source: pacpussensors/trunk/Vislab/lib3dv/eigen/Eigen/src/Core/products/SelfadjointMatrixMatrix.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_SELFADJOINT_MATRIX_MATRIX_H
11#define EIGEN_SELFADJOINT_MATRIX_MATRIX_H
12
13namespace Eigen {
14
15namespace internal {
16
17// pack a selfadjoint block diagonal for use with the gebp_kernel
18template<typename Scalar, typename Index, int Pack1, int Pack2, int StorageOrder>
19struct symm_pack_lhs
20{
21 template<int BlockRows> inline
22 void pack(Scalar* blockA, const const_blas_data_mapper<Scalar,Index,StorageOrder>& lhs, Index cols, Index i, Index& count)
23 {
24 // normal copy
25 for(Index k=0; k<i; k++)
26 for(Index w=0; w<BlockRows; w++)
27 blockA[count++] = lhs(i+w,k); // normal
28 // symmetric copy
29 Index h = 0;
30 for(Index k=i; k<i+BlockRows; k++)
31 {
32 for(Index w=0; w<h; w++)
33 blockA[count++] = numext::conj(lhs(k, i+w)); // transposed
34
35 blockA[count++] = numext::real(lhs(k,k)); // real (diagonal)
36
37 for(Index w=h+1; w<BlockRows; w++)
38 blockA[count++] = lhs(i+w, k); // normal
39 ++h;
40 }
41 // transposed copy
42 for(Index k=i+BlockRows; k<cols; k++)
43 for(Index w=0; w<BlockRows; w++)
44 blockA[count++] = numext::conj(lhs(k, i+w)); // transposed
45 }
46 void operator()(Scalar* blockA, const Scalar* _lhs, Index lhsStride, Index cols, Index rows)
47 {
48 const_blas_data_mapper<Scalar,Index,StorageOrder> lhs(_lhs,lhsStride);
49 Index count = 0;
50 Index peeled_mc = (rows/Pack1)*Pack1;
51 for(Index i=0; i<peeled_mc; i+=Pack1)
52 {
53 pack<Pack1>(blockA, lhs, cols, i, count);
54 }
55
56 if(rows-peeled_mc>=Pack2)
57 {
58 pack<Pack2>(blockA, lhs, cols, peeled_mc, count);
59 peeled_mc += Pack2;
60 }
61
62 // do the same with mr==1
63 for(Index i=peeled_mc; i<rows; i++)
64 {
65 for(Index k=0; k<i; k++)
66 blockA[count++] = lhs(i, k); // normal
67
68 blockA[count++] = numext::real(lhs(i, i)); // real (diagonal)
69
70 for(Index k=i+1; k<cols; k++)
71 blockA[count++] = numext::conj(lhs(k, i)); // transposed
72 }
73 }
74};
75
76template<typename Scalar, typename Index, int nr, int StorageOrder>
77struct symm_pack_rhs
78{
79 enum { PacketSize = packet_traits<Scalar>::size };
80 void operator()(Scalar* blockB, const Scalar* _rhs, Index rhsStride, Index rows, Index cols, Index k2)
81 {
82 Index end_k = k2 + rows;
83 Index count = 0;
84 const_blas_data_mapper<Scalar,Index,StorageOrder> rhs(_rhs,rhsStride);
85 Index packet_cols = (cols/nr)*nr;
86
87 // first part: normal case
88 for(Index j2=0; j2<k2; j2+=nr)
89 {
90 for(Index k=k2; k<end_k; k++)
91 {
92 blockB[count+0] = rhs(k,j2+0);
93 blockB[count+1] = rhs(k,j2+1);
94 if (nr==4)
95 {
96 blockB[count+2] = rhs(k,j2+2);
97 blockB[count+3] = rhs(k,j2+3);
98 }
99 count += nr;
100 }
101 }
102
103 // second part: diagonal block
104 for(Index j2=k2; j2<(std::min)(k2+rows,packet_cols); j2+=nr)
105 {
106 // again we can split vertically in three different parts (transpose, symmetric, normal)
107 // transpose
108 for(Index k=k2; k<j2; k++)
109 {
110 blockB[count+0] = numext::conj(rhs(j2+0,k));
111 blockB[count+1] = numext::conj(rhs(j2+1,k));
112 if (nr==4)
113 {
114 blockB[count+2] = numext::conj(rhs(j2+2,k));
115 blockB[count+3] = numext::conj(rhs(j2+3,k));
116 }
117 count += nr;
118 }
119 // symmetric
120 Index h = 0;
121 for(Index k=j2; k<j2+nr; k++)
122 {
123 // normal
124 for (Index w=0 ; w<h; ++w)
125 blockB[count+w] = rhs(k,j2+w);
126
127 blockB[count+h] = numext::real(rhs(k,k));
128
129 // transpose
130 for (Index w=h+1 ; w<nr; ++w)
131 blockB[count+w] = numext::conj(rhs(j2+w,k));
132 count += nr;
133 ++h;
134 }
135 // normal
136 for(Index k=j2+nr; k<end_k; k++)
137 {
138 blockB[count+0] = rhs(k,j2+0);
139 blockB[count+1] = rhs(k,j2+1);
