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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,
73 ColMajor>
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
130 std::size_t sizeA = kc*mc;
131 std::size_t sizeB = kc*cols;
132
133 ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
134 ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
135
136 Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,LhsStorageOrder> triangularBuffer;
137 triangularBuffer.setZero();
138 if((Mode&ZeroDiag)==ZeroDiag)
139 triangularBuffer.diagonal().setZero();
140 else
141 triangularBuffer.diagonal().setOnes();
142
143 gebp_kernel<Scalar, Scalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
144 gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
145 gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr,RhsStorageOrder> pack_rhs;
146
147 for(Index k2=IsLower ? depth : 0;
148 IsLower ? k2>0 : k2<depth;
149 IsLower ? k2-=kc : k2+=kc)
150 {
151 Index actual_kc = (std::min)(IsLower ? k2 : depth-k2, kc);
152 Index actual_k2 = IsLower ? k2-actual_kc : k2;
153
154 // align blocks with the end of the triangular part for trapezoidal lhs
155 if((!IsLower)&&(k2<rows)&&(k2+actual_kc>rows))
156 {
157 actual_kc = rows-k2;
158 k2 = k2+actual_kc-kc;
159 }
160
161 pack_rhs(blockB, rhs.getSubMapper(actual_k2,0), actual_kc, cols);
162
163 // the selected lhs's panel has to be split in three different parts:
164 // 1 - the part which is zero => skip it
165 // 2 - the diagonal block => special kernel
166 // 3 - the dense panel below (lower case) or above (upper case) the diagonal block => GEPP
167
168 // the block diagonal, if any:
169 if(IsLower || actual_k2<rows)
170 {
171 // for each small vertical panels of lhs
172 for (Index k1=0; k1<actual_kc; k1+=SmallPanelWidth)
173 {
174 Index actualPanelWidth = std::min<Index>(actual_kc-k1, SmallPanelWidth);
175 Index lengthTarget = IsLower ? actual_kc-k1-actualPanelWidth : k1;
176 Index startBlock = actual_k2+k1;
177 Index blockBOffset = k1;
178
179 // => GEBP with the micro triangular block
180 // The trick is to pack this micro block while filling the opposite triangular part with zeros.
181 // To this end we do an extra triangular copy to a small temporary buffer
182 for (Index k=0;k<actualPanelWidth;++k)
183 {
184 if (SetDiag)
185 triangularBuffer.coeffRef(k,k) = lhs(startBlock+k,startBlock+k);
186 for (Index i=IsLower ? k+1 : 0; IsLower ? i<actualPanelWidth : i<k; ++i)
187 triangularBuffer.coeffRef(i,k) = lhs(startBlock+i,startBlock+k);
188 }
189 pack_lhs(blockA, LhsMapper(triangularBuffer.data(), triangularBuffer.outerStride()), actualPanelWidth, actualPanelWidth);
190
191 gebp_kernel(res.getSubMapper(startBlock, 0), blockA, blockB,
192 actualPanelWidth, actualPanelWidth, cols, alpha,
193 actualPanelWidth, actual_kc, 0, blockBOffset);
194
195 // GEBP with remaining micro panel
196 if (lengthTarget>0)
197 {
198 Index startTarget = IsLower ? actual_k2+k1+actualPanelWidth : actual_k2;
199
200 pack_lhs(blockA, lhs.getSubMapper(startTarget,startBlock), actualPanelWidth, lengthTarget);
201
202 gebp_kernel(res.getSubMapper(startTarget, 0), blockA, blockB,
203 lengthTarget, actualPanelWidth, cols, alpha,
204 actualPanelWidth, actual_kc, 0, blockBOffset);
205 }
206 }
207 }
208 // the part below (lower case) or above (upper case) the diagonal => GEPP
209 {
210 Index start = IsLower ? k2 : 0;
211 Index end = IsLower ? rows : (std::min)(actual_k2,rows);
212 for(Index i2=start; i2<end; i2+=mc)
