth;
118 Index cols = _cols;
119
120 typedef const_blas_data_mapper<Scalar, Index, LhsStorageOrder> LhsMapper;
121 typedef const_blas_data_mapper<Scalar, Index, RhsStorageOrder> RhsMapper;
122 typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor> ResMapper;
123 LhsMapper lhs(_lhs,lhsStride);
124 RhsMapper rhs(_rhs,rhsStride);
125 ResMapper res(_res, resStride);
126
127 Index kc = blocking.kc(); // cache block size along the K direction
128 Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction
129 // The small panel size must not be larger than blocking size.
130 // Usually this should never be the case because SmallPanelWidth^2 is very small
131 // compared to L2 cache size, but let's be safe:
132 Index panelWidth = (std::min)(Index(SmallPanelWidth),(std::min)(kc,mc));
133
134 std::size_t sizeA = kc*mc;
135 std::size_t sizeB = kc*cols;
136
137 ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
138 ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
139
140 Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,LhsStorageOrder> triangularBuffer;
141 triangularBuffer.setZero();
142 if((Mode&ZeroDiag)==ZeroDiag)
143 triangularBuffer.diagonal().setZero();
144 else
145 triangularBuffer.diagonal().setOnes();
146
147 gebp_kernel<Scalar, Scalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
148 gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
149 gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr,RhsStorageOrder> pack_rhs;
150
151 for(Index k2=IsLower ? depth : 0;
152 IsLower ? k2>0 : k2<depth;
153 IsLower ? k2-=kc : k2+=kc)
154 {
155 Index actual_kc = (std::min)(IsLower ? k2 : depth-k2, kc);
156 Index actual_k2 = IsLower ? k2-actual_kc : k2;
157
158 // align blocks with the end of the triangular part for trapezoidal lhs
159 if((!IsLower)&&(k2<rows)&&(k2+actual_kc>rows))
160 {
161 actual_kc = rows-k2;
162 k2 = k2+actual_kc-kc;
163 }
164
165 pack_rhs(blockB, rhs.getSubMapper(actual_k2,0), actual_kc, cols);
166
167 // the selected lhs's panel has to be split in three different parts:
168 // 1 - the part which is zero => skip it
169 // 2 - the diagonal block => special kernel
170 // 3 - the dense panel below (lower case) or above (upper case) the diagonal block => GEPP
171
172 // the block diagonal, if any:
173 if(IsLower || actual_k2<rows)
174 {
175 // for each small vertical panels of lhs
176 for (Index k1=0; k1<actual_kc; k1+=panelWidth)
177 {
178 Index actualPanelWidth = std::min<Index>(actual_kc-k1, panelWidth);
179 Index lengthTarget = IsLower ? actual_kc-k1-actualPanelWidth : k1;
180 Index startBlock = actual_k2+k1;
181 Index blockBOffset = k1;
182
183 // => GEBP with the micro triangular block
184 // The trick is to pack this micro block while filling the opposite triangular part with zeros.
185 // To this end we do an extra triangular copy to a small temporary buffer
186 for (Index k=0;k<actualPanelWidth;++k)
187 {
188 if (SetDiag)
189 triangularBuffer.coeffRef(k,k) = lhs(startBlock+k,startBlock+k);
190 for (Index i=IsLower ? k+1 : 0; IsLower ? i<actualPanelWidth : i<k; ++i)
191 triangularBuffer.coeffRef(i,k) = lhs(startBlock+i,startBlock+k);
192 }
193 pack_lhs(blockA, LhsMapper(triangularBuffer.data(), triangularBuffer.outerStride()), actualPanelWidth, actualPanelWidth);
194
195 gebp_kernel(res.getSubMapper(startBlock, 0), blockA, blockB,
196 actualPanelWidth, actualPanelWidth, cols, alpha,
197 actualPanelWidth, actual_kc, 0, blockBOffset);
198
199 // GEBP with remaining micro panel
200 if (lengthTarget>0)
201 {
202 Index startTarget = IsLower ? actual_k2+k1+actualPanelWidth : actual_k2;
203
204 pack_lhs(blockA, lhs.getSubMapper(startTarget,startBlock), actualPanelWidth, lengthTarget);
205
206 gebp_kernel(res.getSubMapper(startTarget, 0), blockA, blockB,
207 lengthTarget, actualPanelWidth, cols, alpha,
208 actualPanelWidth, actual_kc, 0, blockBOffset);
209 }
210 }
211 }
212 // the part below (lower case) or above (upper case) the diagonal => GEPP
213 {
214 Index start = IsLower ? k2 : 0;
215 Index end = IsLower ? rows : (std::min)(actual_k2,rows);
216 for(Index i2=start; i2<end; i2+=mc)
217 {
218 const Index actual_mc = (std::min)(i2+mc,end)-i2;
219 gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr,Traits::LhsProgress, LhsStorageOrder,false>()
220 (blockA, lhs.getSubMapper(i2, actual_k2), actual_kc, actual_mc);
221
222 gebp_kernel(res.getSubMapper(i2, 0), blockA, blockB, actual_mc,
223 actual_kc, cols, alpha, -1, -1, 0, 0);
224 }
225 }
226 }
227 }
228
