compbio
GeneralMatrixMatrix.h
1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008-2009 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_GENERAL_MATRIX_MATRIX_H
11 #define EIGEN_GENERAL_MATRIX_MATRIX_H
12 
13 namespace Eigen {
14 
15 namespace internal {
16 
17 template<typename _LhsScalar, typename _RhsScalar> class level3_blocking;
18 
19 /* Specialization for a row-major destination matrix => simple transposition of the product */
20 template<
21  typename Index,
22  typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
23  typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs>
24 struct general_matrix_matrix_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,RowMajor>
25 {
27 
29  static EIGEN_STRONG_INLINE void run(
30  Index rows, Index cols, Index depth,
31  const LhsScalar* lhs, Index lhsStride,
32  const RhsScalar* rhs, Index rhsStride,
33  ResScalar* res, Index resStride,
34  ResScalar alpha,
36  GemmParallelInfo<Index>* info = 0)
37  {
38  // transpose the product such that the result is column major
40  RhsScalar, RhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateRhs,
41  LhsScalar, LhsStorageOrder==RowMajor ? ColMajor : RowMajor, ConjugateLhs,
42  ColMajor>
43  ::run(cols,rows,depth,rhs,rhsStride,lhs,lhsStride,res,resStride,alpha,blocking,info);
44  }
45 };
46 
47 /* Specialization for a col-major destination matrix
48  * => Blocking algorithm following Goto's paper */
49 template<
50  typename Index,
51  typename LhsScalar, int LhsStorageOrder, bool ConjugateLhs,
52  typename RhsScalar, int RhsStorageOrder, bool ConjugateRhs>
53 struct general_matrix_matrix_product<Index,LhsScalar,LhsStorageOrder,ConjugateLhs,RhsScalar,RhsStorageOrder,ConjugateRhs,ColMajor>
54 {
55 
57 
59 static void run(Index rows, Index cols, Index depth,
60  const LhsScalar* _lhs, Index lhsStride,
61  const RhsScalar* _rhs, Index rhsStride,
62  ResScalar* _res, Index resStride,
63  ResScalar alpha,
65  GemmParallelInfo<Index>* info = 0)
66 {
70  LhsMapper lhs(_lhs,lhsStride);
71  RhsMapper rhs(_rhs,rhsStride);
72  ResMapper res(_res, resStride);
73 
74  Index kc = blocking.kc(); // cache block size along the K direction
75  Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction
76  Index nc = (std::min)(cols,blocking.nc()); // cache block size along the N direction
77 
81 
82 #ifdef EIGEN_HAS_OPENMP
83  if(info)
84  {
85  // this is the parallel version!
86  Index tid = omp_get_thread_num();
87  Index threads = omp_get_num_threads();
88 
89  LhsScalar* blockA = blocking.blockA();
90  eigen_internal_assert(blockA!=0);
91 
92  std::size_t sizeB = kc*nc;
93  ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, 0);
94 
95  // For each horizontal panel of the rhs, and corresponding vertical panel of the lhs...
96  for(Index k=0; k<depth; k+=kc)
97  {
98  const Index actual_kc = (std::min)(k+kc,depth)-k; // => rows of B', and cols of the A'
99 
100  // In order to reduce the chance that a thread has to wait for the other,
101  // let's start by packing B'.
102  pack_rhs(blockB, rhs.getSubMapper(k,0), actual_kc, nc);
103 
104  // Pack A_k to A' in a parallel fashion:
105  // each thread packs the sub block A_k,i to A'_i where i is the thread id.
106 
107  // However, before copying to A'_i, we have to make sure that no other thread is still using it,
108  // i.e., we test that info[tid].users equals 0.
109  // Then, we set info[tid].users to the number of threads to mark that all other threads are going to use it.
110  while(info[tid].users!=0) {}
111  info[tid].users += threads;
112 
113  pack_lhs(blockA+info[tid].lhs_start*actual_kc, lhs.getSubMapper(info[tid].lhs_start,k), actual_kc, info[tid].lhs_length);
114 
115  // Notify the other threads that the part A'_i is ready to go.
116  info[tid].sync = k;
117 
118  // Computes C_i += A' * B' per A'_i
119  for(Index shift=0; shift<threads; ++shift)
120  {
121  Index i = (tid+shift)%threads;
122 
123  // At this point we have to make sure that A'_i has been updated by the thread i,
124  // we use testAndSetOrdered to mimic a volatile access.
125  // However, no need to wait for the B' part which has been updated by the current thread!