213 {
214 const Index actual_mc = (std::min)(i2+mc,end)-i2;
215 gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr,Traits::LhsProgress, LhsStorageOrder,false>()
216 (blockA, lhs.getSubMapper(i2, actual_k2), actual_kc, actual_mc);
217
218 gebp_kernel(res.getSubMapper(i2, 0), blockA, blockB, actual_mc,
219 actual_kc, cols, alpha, -1, -1, 0, 0);
220 }
221 }
222 }
223 }
224
225// implements col-major += alpha * op(general) * op(triangular)
226template <typename Scalar, typename Index, int Mode,
227 int LhsStorageOrder, bool ConjugateLhs,
228 int RhsStorageOrder, bool ConjugateRhs, int Version>
229struct product_triangular_matrix_matrix<Scalar,Index,Mode,false,
230 LhsStorageOrder,ConjugateLhs,
231 RhsStorageOrder,ConjugateRhs,ColMajor,Version>
232{
233 typedef gebp_traits<Scalar,Scalar> Traits;
234 enum {
235 SmallPanelWidth = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),
236 IsLower = (Mode&Lower) == Lower,
237 SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1
238 };
239
240 static EIGEN_DONT_INLINE void run(
241 Index _rows, Index _cols, Index _depth,
242 const Scalar* _lhs, Index lhsStride,
243 const Scalar* _rhs, Index rhsStride,
244 Scalar* res, Index resStride,
245 const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking);
246};
247
248template <typename Scalar, typename Index, int Mode,
249 int LhsStorageOrder, bool ConjugateLhs,
250 int RhsStorageOrder, bool ConjugateRhs, int Version>
251EIGEN_DONT_INLINE void product_triangular_matrix_matrix<Scalar,Index,Mode,false,
252 LhsStorageOrder,ConjugateLhs,
253 RhsStorageOrder,ConjugateRhs,ColMajor,Version>::run(
254 Index _rows, Index _cols, Index _depth,
255 const Scalar* _lhs, Index lhsStride,
256 const Scalar* _rhs, Index rhsStride,
257 Scalar* _res, Index resStride,
258 const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)
259 {
260 const Index PacketBytes = packet_traits<Scalar>::size*sizeof(Scalar);
261 // strip zeros
262 Index diagSize = (std::min)(_cols,_depth);
263 Index rows = _rows;
264 Index depth = IsLower ? _depth : diagSize;
265 Index cols = IsLower ? diagSize : _cols;
266
267 typedef const_blas_data_mapper<Scalar, Index, LhsStorageOrder> LhsMapper;
268 typedef const_blas_data_mapper<Scalar, Index, RhsStorageOrder> RhsMapper;
269 typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor> ResMapper;
270 LhsMapper lhs(_lhs,lhsStride);
271 RhsMapper rhs(_rhs,rhsStride);
272 ResMapper res(_res, resStride);
273
274 Index kc = blocking.kc(); // cache block size along the K direction
275 Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction
276
277 std::size_t sizeA = kc*mc;
278 std::size_t sizeB = kc*cols+EIGEN_MAX_ALIGN_BYTES/sizeof(Scalar);
279
280 ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
281 ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
282
283 Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,RhsStorageOrder> triangularBuffer;
284 triangularBuffer.setZero();
285 if((Mode&ZeroDiag)==ZeroDiag)
286 triangularBuffer.diagonal().setZero();
287 else
288 triangularBuffer.diagonal().setOnes();
289
290 gebp_kernel<Scalar, Scalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
291 gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
292 gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr,RhsStorageOrder> pack_rhs;
293 gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr,RhsStorageOrder,false,true> pack_rhs_panel;
294
295 for(Index k2=IsLower ? 0 : depth;
