source: pacpussensors/trunk/Vislab/lib3dv/eigen/Eigen/src/Core/products/TriangularMatrixMatrix.h@ 136

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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_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 const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
121 const_blas_data_mapper<Scalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
122
123 Index kc = blocking.kc(); // cache block size along the K direction
124 Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction
125
126 std::size_t sizeA = kc*mc;
127 std::size_t sizeB = kc*cols;
128 std::size_t sizeW = kc*Traits::WorkSpaceFactor;
129
130 ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
131 ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
132 ei_declare_aligned_stack_constructed_variable(Scalar, blockW, sizeW, blocking.blockW());
133
134 Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,LhsStorageOrder> triangularBuffer;
135 triangularBuffer.setZero();
136 if((Mode&ZeroDiag)==ZeroDiag)
137 triangularBuffer.diagonal().setZero();
138 else
139 triangularBuffer.diagonal().setOnes();
140
141 gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
142 gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
143 gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
144
145 for(Index k2=IsLower ? depth : 0;
146 IsLower ? k2>0 : k2<depth;
147 IsLower ? k2-=kc : k2+=kc)
148 {
149 Index actual_kc = (std::min)(IsLower ? k2 : depth-k2, kc);
150 Index actual_k2 = IsLower ? k2-actual_kc : k2;
151
152 // align blocks with the end of the triangular part for trapezoidal lhs
153 if((!IsLower)&&(k2<rows)&&(k2+actual_kc>rows))
154 {
155 actual_kc = rows-k2;
156 k2 = k2+actual_kc-kc;
157 }
158
159 pack_rhs(blockB, &rhs(actual_k2,0), rhsStride, actual_kc, cols);
160
161 // the selected lhs's panel has to be split in three different parts:
162 // 1 - the part which is zero => skip it
163 // 2 - the diagonal block => special kernel
164 // 3 - the dense panel below (lower case) or above (upper case) the diagonal block => GEPP
165
166 // the block diagonal, if any:
167 if(IsLower || actual_k2<rows)
168 {
169 // for each small vertical panels of lhs
170 for (Index k1=0; k1<actual_kc; k1+=SmallPanelWidth)
171 {
172 Index actualPanelWidth = std::min<Index>(actual_kc-k1, SmallPanelWidth);
173 Index lengthTarget = IsLower ? actual_kc-k1-actualPanelWidth : k1;
174 Index startBlock = actual_k2+k1;
175 Index blockBOffset = k1;
176
177 // => GEBP with the micro triangular block
178 // The trick is to pack this micro block while filling the opposite triangular part with zeros.
179 // To this end we do an extra triangular copy to a small temporary buffer
180 for (Index k=0;k<actualPanelWidth;++k)
181 {
182 if (SetDiag)
183 triangularBuffer.coeffRef(k,k) = lhs(startBlock+k,startBlock+k);
184 for (Index i=IsLower ? k+1 : 0; IsLower ? i<actualPanelWidth : i<k; ++i)
185 triangularBuffer.coeffRef(i,k) = lhs(startBlock+i,startBlock+k);
186 }
187 pack_lhs(blockA, triangularBuffer.data(), triangularBuffer.outerStride(), actualPanelWidth, actualPanelWidth);
188
189 gebp_kernel(res+startBlock, resStride, blockA, blockB, actualPanelWidth, actualPanelWidth, cols, alpha,
190 actualPanelWidth, actual_kc, 0, blockBOffset, blockW);
191
192 // GEBP with remaining micro panel
193 if (lengthTarget>0)
194 {
195 Index startTarget = IsLower ? actual_k2+k1+actualPanelWidth : actual_k2;
196
197 pack_lhs(blockA, &lhs(startTarget,startBlock), lhsStride, actualPanelWidth, lengthTarget);
198
199 gebp_kernel(res+startTarget, resStride, blockA, blockB, lengthTarget, actualPanelWidth, cols, alpha,
200 actualPanelWidth, actual_kc, 0, blockBOffset, blockW);
201 }
202 }
203 }
204 // the part below (lower case) or above (upper case) the diagonal => GEPP
205 {
206 Index start = IsLower ? k2 : 0;
207 Index end = IsLower ? rows : (std::min)(actual_k2,rows);
208 for(Index i2=start; i2<end; i2+=mc)
209 {
210 const Index actual_mc = (std::min)(i2+mc,end)-i2;
211 gemm_pack_lhs<Scalar, Index, Traits::mr,Traits::LhsProgress, LhsStorageOrder,false>()
212 (blockA, &lhs(i2, actual_k2), lhsStride, actual_kc, actual_mc);