140 if (nr==4)
141 {
142 blockB[count+2] = rhs(k,j2+2);
143 blockB[count+3] = rhs(k,j2+3);
144 }
145 count += nr;
146 }
147 }
148
149 // third part: transposed
150 for(Index j2=k2+rows; j2<packet_cols; j2+=nr)
151 {
152 for(Index k=k2; k<end_k; k++)
153 {
154 blockB[count+0] = numext::conj(rhs(j2+0,k));
155 blockB[count+1] = numext::conj(rhs(j2+1,k));
156 if (nr==4)
157 {
158 blockB[count+2] = numext::conj(rhs(j2+2,k));
159 blockB[count+3] = numext::conj(rhs(j2+3,k));
160 }
161 count += nr;
162 }
163 }
164
165 // copy the remaining columns one at a time (=> the same with nr==1)
166 for(Index j2=packet_cols; j2<cols; ++j2)
167 {
168 // transpose
169 Index half = (std::min)(end_k,j2);
170 for(Index k=k2; k<half; k++)
171 {
172 blockB[count] = numext::conj(rhs(j2,k));
173 count += 1;
174 }
175
176 if(half==j2 && half<k2+rows)
177 {
178 blockB[count] = numext::real(rhs(j2,j2));
179 count += 1;
180 }
181 else
182 half--;
183
184 // normal
185 for(Index k=half+1; k<k2+rows; k++)
186 {
187 blockB[count] = rhs(k,j2);
188 count += 1;
189 }
190 }
191 }
192};
193
194/* Optimized selfadjoint matrix * matrix (_SYMM) product built on top of
195 * the general matrix matrix product.
196 */
197template <typename Scalar, typename Index,
198 int LhsStorageOrder, bool LhsSelfAdjoint, bool ConjugateLhs,
199 int RhsStorageOrder, bool RhsSelfAdjoint, bool ConjugateRhs,
200 int ResStorageOrder>
201struct product_selfadjoint_matrix;
202
203template <typename Scalar, typename Index,
204 int LhsStorageOrder, bool LhsSelfAdjoint, bool ConjugateLhs,
205 int RhsStorageOrder, bool RhsSelfAdjoint, bool ConjugateRhs>
206struct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,LhsSelfAdjoint,ConjugateLhs, RhsStorageOrder,RhsSelfAdjoint,ConjugateRhs,RowMajor>
207{
208
209 static EIGEN_STRONG_INLINE void run(
210 Index rows, Index cols,
211 const Scalar* lhs, Index lhsStride,
212 const Scalar* rhs, Index rhsStride,
213 Scalar* res, Index resStride,
214 const Scalar& alpha)
215 {
216 product_selfadjoint_matrix<Scalar, Index,
217 EIGEN_LOGICAL_XOR(RhsSelfAdjoint,RhsStorageOrder==RowMajor) ? ColMajor : RowMajor,
218 RhsSelfAdjoint, NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(RhsSelfAdjoint,ConjugateRhs),
219 EIGEN_LOGICAL_XOR(LhsSelfAdjoint,LhsStorageOrder==RowMajor) ? ColMajor : RowMajor,
220 LhsSelfAdjoint, NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(LhsSelfAdjoint,ConjugateLhs),
221 ColMajor>
222 ::run(cols, rows, rhs, rhsStride, lhs, lhsStride, res, resStride, alpha);
223 }
224};
225
226template <typename Scalar, typename Index,
227 int LhsStorageOrder, bool ConjugateLhs,
228 int RhsStorageOrder, bool ConjugateRhs>
229struct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,true,ConjugateLhs, RhsStorageOrder,false,ConjugateRhs,ColMajor>
230{
231
232 static EIGEN_DONT_INLINE void run(
233 Index rows, Index cols,
234 const Scalar* _lhs, Index lhsStride,
235 const Scalar* _rhs, Index rhsStride,
236 Scalar* res, Index resStride,
237 const Scalar& alpha);
238};
239
240template <typename Scalar, typename Index,
241 int LhsStorageOrder, bool ConjugateLhs,
242 int RhsStorageOrder, bool ConjugateRhs>
243EIGEN_DONT_INLINE void product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,true,ConjugateLhs, RhsStorageOrder,false,ConjugateRhs,ColMajor>::run(
244 Index rows, Index cols,
245 const Scalar* _lhs, Index lhsStride,
246 const Scalar* _rhs, Index rhsStride,
247 Scalar* res, Index resStride,
248 const Scalar& alpha)
249 {
250 Index size = rows;
251
252 const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
253 const_blas_data_mapper<Scalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
254
255 typedef gebp_traits<Scalar,Scalar> Traits;
