Medial Code Documentation
Loading...
Searching...
No Matches
SelfadjointMatrixMatrix.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_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_dummy, 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 enum { PacketSize = packet_traits<Scalar>::size };
49 const_blas_data_mapper<Scalar,Index,StorageOrder> lhs(_lhs,lhsStride);
50 Index count = 0;
51 //Index peeled_mc3 = (rows/Pack1)*Pack1;
52
53 const Index peeled_mc3 = Pack1>=3*PacketSize ? (rows/(3*PacketSize))*(3*PacketSize) : 0;
54 const Index peeled_mc2 = Pack1>=2*PacketSize ? peeled_mc3+((rows-peeled_mc3)/(2*PacketSize))*(2*PacketSize) : 0;
55 const Index peeled_mc1 = Pack1>=1*PacketSize ? (rows/(1*PacketSize))*(1*PacketSize) : 0;
56
57 if(Pack1>=3*PacketSize)
58 for(Index i=0; i<peeled_mc3; i+=3*PacketSize)
59 pack<3*PacketSize>(blockA, lhs, cols, i, count);
60
61 if(Pack1>=2*PacketSize)
62 for(Index i=peeled_mc3; i<peeled_mc2; i+=2*PacketSize)
63 pack<2*PacketSize>(blockA, lhs, cols, i, count);
64
65 if(Pack1>=1*PacketSize)
66 for(Index i=peeled_mc2; i<peeled_mc1; i+=1*PacketSize)
67 pack<1*PacketSize>(blockA, lhs, cols, i, count);
68
69 // do the same with mr==1
70 for(Index i=peeled_mc1; i<rows; i++)
71 {
72 for(Index k=0; k<i; k++)
73 blockA[count++] = lhs(i, k); // normal
74
75 blockA[count++] = numext::real(lhs(i, i)); // real (diagonal)
76
77 for(Index k=i+1; k<cols; k++)
78 blockA[count++] = numext::conj(lhs(k, i)); // transposed
79 }
80 }
81};
82
83template<typename Scalar, typename Index, int nr, int StorageOrder>
84struct symm_pack_rhs
85{
86 enum { PacketSize = packet_traits<Scalar>::size };
87 void operator()(Scalar* blockB, const Scalar* _rhs, Index rhsStride, Index rows, Index cols, Index k2)
88 {
89 Index end_k = k2 + rows;
90 Index count = 0;
91 const_blas_data_mapper<Scalar,Index,StorageOrder> rhs(_rhs,rhsStride);
92 Index packet_cols8 = nr>=8 ? (cols/8) * 8 : 0;
93 Index packet_cols4 = nr>=4 ? (cols/4) * 4 : 0;
94
95 // first part: normal case
96 for(Index j2=0; j2<k2; j2+=nr)
97 {
98 for(Index k=k2; k<end_k; k++)
99 {
100 blockB[count+0] = rhs(k,j2+0);
101 blockB[count+1] = rhs(k,j2+1);
102 if (nr>=4)
103 {
104 blockB[count+2] = rhs(k,j2+2);
105 blockB[count+3] = rhs(k,j2+3);
106 }
107 if (nr>=8)
108 {
109 blockB[count+4] = rhs(k,j2+4);
110 blockB[count+5] = rhs(k,j2+5);
111 blockB[count+6] = rhs(k,j2+6);
112 blockB[count+7] = rhs(k,j2+7);
113 }
114 count += nr;
115 }
116 }
117
118 // second part: diagonal block
119 Index end8 = nr>=8 ? (std::min)(k2+rows,packet_cols8) : k2;
120 if(nr>=8)
121 {
122 for(Index j2=k2; j2<end8; j2+=8)
123 {
124 // again we can split vertically in three different parts (transpose, symmetric, normal)
125 // transpose
126 for(Index k=k2; k<j2; k++)
127 {
128 blockB[count+0] = numext::conj(rhs(j2+0,k));
129 blockB[count+1] = numext::conj(rhs(j2+1,k));
130 blockB[count+2] = numext::conj(rhs(j2+2,k));
131 blockB[count+3] = numext::conj(rhs(j2+3,k));
132 blockB[count+4] = numext::conj(rhs(j2+4,k));
133 blockB[count+5] = numext::conj(rhs(j2+5,k));
134 blockB[count+6] = numext::conj(rhs(j2+6,k));
135 blockB[count+7] = numext::conj(rhs(j2+7,k));
136 count += 8;
137 }
138 // symmetric
139 Index h = 0;
140 for(Index k=j2; k<j2+8; k++)
141 {
142 // normal