229// implements col-major += alpha * op(general) * op(triangular)
230template <typename Scalar, typename Index, int Mode,
231 int LhsStorageOrder, bool ConjugateLhs,
232 int RhsStorageOrder, bool ConjugateRhs, int Version>
233struct product_triangular_matrix_matrix<Scalar,Index,Mode,false,
234 LhsStorageOrder,ConjugateLhs,
235 RhsStorageOrder,ConjugateRhs,ColMajor,Version>
236{
237 typedef gebp_traits<Scalar,Scalar> Traits;
238 enum {
239 SmallPanelWidth = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),
240 IsLower = (Mode&Lower) == Lower,
241 SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1
242 };
243
244 static EIGEN_DONT_INLINE void run(
245 Index _rows, Index _cols, Index _depth,
246 const Scalar* _lhs, Index lhsStride,
247 const Scalar* _rhs, Index rhsStride,
248 Scalar* res, Index resStride,
249 const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking);
250};
251
252template <typename Scalar, typename Index, int Mode,
253 int LhsStorageOrder, bool ConjugateLhs,
254 int RhsStorageOrder, bool ConjugateRhs, int Version>
255EIGEN_DONT_INLINE void product_triangular_matrix_matrix<Scalar,Index,Mode,false,
256 LhsStorageOrder,ConjugateLhs,
257 RhsStorageOrder,ConjugateRhs,ColMajor,Version>::run(
258 Index _rows, Index _cols, Index _depth,
259 const Scalar* _lhs, Index lhsStride,
260 const Scalar* _rhs, Index rhsStride,
261 Scalar* _res, Index resStride,
262 const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)
263 {
264 const Index PacketBytes = packet_traits<Scalar>::size*sizeof(Scalar);
265 // strip zeros
266 Index diagSize = (std::min)(_cols,_depth);
267 Index rows = _rows;
268 Index depth = IsLower ? _depth : diagSize;
269 Index cols = IsLower ? diagSize : _cols;
270
271 typedef const_blas_data_mapper<Scalar, Index, LhsStorageOrder> LhsMapper;
272 typedef const_blas_data_mapper<Scalar, Index, RhsStorageOrder> RhsMapper;
273 typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor> ResMapper;
274 LhsMapper lhs(_lhs,lhsStride);
275 RhsMapper rhs(_rhs,rhsStride);
276 ResMapper res(_res, resStride);
277
278 Index kc = blocking.kc(); // cache block size along the K direction
279 Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction
280
281 std::size_t sizeA = kc*mc;
282 std::size_t sizeB = kc*cols+EIGEN_MAX_ALIGN_BYTES/sizeof(Scalar);
283
284 ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
285 ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
286
287 Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,RhsStorageOrder> triangularBuffer;
288 triangularBuffer.setZero();
289 if((Mode&ZeroDiag)==ZeroDiag)
290 triangularBuffer.diagonal().setZero();
291 else
292 triangularBuffer.diagonal().setOnes();
293
294 gebp_kernel<Scalar, Scalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
295 gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
296 gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr,RhsStorageOrder> pack_rhs;
297 gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr,RhsStorageOrder,false,true> pack_rhs_panel;
298
299 for(Index k2=IsLower ? 0 : depth;
300 IsLower ? k2<depth : k2>0;
301 IsLower ? k2+=kc : k2-=kc)
302 {
303 Index actual_kc = (std::min)(IsLower ? depth-k2 : k2, kc);
304 Index actual_k2 = IsLower ? k2 : k2-actual_kc;
305
306 // align blocks with the end of the triangular part for trapezoidal rhs
307 if(IsLower && (k2<cols) && (actual_k2+actual_kc>cols))
308 {
309 actual_kc = cols-k2;
310 k2 = actual_k2 + actual_kc - kc;
311 }
312
313 // remaining size
314 Index rs = IsLower ? (std::min)(cols,actual_k2) : cols - k2;
315 // size of the triangular part
316 Index ts = (IsLower && actual_k2>=cols) ? 0 : actual_kc;
317
318 Scalar* geb = blockB+ts*ts;
319 geb = geb + internal::first_aligned<PacketBytes>(geb,PacketBytes/sizeof(Scalar));
320
321 pack_rhs(geb, rhs.getSubMapper(actual_k2,IsLower ? 0 : k2), actual_kc, rs);
322
323 // pack the triangular part of the rhs padding the unrolled blocks with zeros
324 if(ts>0)
325 {
326 for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
327 {
328 Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
329 Index actual_j2 = actual_k2 + j2;
330 Index panelOffset = IsLower ? j2+actualPanelWidth : 0;
331 Index panelLength = IsLower ? actual_kc-j2-actualPanelWidth : j2;
332 // general part
333 pack_rhs_panel(blockB+j2*actual_kc,
334 rhs.getSubMapper(actual_k2+panelOffset, actual_j2),
335 panelLength, actualPanelWidth,
336 actual_kc, panelOffset);
337
338 // append the triangular part via a temporary buffer