256
257 Index kc = size; // cache block size along the K direction
258 Index mc = rows; // cache block size along the M direction
259 Index nc = cols; // cache block size along the N direction
260 computeProductBlockingSizes<Scalar,Scalar>(kc, mc, nc);
261 // kc must smaller than mc
262 kc = (std::min)(kc,mc);
263
264 std::size_t sizeW = kc*Traits::WorkSpaceFactor;
265 std::size_t sizeB = sizeW + kc*cols;
266 ei_declare_aligned_stack_constructed_variable(Scalar, blockA, kc*mc, 0);
267 ei_declare_aligned_stack_constructed_variable(Scalar, allocatedBlockB, sizeB, 0);
268 Scalar* blockB = allocatedBlockB + sizeW;
269
270 gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
271 symm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
272 gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
273 gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder==RowMajor?ColMajor:RowMajor, true> pack_lhs_transposed;
274
275 for(Index k2=0; k2<size; k2+=kc)
276 {
277 const Index actual_kc = (std::min)(k2+kc,size)-k2;
278
279 // we have selected one row panel of rhs and one column panel of lhs
280 // pack rhs's panel into a sequential chunk of memory
281 // and expand each coeff to a constant packet for further reuse
282 pack_rhs(blockB, &rhs(k2,0), rhsStride, actual_kc, cols);
283
284 // the select lhs's panel has to be split in three different parts:
285 // 1 - the transposed panel above the diagonal block => transposed packed copy
286 // 2 - the diagonal block => special packed copy
287 // 3 - the panel below the diagonal block => generic packed copy
288 for(Index i2=0; i2<k2; i2+=mc)
289 {
290 const Index actual_mc = (std::min)(i2+mc,k2)-i2;
291 // transposed packed copy
292 pack_lhs_transposed(blockA, &lhs(k2, i2), lhsStride, actual_kc, actual_mc);
293
294 gebp_kernel(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha);
295 }
296 // the block diagonal
297 {
298 const Index actual_mc = (std::min)(k2+kc,size)-k2;
299 // symmetric packed copy
300 pack_lhs(blockA, &lhs(k2,k2), lhsStride, actual_kc, actual_mc);
301
302 gebp_kernel(res+k2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha);
303 }
304
305 for(Index i2=k2+kc; i2<size; i2+=mc)
306 {
307 const Index actual_mc = (std::min)(i2+mc,size)-i2;
308 gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder,false>()
309 (blockA, &lhs(i2, k2), lhsStride, actual_kc, actual_mc);
310
311 gebp_kernel(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha);
312 }
313 }
314 }
315
316// matrix * selfadjoint product
317template <typename Scalar, typename Index,
318 int LhsStorageOrder, bool ConjugateLhs,
319 int RhsStorageOrder, bool ConjugateRhs>
320struct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,false,ConjugateLhs, RhsStorageOrder,true,ConjugateRhs,ColMajor>
321{
322
323 static EIGEN_DONT_INLINE void run(
324 Index rows, Index cols,
325 const Scalar* _lhs, Index lhsStride,
326 const Scalar* _rhs, Index rhsStride,
327 Scalar* res, Index resStride,
328 const Scalar& alpha);
329};
330
331template <typename Scalar, typename Index,
332 int LhsStorageOrder, bool ConjugateLhs,
333 int RhsStorageOrder, bool ConjugateRhs>
334EIGEN_DONT_INLINE void product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,false,ConjugateLhs, RhsStorageOrder,true,ConjugateRhs,ColMajor>::run(
335 Index rows, Index cols,
336 const Scalar* _lhs, Index lhsStride,
337 const Scalar* _rhs, Index rhsStride,
338 Scalar* res, Index resStride,
339 const Scalar& alpha)
340 {
341 Index size = cols;
342
343 const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
344
345 typedef gebp_traits<Scalar,Scalar> Traits;
346
347 Index kc = size; // cache block size along the K direction