126  if (shift>0) {
127  while(info[i].sync!=k) {
128  }
129  }
130 
131  gebp(res.getSubMapper(info[i].lhs_start, 0), blockA+info[i].lhs_start*actual_kc, blockB, info[i].lhs_length, actual_kc, nc, alpha);
132  }
133 
134  // Then keep going as usual with the remaining B'
135  for(Index j=nc; j<cols; j+=nc)
136  {
137  const Index actual_nc = (std::min)(j+nc,cols)-j;
138 
139  // pack B_k,j to B'
140  pack_rhs(blockB, rhs.getSubMapper(k,j), actual_kc, actual_nc);
141 
142  // C_j += A' * B'
143  gebp(res.getSubMapper(0, j), blockA, blockB, rows, actual_kc, actual_nc, alpha);
144  }
145 
146  // Release all the sub blocks A'_i of A' for the current thread,
147  // i.e., we simply decrement the number of users by 1
148  for(Index i=0; i<threads; ++i)
149  #pragma omp atomic
150  info[i].users -= 1;
151  }
152  }
153  else
154 #endif // EIGEN_HAS_OPENMP
155  {
156  EIGEN_UNUSED_VARIABLE(info);
157 
158  // this is the sequential version!
159  std::size_t sizeA = kc*mc;
160  std::size_t sizeB = kc*nc;
161 
162  ei_declare_aligned_stack_constructed_variable(LhsScalar, blockA, sizeA, blocking.blockA());
163  ei_declare_aligned_stack_constructed_variable(RhsScalar, blockB, sizeB, blocking.blockB());
164 
165  const bool pack_rhs_once = mc!=rows && kc==depth && nc==cols;
166 
167  // For each horizontal panel of the rhs, and corresponding panel of the lhs...
168  for(Index i2=0; i2<rows; i2+=mc)
169  {
170  const Index actual_mc = (std::min)(i2+mc,rows)-i2;
171 
172  for(Index k2=0; k2<depth; k2+=kc)
173  {
174  const Index actual_kc = (std::min)(k2+kc,depth)-k2;
175 
176  // OK, here we have selected one horizontal panel of rhs and one vertical panel of lhs.
177  // => Pack lhs's panel into a sequential chunk of memory (L2/L3 caching)
178  // Note that this panel will be read as many times as the number of blocks in the rhs's
179  // horizontal panel which is, in practice, a very low number.
180  pack_lhs(blockA, lhs.getSubMapper(i2,k2), actual_kc, actual_mc);
181 
182  // For each kc x nc block of the rhs's horizontal panel...
183  for(Index j2=0; j2<cols; j2+=nc)
184  {
185  const Index actual_nc = (std::min)(j2+nc,cols)-j2;
186 
187  // We pack the rhs's block into a sequential chunk of memory (L2 caching)
188  // Note that this block will be read a very high number of times, which is equal to the number of
189  // micro horizontal panel of the large rhs's panel (e.g., rows/12 times).
190  if((!pack_rhs_once) || i2==0)
191  pack_rhs(blockB, rhs.getSubMapper(k2,j2), actual_kc, actual_nc);
192 
193  // Everything is packed, we can now call the panel * block kernel:
194  gebp(res.getSubMapper(i2, j2), blockA, blockB, actual_mc, actual_kc, actual_nc, alpha);
195  }
196  }
197  }
198  }
199 }
200 
201 };
202 
203 /*********************************************************************************
204 * Specialization of generic_product_impl for "large" GEMM, i.e.,
205 * implementation of the high level wrapper to general_matrix_matrix_product
206 **********************************************************************************/
207 
208 template<typename Scalar, typename Index, typename Gemm, typename Lhs, typename Rhs, typename Dest, typename BlockingType>
210 {
211  gemm_functor(const Lhs& lhs, const Rhs& rhs, Dest& dest, const Scalar& actualAlpha, BlockingType& blocking)
212  : m_lhs(lhs), m_rhs(rhs), m_dest(dest), m_actualAlpha(actualAlpha), m_blocking(blocking)
213  {}
214 
215  void initParallelSession(Index num_threads) const
216  {
217  m_blocking.initParallel(m_lhs.rows(), m_rhs.cols(), m_lhs.cols(), num_threads);