339 for (Index j=0;j<actualPanelWidth;++j)
340 {
341 if (SetDiag)
342 triangularBuffer.coeffRef(j,j) = rhs(actual_j2+j,actual_j2+j);
343 for (Index k=IsLower ? j+1 : 0; IsLower ? k<actualPanelWidth : k<j; ++k)
344 triangularBuffer.coeffRef(k,j) = rhs(actual_j2+k,actual_j2+j);
345 }
346
347 pack_rhs_panel(blockB+j2*actual_kc,
348 RhsMapper(triangularBuffer.data(), triangularBuffer.outerStride()),
349 actualPanelWidth, actualPanelWidth,
350 actual_kc, j2);
351 }
352 }
353
354 for (Index i2=0; i2<rows; i2+=mc)
355 {
356 const Index actual_mc = (std::min)(mc,rows-i2);
357 pack_lhs(blockA, lhs.getSubMapper(i2, actual_k2), actual_kc, actual_mc);
358
359 // triangular kernel
360 if(ts>0)
361 {
362 for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
363 {
364 Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
365 Index panelLength = IsLower ? actual_kc-j2 : j2+actualPanelWidth;
366 Index blockOffset = IsLower ? j2 : 0;
367
368 gebp_kernel(res.getSubMapper(i2, actual_k2 + j2),
369 blockA, blockB+j2*actual_kc,
370 actual_mc, panelLength, actualPanelWidth,
371 alpha,
372 actual_kc, actual_kc, // strides
373 blockOffset, blockOffset);// offsets
374 }
375 }
376 gebp_kernel(res.getSubMapper(i2, IsLower ? 0 : k2),
377 blockA, geb, actual_mc, actual_kc, rs,
378 alpha,
379 -1, -1, 0, 0);
380 }
381 }
382 }
383
384/***************************************************************************
385* Wrapper to product_triangular_matrix_matrix
386***************************************************************************/
387
388} // end namespace internal
389
390namespace internal {
391template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
392struct triangular_product_impl<Mode,LhsIsTriangular,Lhs,false,Rhs,false>
393{
394 template<typename Dest> static void run(Dest& dst, const Lhs &a_lhs, const Rhs &a_rhs, const typename Dest::Scalar& alpha)
395 {
396 typedef typename Dest::Scalar Scalar;
397
398 typedef internal::blas_traits<Lhs> LhsBlasTraits;
399 typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
400 typedef typename internal::remove_all<ActualLhsType>::type ActualLhsTypeCleaned;
401 typedef internal::blas_traits<Rhs> RhsBlasTraits;
402 typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
403 typedef typename internal::remove_all<ActualRhsType>::type ActualRhsTypeCleaned;
404
405 typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(a_lhs);
406 typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(a_rhs);
407
408 Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(a_lhs)
409 * RhsBlasTraits::extractScalarFactor(a_rhs);
410
411 typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar,
412 Lhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxColsAtCompileTime,4> BlockingType;
413
414 enum { IsLower = (Mode&Lower) == Lower };
415 Index stripedRows = ((!LhsIsTriangular) || (IsLower)) ? lhs.rows() : (std::min)(lhs.rows(),lhs.cols());
416 Index stripedCols = ((LhsIsTriangular) || (!IsLower)) ? rhs.cols() : (std::min)(rhs.cols(),rhs.rows());
417 Index stripedDepth = LhsIsTriangular ? ((!IsLower) ? lhs.cols() : (std::min)(lhs.cols(),lhs.rows()))
418 : ((IsLower) ? rhs.rows() : (std::min)(rhs.rows(),rhs.cols()));
419
420 BlockingType blocking(stripedRows, stripedCols, stripedDepth, 1, false);
421
422 internal::product_triangular_matrix_matrix<Scalar, Index,
423 Mode, LhsIsTriangular,
424 (internal::traits<ActualLhsTypeCleaned>::Flags&RowMajorBit) ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
425 (internal::traits<ActualRhsTypeCleaned>::Flags&RowMajorBit) ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
426 (internal::traits<Dest >::Flags&RowMajorBit) ? RowMajor : ColMajor>
427 ::run(
428 stripedRows, stripedCols, stripedDepth, // sizes
429 &lhs.coeffRef(0,0), lhs.outerStride(), // lhs info
430 &rhs.coeffRef(0,0), rhs.outerStride(), // rhs info
431 &dst.coeffRef(0,0), dst.outerStride(), // result info
432 actualAlpha, blocking
433 );
434 }
435};
436
437} // end namespace internal
438
439} // end namespace Eigen
440
441#endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_H
@ UnitDiag
Definition: Constants.h:208
@ ZeroDiag
Definition: Constants.h:210
@ Lower
Definition: Constants.h:204
@ Upper
Definition: Constants.h:206
@ ColMajor
Definition: Constants.h:320
@ RowMajor
Definition: Constants.h:322
const unsigned int RowMajorBit
Definition: Constants.h:61
Namespace containing all symbols from the Eigen library.
Definition: Core:287
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:33