143 for (Index w=0 ; w<h; ++w)
144 blockB[count+w] = rhs(k,j2+w);
145
146 blockB[count+h] = numext::real(rhs(k,k));
147
148 // transpose
149 for (Index w=h+1 ; w<8; ++w)
150 blockB[count+w] = numext::conj(rhs(j2+w,k));
151 count += 8;
152 ++h;
153 }
154 // normal
155 for(Index k=j2+8; k<end_k; k++)
156 {
157 blockB[count+0] = rhs(k,j2+0);
158 blockB[count+1] = rhs(k,j2+1);
159 blockB[count+2] = rhs(k,j2+2);
160 blockB[count+3] = rhs(k,j2+3);
161 blockB[count+4] = rhs(k,j2+4);
162 blockB[count+5] = rhs(k,j2+5);
163 blockB[count+6] = rhs(k,j2+6);
164 blockB[count+7] = rhs(k,j2+7);
165 count += 8;
166 }
167 }
168 }
169 if(nr>=4)
170 {
171 for(Index j2=end8; j2<(std::min)(k2+rows,packet_cols4); j2+=4)
172 {
173 // again we can split vertically in three different parts (transpose, symmetric, normal)
174 // transpose
175 for(Index k=k2; k<j2; k++)
176 {
177 blockB[count+0] = numext::conj(rhs(j2+0,k));
178 blockB[count+1] = numext::conj(rhs(j2+1,k));
179 blockB[count+2] = numext::conj(rhs(j2+2,k));
180 blockB[count+3] = numext::conj(rhs(j2+3,k));
181 count += 4;
182 }
183 // symmetric
184 Index h = 0;
185 for(Index k=j2; k<j2+4; k++)
186 {
187 // normal
188 for (Index w=0 ; w<h; ++w)
189 blockB[count+w] = rhs(k,j2+w);
190
191 blockB[count+h] = numext::real(rhs(k,k));
192
193 // transpose
194 for (Index w=h+1 ; w<4; ++w)
195 blockB[count+w] = numext::conj(rhs(j2+w,k));
196 count += 4;
197 ++h;
198 }
199 // normal
200 for(Index k=j2+4; k<end_k; k++)
201 {
202 blockB[count+0] = rhs(k,j2+0);
203 blockB[count+1] = rhs(k,j2+1);
204 blockB[count+2] = rhs(k,j2+2);
205 blockB[count+3] = rhs(k,j2+3);
206 count += 4;
207 }
208 }
209 }
210
211 // third part: transposed
212 if(nr>=8)
213 {
214 for(Index j2=k2+rows; j2<packet_cols8; j2+=8)
215 {
216 for(Index k=k2; k<end_k; k++)
217 {
218 blockB[count+0] = numext::conj(rhs(j2+0,k));
219 blockB[count+1] = numext::conj(rhs(j2+1,k));
220 blockB[count+2] = numext::conj(rhs(j2+2,k));
221 blockB[count+3] = numext::conj(rhs(j2+3,k));
222 blockB[count+4] = numext::conj(rhs(j2+4,k));
223 blockB[count+5] = numext::conj(rhs(j2+5,k));
224 blockB[count+6] = numext::conj(rhs(j2+6,k));
225 blockB[count+7] = numext::conj(rhs(j2+7,k));
226 count += 8;
227 }
228 }
229 }
230 if(nr>=4)
231 {
232 for(Index j2=(std::max)(packet_cols8,k2+rows); j2<packet_cols4; j2+=4)
233 {
234 for(Index k=k2; k<end_k; k++)
235 {
236 blockB[count+0] = numext::conj(rhs(j2+0,k));
237 blockB[count+1] = numext::conj(rhs(j2+1,k));
238 blockB[count+2] = numext::conj(rhs(j2+2,k));
239 blockB[count+3] = numext::conj(rhs(j2+3,k));
240 count += 4;
241 }
242 }
243 }
244
245 // copy the remaining columns one at a time (=> the same with nr==1)
246 for(Index j2=packet_cols4; j2<cols; ++j2)
247 {
248 // transpose
249 Index half = (std::min)(end_k,j2);
250 for(Index k=k2; k<half; k++)
251 {
252 blockB[count] = numext::conj(rhs(j2,k));
253 count += 1;
254 }
255
256 if(half==j2 && half<k2+rows)
257 {
258 blockB[count] = numext::real(rhs(j2,j2));
259 count += 1;
260 }
261 else
262 half--;
263
264 // normal
265 for(Index k=half+1; k<k2+rows; k++)
266 {
267 blockB[count] = rhs(k,j2);
268 count += 1;
269 }
270 }
271 }
272};
273
274/* Optimized selfadjoint matrix * matrix (_SYMM) product built on top of
275 * the general matrix matrix product.