348 Index mc = rows; // cache block size along the M direction
349 Index nc = cols; // cache block size along the N direction
350 computeProductBlockingSizes<Scalar,Scalar>(kc, mc, nc);
351 std::size_t sizeW = kc*Traits::WorkSpaceFactor;
352 std::size_t sizeB = sizeW + kc*cols;
353 ei_declare_aligned_stack_constructed_variable(Scalar, blockA, kc*mc, 0);
354 ei_declare_aligned_stack_constructed_variable(Scalar, allocatedBlockB, sizeB, 0);
355 Scalar* blockB = allocatedBlockB + sizeW;
356
357 gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
358 gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
359 symm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
360
361 for(Index k2=0; k2<size; k2+=kc)
362 {
363 const Index actual_kc = (std::min)(k2+kc,size)-k2;
364
365 pack_rhs(blockB, _rhs, rhsStride, actual_kc, cols, k2);
366
367 // => GEPP
368 for(Index i2=0; i2<rows; i2+=mc)
369 {
370 const Index actual_mc = (std::min)(i2+mc,rows)-i2;
371 pack_lhs(blockA, &lhs(i2, k2), lhsStride, actual_kc, actual_mc);
372
373 gebp_kernel(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha);
374 }
375 }
376 }
377
378} // end namespace internal
379
380/***************************************************************************
381* Wrapper to product_selfadjoint_matrix
382***************************************************************************/
383
384namespace internal {
385template<typename Lhs, int LhsMode, typename Rhs, int RhsMode>
386struct traits<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,RhsMode,false> >
387 : traits<ProductBase<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,RhsMode,false>, Lhs, Rhs> >
388{};
389}
390
391template<typename Lhs, int LhsMode, typename Rhs, int RhsMode>
392struct SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,RhsMode,false>
393 : public ProductBase<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,RhsMode,false>, Lhs, Rhs >
394{
395 EIGEN_PRODUCT_PUBLIC_INTERFACE(SelfadjointProductMatrix)
396
397 SelfadjointProductMatrix(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) {}
398
399 enum {
400 LhsIsUpper = (LhsMode&(Upper|Lower))==Upper,
401 LhsIsSelfAdjoint = (LhsMode&SelfAdjoint)==SelfAdjoint,
402 RhsIsUpper = (RhsMode&(Upper|Lower))==Upper,
403 RhsIsSelfAdjoint = (RhsMode&SelfAdjoint)==SelfAdjoint
404 };
405
406 template<typename Dest> void scaleAndAddTo(Dest& dst, const Scalar& alpha) const
407 {
408 eigen_assert(dst.rows()==m_lhs.rows() && dst.cols()==m_rhs.cols());
409
410 typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(m_lhs);
411 typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(m_rhs);
412
413 Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs)
414 * RhsBlasTraits::extractScalarFactor(m_rhs);
415
416 internal::product_selfadjoint_matrix<Scalar, Index,
417 EIGEN_LOGICAL_XOR(LhsIsUpper,
418 internal::traits<Lhs>::Flags &RowMajorBit) ? RowMajor : ColMajor, LhsIsSelfAdjoint,
419 NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(LhsIsUpper,bool(LhsBlasTraits::NeedToConjugate)),
420 EIGEN_LOGICAL_XOR(RhsIsUpper,
421 internal::traits<Rhs>::Flags &RowMajorBit) ? RowMajor : ColMajor, RhsIsSelfAdjoint,
422 NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(RhsIsUpper,bool(RhsBlasTraits::NeedToConjugate)),
423 internal::traits<Dest>::Flags&RowMajorBit ? RowMajor : ColMajor>
424 ::run(
425 lhs.rows(), rhs.cols(), // sizes
426 &lhs.coeffRef(0,0), lhs.outerStride(), // lhs info
427 &rhs.coeffRef(0,0), rhs.outerStride(), // rhs info
428 &dst.coeffRef(0,0), dst.outerStride(), // result info
429 actualAlpha // alpha
430 );
431 }
432};
433
434} // end namespace Eigen
435
436#endif // EIGEN_SELFADJOINT_MATRIX_MATRIX_H
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