218  m_blocking.allocateA();
219  }
220 
221  void operator() (Index row, Index rows, Index col=0, Index cols=-1, GemmParallelInfo<Index>* info=0) const
222  {
223  if(cols==-1)
224  cols = m_rhs.cols();
225 
226  Gemm::run(rows, cols, m_lhs.cols(),
227  &m_lhs.coeffRef(row,0), m_lhs.outerStride(),
228  &m_rhs.coeffRef(0,col), m_rhs.outerStride(),
229  (Scalar*)&(m_dest.coeffRef(row,col)), m_dest.outerStride(),
230  m_actualAlpha, m_blocking, info);
231  }
232 
233  typedef typename Gemm::Traits Traits;
234 
235  protected:
236  const Lhs& m_lhs;
237  const Rhs& m_rhs;
238  Dest& m_dest;
239  Scalar m_actualAlpha;
240  BlockingType& m_blocking;
241 };
242 
243 template<int StorageOrder, typename LhsScalar, typename RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor=1,
244 bool FiniteAtCompileTime = MaxRows!=Dynamic && MaxCols!=Dynamic && MaxDepth != Dynamic> class gemm_blocking_space;
245 
246 template<typename _LhsScalar, typename _RhsScalar>
247 class level3_blocking
248 {
249  typedef _LhsScalar LhsScalar;
250  typedef _RhsScalar RhsScalar;
251 
252  protected:
253  LhsScalar* m_blockA;
254  RhsScalar* m_blockB;
255 
256  Index m_mc;
257  Index m_nc;
258  Index m_kc;
259 
260  public:
261 
263  : m_blockA(0), m_blockB(0), m_mc(0), m_nc(0), m_kc(0)
264  {}
265 
266  inline Index mc() const { return m_mc; }
267  inline Index nc() const { return m_nc; }
268  inline Index kc() const { return m_kc; }
269 
270  inline LhsScalar* blockA() { return m_blockA; }
271  inline RhsScalar* blockB() { return m_blockB; }
272 };
273 
274 template<int StorageOrder, typename _LhsScalar, typename _RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor>
275 class gemm_blocking_space<StorageOrder,_LhsScalar,_RhsScalar,MaxRows, MaxCols, MaxDepth, KcFactor, true /* == FiniteAtCompileTime */>
276  : public level3_blocking<
277  typename conditional<StorageOrder==RowMajor,_RhsScalar,_LhsScalar>::type,
278  typename conditional<StorageOrder==RowMajor,_LhsScalar,_RhsScalar>::type>
279 {
280  enum {
281  Transpose = StorageOrder==RowMajor,
282  ActualRows = Transpose ? MaxCols : MaxRows,
283  ActualCols = Transpose ? MaxRows : MaxCols
284  };
285  typedef typename conditional<Transpose,_RhsScalar,_LhsScalar>::type LhsScalar;
286  typedef typename conditional<Transpose,_LhsScalar,_RhsScalar>::type RhsScalar;
288  enum {
289  SizeA = ActualRows * MaxDepth,
290  SizeB = ActualCols * MaxDepth
291  };
292 
293 #if EIGEN_MAX_STATIC_ALIGN_BYTES >= EIGEN_DEFAULT_ALIGN_BYTES
294  EIGEN_ALIGN_MAX LhsScalar m_staticA[SizeA];
295  EIGEN_ALIGN_MAX RhsScalar m_staticB[SizeB];
296 #else
297  EIGEN_ALIGN_MAX char m_staticA[SizeA * sizeof(LhsScalar) + EIGEN_DEFAULT_ALIGN_BYTES-1];
298  EIGEN_ALIGN_MAX char m_staticB[SizeB * sizeof(RhsScalar) + EIGEN_DEFAULT_ALIGN_BYTES-1];
299 #endif
300 
301  public:
302 
303  gemm_blocking_space(Index /*rows*/, Index /*cols*/, Index /*depth*/, Index /*num_threads*/, bool /*full_rows = false*/)
304  {
305  this->m_mc = ActualRows;
306  this->m_nc = ActualCols;
307  this->m_kc = MaxDepth;
308 #if EIGEN_MAX_STATIC_ALIGN_BYTES >= EIGEN_DEFAULT_ALIGN_BYTES
309  this->m_blockA = m_staticA;
310  this->m_blockB = m_staticB;
311 #else
312  this->m_blockA = reinterpret_cast<LhsScalar*>((internal::UIntPtr(m_staticA) + (EIGEN_DEFAULT_ALIGN_BYTES-1)) & ~std::size_t(EIGEN_DEFAULT_ALIGN_BYTES-1));
313  this->m_blockB = reinterpret_cast<RhsScalar*>((internal::UIntPtr(m_staticB) + (EIGEN_DEFAULT_ALIGN_BYTES-1)) & ~std::size_t(EIGEN_DEFAULT_ALIGN_BYTES-1));
314 #endif
315  }
316 
318  {}
319 