276 */
277template <typename Scalar, typename Index,
278 int LhsStorageOrder, bool LhsSelfAdjoint, bool ConjugateLhs,
279 int RhsStorageOrder, bool RhsSelfAdjoint, bool ConjugateRhs,
280 int ResStorageOrder>
281struct product_selfadjoint_matrix;
282
283template <typename Scalar, typename Index,
284 int LhsStorageOrder, bool LhsSelfAdjoint, bool ConjugateLhs,
285 int RhsStorageOrder, bool RhsSelfAdjoint, bool ConjugateRhs>
286struct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,LhsSelfAdjoint,ConjugateLhs, RhsStorageOrder,RhsSelfAdjoint,ConjugateRhs,RowMajor>
287{
288
289 static EIGEN_STRONG_INLINE void run(
290 Index rows, Index cols,
291 const Scalar* lhs, Index lhsStride,
292 const Scalar* rhs, Index rhsStride,
293 Scalar* res, Index resStride,
294 const Scalar& alpha)
295 {
296 product_selfadjoint_matrix<Scalar, Index,
297 EIGEN_LOGICAL_XOR(RhsSelfAdjoint,RhsStorageOrder==RowMajor) ? ColMajor : RowMajor,
298 RhsSelfAdjoint, NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(RhsSelfAdjoint,ConjugateRhs),
299 EIGEN_LOGICAL_XOR(LhsSelfAdjoint,LhsStorageOrder==RowMajor) ? ColMajor : RowMajor,
300 LhsSelfAdjoint, NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(LhsSelfAdjoint,ConjugateLhs),
301 ColMajor>
302 ::run(cols, rows, rhs, rhsStride, lhs, lhsStride, res, resStride, alpha);
303 }
304};
305
306template <typename Scalar, typename Index,
307 int LhsStorageOrder, bool ConjugateLhs,
308 int RhsStorageOrder, bool ConjugateRhs>
309struct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,true,ConjugateLhs, RhsStorageOrder,false,ConjugateRhs,ColMajor>
310{
311
312 static EIGEN_DONT_INLINE void run(
313 Index rows, Index cols,
314 const Scalar* _lhs, Index lhsStride,
315 const Scalar* _rhs, Index rhsStride,
316 Scalar* res, Index resStride,
317 const Scalar& alpha);
318};
319
320template <typename Scalar, typename Index,
321 int LhsStorageOrder, bool ConjugateLhs,
322 int RhsStorageOrder, bool ConjugateRhs>
323EIGEN_DONT_INLINE void product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,true,ConjugateLhs, RhsStorageOrder,false,ConjugateRhs,ColMajor>::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 Index size = rows;
331
332 typedef gebp_traits<Scalar,Scalar> Traits;
333
334 typedef const_blas_data_mapper<Scalar, Index, LhsStorageOrder> LhsMapper;
335 typedef const_blas_data_mapper<Scalar, Index, (LhsStorageOrder == RowMajor) ? ColMajor : RowMajor> LhsTransposeMapper;
336 typedef const_blas_data_mapper<Scalar, Index, RhsStorageOrder> RhsMapper;
337 typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor> ResMapper;
338 LhsMapper lhs(_lhs,lhsStride);
339 LhsTransposeMapper lhs_transpose(_lhs,lhsStride);
340 RhsMapper rhs(_rhs,rhsStride);
341 ResMapper res(_res, resStride);
342
343 Index kc = size; // cache block size along the K direction
344 Index mc = rows; // cache block size along the M direction
345 Index nc = cols; // cache block size along the N direction
346 computeProductBlockingSizes<Scalar,Scalar>(kc, mc, nc, 1);
347 // kc must smaller than mc
348 kc = (std::min)(kc,mc);
349
350 std::size_t sizeB = kc*cols;
351 ei_declare_aligned_stack_constructed_variable(Scalar, blockA, kc*mc, 0);
352 ei_declare_aligned_stack_constructed_variable(Scalar, allocatedBlockB, sizeB, 0);
353 Scalar* blockB = allocatedBlockB;
354
355 gebp_kernel<Scalar, Scalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
356 symm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
357 gemm_pack_rhs<Scalar, Index, RhsMapper, Traits::nr,RhsStorageOrder> pack_rhs;
358 gemm_pack_lhs<Scalar, Index, LhsTransposeMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder==RowMajor?ColMajor:RowMajor, true> pack_lhs_transposed;
359
360 for(Index k2=0; k2<size; k2+=kc)
361 {