213
214 gebp_kernel(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha, -1, -1, 0, 0, blockW);
215 }
216 }
217 }
218 }
219
220// implements col-major += alpha * op(general) * op(triangular)
221template <typename Scalar, typename Index, int Mode,
222 int LhsStorageOrder, bool ConjugateLhs,
223 int RhsStorageOrder, bool ConjugateRhs, int Version>
224struct product_triangular_matrix_matrix<Scalar,Index,Mode,false,
225 LhsStorageOrder,ConjugateLhs,
226 RhsStorageOrder,ConjugateRhs,ColMajor,Version>
227{
228 typedef gebp_traits<Scalar,Scalar> Traits;
229 enum {
230 SmallPanelWidth = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),
231 IsLower = (Mode&Lower) == Lower,
232 SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1
233 };
234
235 static EIGEN_DONT_INLINE void run(
236 Index _rows, Index _cols, Index _depth,
237 const Scalar* _lhs, Index lhsStride,
238 const Scalar* _rhs, Index rhsStride,
239 Scalar* res, Index resStride,
240 const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking);
241};
242
243template <typename Scalar, typename Index, int Mode,
244 int LhsStorageOrder, bool ConjugateLhs,
245 int RhsStorageOrder, bool ConjugateRhs, int Version>
246EIGEN_DONT_INLINE void product_triangular_matrix_matrix<Scalar,Index,Mode,false,
247 LhsStorageOrder,ConjugateLhs,
248 RhsStorageOrder,ConjugateRhs,ColMajor,Version>::run(
249 Index _rows, Index _cols, Index _depth,
250 const Scalar* _lhs, Index lhsStride,
251 const Scalar* _rhs, Index rhsStride,
252 Scalar* res, Index resStride,
253 const Scalar& alpha, level3_blocking<Scalar,Scalar>& blocking)
254 {
255 // strip zeros
256 Index diagSize = (std::min)(_cols,_depth);
257 Index rows = _rows;
258 Index depth = IsLower ? _depth : diagSize;
259 Index cols = IsLower ? diagSize : _cols;
260
261 const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
262 const_blas_data_mapper<Scalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
263
264 Index kc = blocking.kc(); // cache block size along the K direction
265 Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction
266
267 std::size_t sizeA = kc*mc;
268 std::size_t sizeB = kc*cols;
269 std::size_t sizeW = kc*Traits::WorkSpaceFactor;
270
271 ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
272 ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
273 ei_declare_aligned_stack_constructed_variable(Scalar, blockW, sizeW, blocking.blockW());
274
275 Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,RhsStorageOrder> triangularBuffer;
276 triangularBuffer.setZero();
277 if((Mode&ZeroDiag)==ZeroDiag)
278 triangularBuffer.diagonal().setZero();
279 else
280 triangularBuffer.diagonal().setOnes();
281
282 gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
283 gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
284 gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
285 gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder,false,true> pack_rhs_panel;
286
287 for(Index k2=IsLower ? 0 : depth;
288 IsLower ? k2<depth : k2>0;
289 IsLower ? k2+=kc : k2-=kc)
290 {
291 Index actual_kc = (std::min)(IsLower ? depth-k2 : k2, kc);
292 Index actual_k2 = IsLower ? k2 : k2-actual_kc;
293
294 // align blocks with the end of the triangular part for trapezoidal rhs
295 if(IsLower && (k2<cols) && (actual_k2+actual_kc>cols))
296 {
297 actual_kc = cols-k2;
298 k2 = actual_k2 + actual_kc - kc;
299 }
300
301 // remaining size
302 Index rs = IsLower ? (std::min)(cols,actual_k2) : cols - k2;
303 // size of the triangular part
304 Index ts = (IsLower && actual_k2>=cols) ? 0 : actual_kc;
305
306 Scalar* geb = blockB+ts*ts;
307
308 pack_rhs(geb, &rhs(actual_k2,IsLower ? 0 : k2), rhsStride, actual_kc, rs);
309
310 // pack the triangular part of the rhs padding the unrolled blocks with zeros
311 if(ts>0)
312 {
313 for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
314 {
315 Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
316 Index actual_j2 = actual_k2 + j2;
317 Index panelOffset = IsLower ? j2+actualPanelWidth : 0;
318 Index panelLength = IsLower ? actual_kc-j2-actualPanelWidth : j2;
319 // general part
320 pack_rhs_panel(blockB+j2*actual_kc,