296 IsLower ? k2<depth : k2>0;
297 IsLower ? k2+=kc : k2-=kc)
298 {
299 Index actual_kc = (std::min)(IsLower ? depth-k2 : k2, kc);
300 Index actual_k2 = IsLower ? k2 : k2-actual_kc;
301
302 // align blocks with the end of the triangular part for trapezoidal rhs
303 if(IsLower && (k2<cols) && (actual_k2+actual_kc>cols))
304 {
305 actual_kc = cols-k2;
306 k2 = actual_k2 + actual_kc - kc;
307 }
308
309 // remaining size
310 Index rs = IsLower ? (std::min)(cols,actual_k2) : cols - k2;
311 // size of the triangular part
312 Index ts = (IsLower && actual_k2>=cols) ? 0 : actual_kc;
313
314 Scalar* geb = blockB+ts*ts;
315 geb = geb + internal::first_aligned<PacketBytes>(geb,PacketBytes/sizeof(Scalar));
316
317 pack_rhs(geb, rhs.getSubMapper(actual_k2,IsLower ? 0 : k2), actual_kc, rs);
318
319 // pack the triangular part of the rhs padding the unrolled blocks with zeros
320 if(ts>0)
321 {
322 for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
323 {
324 Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
325 Index actual_j2 = actual_k2 + j2;
326 Index panelOffset = IsLower ? j2+actualPanelWidth : 0;
327 Index panelLength = IsLower ? actual_kc-j2-actualPanelWidth : j2;
328 // general part
329 pack_rhs_panel(blockB+j2*actual_kc,
330 rhs.getSubMapper(actual_k2+panelOffset, actual_j2),
331 panelLength, actualPanelWidth,
332 actual_kc, panelOffset);
333
334 // append the triangular part via a temporary buffer
335 for (Index j=0;j<actualPanelWidth;++j)
336 {
337 if (SetDiag)
338 triangularBuffer.coeffRef(j,j) = rhs(actual_j2+j,actual_j2+j);
339 for (Index k=IsLower ? j+1 : 0; IsLower ? k<actualPanelWidth : k<j; ++k)
340 triangularBuffer.coeffRef(k,j) = rhs(actual_j2+k,actual_j2+j);
341 }
342
343 pack_rhs_panel(blockB+j2*actual_kc,
344 RhsMapper(triangularBuffer.data(), triangularBuffer.outerStride()),
345 actualPanelWidth, actualPanelWidth,
346 actual_kc, j2);
347 }
348 }
349
350 for (Index i2=0; i2<rows; i2+=mc)
351 {
352 const Index actual_mc = (std::min)(mc,rows-i2);
353 pack_lhs(blockA, lhs.getSubMapper(i2, actual_k2), actual_kc, actual_mc);
354
355 // triangular kernel
356 if(ts>0)
357 {
358 for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
359 {
360 Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
361 Index panelLength = IsLower ? actual_kc-j2 : j2+actualPanelWidth;
362 Index blockOffset = IsLower ? j2 : 0;
363
364 gebp_kernel(res.getSubMapper(i2, actual_k2 + j2),
365 blockA, blockB+j2*actual_kc,
366 actual_mc, panelLength, actualPanelWidth,
367 alpha,
368 actual_kc, actual_kc, // strides
369 blockOffset, blockOffset);// offsets
370 }
371 }
372 gebp_kernel(res.getSubMapper(i2, IsLower ? 0 : k2),
373 blockA, geb, actual_mc, actual_kc, rs,
374 alpha,
375 -1, -1, 0, 0);
376 }
377 }
378 }
379
380/***************************************************************************
381* Wrapper to product_triangular_matrix_matrix
382***************************************************************************/
383
384} // end namespace internal
385
386namespace internal {
387template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
388struct triangular_product_impl<Mode,LhsIsTriangular,Lhs,false,Rhs,false>
389{
390 template<typename Dest> static void run(Dest& dst, const Lhs &a_lhs, const Rhs &a_rhs, const typename Dest::Scalar& alpha)
391 {
392 typedef typename Dest::Scalar Scalar;
393
394 typedef internal::blas_traits<Lhs> LhsBlasTraits;
395 typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