362 const Index actual_kc = (std::min)(k2+kc,size)-k2;
363
364 // we have selected one row panel of rhs and one column panel of lhs
365 // pack rhs's panel into a sequential chunk of memory
366 // and expand each coeff to a constant packet for further reuse
367 pack_rhs(blockB, rhs.getSubMapper(k2,0), actual_kc, cols);
368
369 // the select lhs's panel has to be split in three different parts:
370 // 1 - the transposed panel above the diagonal block => transposed packed copy
371 // 2 - the diagonal block => special packed copy
372 // 3 - the panel below the diagonal block => generic packed copy
373 for(Index i2=0; i2<k2; i2+=mc)
374 {
375 const Index actual_mc = (std::min)(i2+mc,k2)-i2;
376 // transposed packed copy
377 pack_lhs_transposed(blockA, lhs_transpose.getSubMapper(i2, k2), actual_kc, actual_mc);
378
379 gebp_kernel(res.getSubMapper(i2, 0), blockA, blockB, actual_mc, actual_kc, cols, alpha);
380 }
381 // the block diagonal
382 {
383 const Index actual_mc = (std::min)(k2+kc,size)-k2;
384 // symmetric packed copy
385 pack_lhs(blockA, &lhs(k2,k2), lhsStride, actual_kc, actual_mc);
386
387 gebp_kernel(res.getSubMapper(k2, 0), blockA, blockB, actual_mc, actual_kc, cols, alpha);
388 }
389
390 for(Index i2=k2+kc; i2<size; i2+=mc)
391 {
392 const Index actual_mc = (std::min)(i2+mc,size)-i2;
393 gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder,false>()
394 (blockA, lhs.getSubMapper(i2, k2), actual_kc, actual_mc);
395
396 gebp_kernel(res.getSubMapper(i2, 0), blockA, blockB, actual_mc, actual_kc, cols, alpha);
397 }
398 }
399 }
400
401// matrix * selfadjoint product
402template <typename Scalar, typename Index,
403 int LhsStorageOrder, bool ConjugateLhs,
404 int RhsStorageOrder, bool ConjugateRhs>
405struct product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,false,ConjugateLhs, RhsStorageOrder,true,ConjugateRhs,ColMajor>
406{
407
408 static EIGEN_DONT_INLINE void run(
409 Index rows, Index cols,
410 const Scalar* _lhs, Index lhsStride,
411 const Scalar* _rhs, Index rhsStride,
412 Scalar* res, Index resStride,
413 const Scalar& alpha);
414};
415
416template <typename Scalar, typename Index,
417 int LhsStorageOrder, bool ConjugateLhs,
418 int RhsStorageOrder, bool ConjugateRhs>
419EIGEN_DONT_INLINE void product_selfadjoint_matrix<Scalar,Index,LhsStorageOrder,false,ConjugateLhs, RhsStorageOrder,true,ConjugateRhs,ColMajor>::run(
420 Index rows, Index cols,
421 const Scalar* _lhs, Index lhsStride,
422 const Scalar* _rhs, Index rhsStride,
423 Scalar* _res, Index resStride,
424 const Scalar& alpha)
425 {
426 Index size = cols;
427
428 typedef gebp_traits<Scalar,Scalar> Traits;
429
430 typedef const_blas_data_mapper<Scalar, Index, LhsStorageOrder> LhsMapper;
431 typedef blas_data_mapper<typename Traits::ResScalar, Index, ColMajor> ResMapper;
432 LhsMapper lhs(_lhs,lhsStride);
433 ResMapper res(_res,resStride);
434
435 Index kc = size; // cache block size along the K direction
436 Index mc = rows; // cache block size along the M direction
437 Index nc = cols; // cache block size along the N direction
438 computeProductBlockingSizes<Scalar,Scalar>(kc, mc, nc, 1);
439 std::size_t sizeB = kc*cols;
440 ei_declare_aligned_stack_constructed_variable(Scalar, blockA, kc*mc, 0);
441 ei_declare_aligned_stack_constructed_variable(Scalar, allocatedBlockB, sizeB, 0);
442 Scalar* blockB = allocatedBlockB;
443
444 gebp_kernel<Scalar, Scalar, Index, ResMapper, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
445 gemm_pack_lhs<Scalar, Index, LhsMapper, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
446 symm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
447
448 for(Index k2=0; k2<size; k2+=kc)
449 {
450 const Index actual_kc = (std::min)(k2+kc,size)-k2;
451
452 pack_rhs(blockB, _rhs, rhsStride, actual_kc, cols, k2);