321 &rhs(actual_k2+panelOffset, actual_j2), rhsStride,
322 panelLength, actualPanelWidth,
323 actual_kc, panelOffset);
324
325 // append the triangular part via a temporary buffer
326 for (Index j=0;j<actualPanelWidth;++j)
327 {
328 if (SetDiag)
329 triangularBuffer.coeffRef(j,j) = rhs(actual_j2+j,actual_j2+j);
330 for (Index k=IsLower ? j+1 : 0; IsLower ? k<actualPanelWidth : k<j; ++k)
331 triangularBuffer.coeffRef(k,j) = rhs(actual_j2+k,actual_j2+j);
332 }
333
334 pack_rhs_panel(blockB+j2*actual_kc,
335 triangularBuffer.data(), triangularBuffer.outerStride(),
336 actualPanelWidth, actualPanelWidth,
337 actual_kc, j2);
338 }
339 }
340
341 for (Index i2=0; i2<rows; i2+=mc)
342 {
343 const Index actual_mc = (std::min)(mc,rows-i2);
344 pack_lhs(blockA, &lhs(i2, actual_k2), lhsStride, actual_kc, actual_mc);
345
346 // triangular kernel
347 if(ts>0)
348 {
349 for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
350 {
351 Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
352 Index panelLength = IsLower ? actual_kc-j2 : j2+actualPanelWidth;
353 Index blockOffset = IsLower ? j2 : 0;
354
355 gebp_kernel(res+i2+(actual_k2+j2)*resStride, resStride,
356 blockA, blockB+j2*actual_kc,
357 actual_mc, panelLength, actualPanelWidth,
358 alpha,
359 actual_kc, actual_kc, // strides
360 blockOffset, blockOffset,// offsets
361 blockW); // workspace
362 }
363 }
364 gebp_kernel(res+i2+(IsLower ? 0 : k2)*resStride, resStride,
365 blockA, geb, actual_mc, actual_kc, rs,
366 alpha,
367 -1, -1, 0, 0, blockW);
368 }
369 }
370 }
371
372/***************************************************************************
373* Wrapper to product_triangular_matrix_matrix
374***************************************************************************/
375
376template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
377struct traits<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false> >
378 : traits<ProductBase<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>, Lhs, Rhs> >
379{};
380
381} // end namespace internal
382
383template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
384struct TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>
385 : public ProductBase<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>, Lhs, Rhs >
386{
387 EIGEN_PRODUCT_PUBLIC_INTERFACE(TriangularProduct)
388
389 TriangularProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) {}
390
391 template<typename Dest> void scaleAndAddTo(Dest& dst, const Scalar& alpha) const
392 {
393 typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(m_lhs);
394 typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(m_rhs);
395
396 Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs)
397 * RhsBlasTraits::extractScalarFactor(m_rhs);
398
399 typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar,
400 Lhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxColsAtCompileTime,4> BlockingType;
401
402 enum { IsLower = (Mode&Lower) == Lower };
403 Index stripedRows = ((!LhsIsTriangular) || (IsLower)) ? lhs.rows() : (std::min)(lhs.rows(),lhs.cols());
404 Index stripedCols = ((LhsIsTriangular) || (!IsLower)) ? rhs.cols() : (std::min)(rhs.cols(),rhs.rows());
405 Index stripedDepth = LhsIsTriangular ? ((!IsLower) ? lhs.cols() : (std::min)(lhs.cols(),lhs.rows()))
406 : ((IsLower) ? rhs.rows() : (std::min)(rhs.rows(),rhs.cols()));
407
408 BlockingType blocking(stripedRows, stripedCols, stripedDepth);
409
410 internal::product_triangular_matrix_matrix<Scalar, Index,
411 Mode, LhsIsTriangular,
412 (internal::traits<_ActualLhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
413 (internal::traits<_ActualRhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
414 (internal::traits<Dest >::Flags&RowMajorBit) ? RowMajor : ColMajor>
415 ::run(
416 stripedRows, stripedCols, stripedDepth, // sizes
417 &lhs.coeffRef(0,0), lhs.outerStride(), // lhs info
418 &rhs.coeffRef(0,0), rhs.outerStride(), // rhs info
419 &dst.coeffRef(0,0), dst.outerStride(), // result info
420 actualAlpha, blocking
421 );
422 }
423};
424
425} // end namespace Eigen
426
427#endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_H
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