396 typedef typename internal::remove_all<ActualLhsType>::type ActualLhsTypeCleaned;
397 typedef internal::blas_traits<Rhs> RhsBlasTraits;
398 typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
399 typedef typename internal::remove_all<ActualRhsType>::type ActualRhsTypeCleaned;
400
401 typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(a_lhs);
402 typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(a_rhs);
403
404 Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(a_lhs)
405 * RhsBlasTraits::extractScalarFactor(a_rhs);
406
407 typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar,
408 Lhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxColsAtCompileTime,4> BlockingType;
409
410 enum { IsLower = (Mode&Lower) == Lower };
411 Index stripedRows = ((!LhsIsTriangular) || (IsLower)) ? lhs.rows() : (std::min)(lhs.rows(),lhs.cols());
412 Index stripedCols = ((LhsIsTriangular) || (!IsLower)) ? rhs.cols() : (std::min)(rhs.cols(),rhs.rows());
413 Index stripedDepth = LhsIsTriangular ? ((!IsLower) ? lhs.cols() : (std::min)(lhs.cols(),lhs.rows()))
414 : ((IsLower) ? rhs.rows() : (std::min)(rhs.rows(),rhs.cols()));
415
416 BlockingType blocking(stripedRows, stripedCols, stripedDepth, 1, false);
417
418 internal::product_triangular_matrix_matrix<Scalar, Index,
419 Mode, LhsIsTriangular,
420 (internal::traits<ActualLhsTypeCleaned>::Flags&RowMajorBit) ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
421 (internal::traits<ActualRhsTypeCleaned>::Flags&RowMajorBit) ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
422 (internal::traits<Dest >::Flags&RowMajorBit) ? RowMajor : ColMajor>
423 ::run(
424 stripedRows, stripedCols, stripedDepth, // sizes
425 &lhs.coeffRef(0,0), lhs.outerStride(), // lhs info
426 &rhs.coeffRef(0,0), rhs.outerStride(), // rhs info
427 &dst.coeffRef(0,0), dst.outerStride(), // result info
428 actualAlpha, blocking
429 );
430 }
431};
432
433} // end namespace internal
434
435} // end namespace Eigen
436
437#endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_H
Eigen::Solve
Pseudo expression representing a solving operation.
Definition Solve.h:63
Eigen::internal::gemm_blocking_space
Definition GeneralMatrixMatrix.h:247
Eigen::UnitDiag
@ UnitDiag
Matrix has ones on the diagonal; to be used in combination with #Lower or #Upper.
Definition Constants.h:208
Eigen::ZeroDiag
@ ZeroDiag
Matrix has zeros on the diagonal; to be used in combination with #Lower or #Upper.
Definition Constants.h:210
Eigen::Lower
@ Lower
View matrix as a lower triangular matrix.
Definition Constants.h:204
Eigen::Upper
@ Upper
View matrix as an upper triangular matrix.
Definition Constants.h:206
Eigen::ColMajor
@ ColMajor
Storage order is column major (see TopicStorageOrders).
Definition Constants.h:320
Eigen::RowMajor
@ RowMajor
Storage order is row major (see TopicStorageOrders).
Definition Constants.h:322
Eigen::RowMajorBit
const unsigned int RowMajorBit
for a matrix, this means that the storage order is row-major.
Definition Constants.h:61
Eigen::internal::blas_traits
Definition BlasUtil.h:257
Eigen::internal::gebp_kernel
Definition GeneralBlockPanelKernel.h:949
Eigen::internal::packet_traits
Definition GenericPacketMath.h:90
Eigen::internal::product_triangular_matrix_matrix
Definition TriangularMatrixMatrix.h:49
Eigen::internal::traits
Definition ForwardDeclarations.h:17
Eigen::internal::triangular_product_impl
Definition ProductEvaluators.h:656
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