453
454 // => GEPP
455 for(Index i2=0; i2<rows; i2+=mc)
456 {
457 const Index actual_mc = (std::min)(i2+mc,rows)-i2;
458 pack_lhs(blockA, lhs.getSubMapper(i2, k2), actual_kc, actual_mc);
459
460 gebp_kernel(res.getSubMapper(i2, 0), blockA, blockB, actual_mc, actual_kc, cols, alpha);
461 }
462 }
463 }
464
465} // end namespace internal
466
467/***************************************************************************
468* Wrapper to product_selfadjoint_matrix
469***************************************************************************/
470
471namespace internal {
472
473template<typename Lhs, int LhsMode, typename Rhs, int RhsMode>
474struct selfadjoint_product_impl<Lhs,LhsMode,false,Rhs,RhsMode,false>
475{
476 typedef typename Product<Lhs,Rhs>::Scalar Scalar;
477
478 typedef internal::blas_traits<Lhs> LhsBlasTraits;
479 typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
480 typedef internal::blas_traits<Rhs> RhsBlasTraits;
481 typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
482
483 enum {
484 LhsIsUpper = (LhsMode&(Upper|Lower))==Upper,
485 LhsIsSelfAdjoint = (LhsMode&SelfAdjoint)==SelfAdjoint,
486 RhsIsUpper = (RhsMode&(Upper|Lower))==Upper,
487 RhsIsSelfAdjoint = (RhsMode&SelfAdjoint)==SelfAdjoint
488 };
489
490 template<typename Dest>
491 static void run(Dest &dst, const Lhs &a_lhs, const Rhs &a_rhs, const Scalar& alpha)
492 {
493 eigen_assert(dst.rows()==a_lhs.rows() && dst.cols()==a_rhs.cols());
494
495 typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(a_lhs);
496 typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(a_rhs);
497
498 Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(a_lhs)
499 * RhsBlasTraits::extractScalarFactor(a_rhs);
500
501 internal::product_selfadjoint_matrix<Scalar, Index,
502 EIGEN_LOGICAL_XOR(LhsIsUpper,internal::traits<Lhs>::Flags &RowMajorBit) ? RowMajor : ColMajor, LhsIsSelfAdjoint,
503 NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(LhsIsUpper,bool(LhsBlasTraits::NeedToConjugate)),
504 EIGEN_LOGICAL_XOR(RhsIsUpper,internal::traits<Rhs>::Flags &RowMajorBit) ? RowMajor : ColMajor, RhsIsSelfAdjoint,
505 NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(RhsIsUpper,bool(RhsBlasTraits::NeedToConjugate)),
506 internal::traits<Dest>::Flags&RowMajorBit ? RowMajor : ColMajor>
507 ::run(
508 lhs.rows(), rhs.cols(), // sizes
509 &lhs.coeffRef(0,0), lhs.outerStride(), // lhs info
510 &rhs.coeffRef(0,0), rhs.outerStride(), // rhs info
511 &dst.coeffRef(0,0), dst.outerStride(), // result info
512 actualAlpha // alpha
513 );
514 }
515};
516
517} // end namespace internal
518
519} // end namespace Eigen
520
521#endif // EIGEN_SELFADJOINT_MATRIX_MATRIX_H
Eigen::Product
Expression of the product of two arbitrary matrices or vectors.
Definition Product.h:111
Eigen::Solve
Pseudo expression representing a solving operation.
Definition Solve.h:63
Eigen::internal::const_blas_data_mapper
Definition BlasUtil.h:243
Eigen::SelfAdjoint
@ SelfAdjoint
Used in BandMatrix and SelfAdjointView to indicate that the matrix is self-adjoint.
Definition Constants.h:220
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::NumTraits
Holds information about the various numeric (i.e.
Definition NumTraits.h:108
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_selfadjoint_matrix
Definition SelfadjointMatrixMatrix.h:281
Eigen::internal::selfadjoint_product_impl
Definition ProductEvaluators.h:691
Eigen::internal::symm_pack_lhs
Definition SelfadjointMatrixMatrix.h:20
Eigen::internal::symm_pack_rhs
Definition SelfadjointMatrixMatrix.h:85
Eigen::internal::traits
Definition ForwardDeclarations.h:17
Eigen::internal::true_type
Definition Meta.h:30
Generated on Mon Sep 15 2025 12:11:54 for Medial Code Documentation by doxygen 1.9.8