320  inline void allocateA() {}
321  inline void allocateB() {}
322  inline void allocateAll() {}
323 };
324 
325 template<int StorageOrder, typename _LhsScalar, typename _RhsScalar, int MaxRows, int MaxCols, int MaxDepth, int KcFactor>
326 class gemm_blocking_space<StorageOrder,_LhsScalar,_RhsScalar,MaxRows, MaxCols, MaxDepth, KcFactor, false>
327  : public level3_blocking<
328  typename conditional<StorageOrder==RowMajor,_RhsScalar,_LhsScalar>::type,
329  typename conditional<StorageOrder==RowMajor,_LhsScalar,_RhsScalar>::type>
330 {
331  enum {
332  Transpose = StorageOrder==RowMajor
333  };
334  typedef typename conditional<Transpose,_RhsScalar,_LhsScalar>::type LhsScalar;
335  typedef typename conditional<Transpose,_LhsScalar,_RhsScalar>::type RhsScalar;
337 
338  Index m_sizeA;
339  Index m_sizeB;
340 
341  public:
342 
343  gemm_blocking_space(Index rows, Index cols, Index depth, Index num_threads, bool l3_blocking)
344  {
345  this->m_mc = Transpose ? cols : rows;
346  this->m_nc = Transpose ? rows : cols;
347  this->m_kc = depth;
348 
349  if(l3_blocking)
350  {
351  computeProductBlockingSizes<LhsScalar,RhsScalar,KcFactor>(this->m_kc, this->m_mc, this->m_nc, num_threads);
352  }
353  else // no l3 blocking
354  {
355  Index n = this->m_nc;
356  computeProductBlockingSizes<LhsScalar,RhsScalar,KcFactor>(this->m_kc, this->m_mc, n, num_threads);
357  }
358 
359  m_sizeA = this->m_mc * this->m_kc;
360  m_sizeB = this->m_kc * this->m_nc;
361  }
362 
363  void initParallel(Index rows, Index cols, Index depth, Index num_threads)
364  {
365  this->m_mc = Transpose ? cols : rows;
366  this->m_nc = Transpose ? rows : cols;
367  this->m_kc = depth;
368 
369  eigen_internal_assert(this->m_blockA==0 && this->m_blockB==0);
370  Index m = this->m_mc;
371  computeProductBlockingSizes<LhsScalar,RhsScalar,KcFactor>(this->m_kc, m, this->m_nc, num_threads);
372  m_sizeA = this->m_mc * this->m_kc;
373  m_sizeB = this->m_kc * this->m_nc;
374  }
375 
376  void allocateA()
377  {
378  if(this->m_blockA==0)
379  this->m_blockA = aligned_new<LhsScalar>(m_sizeA);
380  }
381 
382  void allocateB()
383  {
384  if(this->m_blockB==0)
385  this->m_blockB = aligned_new<RhsScalar>(m_sizeB);
386  }
387 
388  void allocateAll()
389  {
390  allocateA();
391  allocateB();
392  }
393 
395  {
396  aligned_delete(this->m_blockA, m_sizeA);
397  aligned_delete(this->m_blockB, m_sizeB);
398  }
399 };
400 
401 } // end namespace internal
402 
403 namespace internal {
404 
405 template<typename Lhs, typename Rhs>
406 struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,GemmProduct>
407  : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,GemmProduct> >
408 {
409  typedef typename Product<Lhs,Rhs>::Scalar Scalar;
410  typedef typename Lhs::Scalar LhsScalar;
411  typedef typename Rhs::Scalar RhsScalar;
412 
416 
420 
421  enum {
422  MaxDepthAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(Lhs::MaxColsAtCompileTime,Rhs::MaxRowsAtCompileTime)
423  };
424 
426 
427  template<typename Dst>
428  static void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
429  {
430  if((rhs.rows()+dst.rows()+dst.cols())<20 && rhs.rows()>0)
431  lazyproduct::evalTo(dst, lhs, rhs);
432  else
433  {
434  dst.setZero();
435  scaleAndAddTo(dst, lhs, rhs, Scalar(1));
436  }
437  }
438 
439  template<typename Dst>
440  static void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
441  {
442  if((rhs.rows()+dst.rows()+dst.cols())<20 && rhs.rows()>0)
443  lazyproduct::addTo(dst, lhs, rhs);
444  else
445  scaleAndAddTo(dst,lhs, rhs, Scalar(1));
446  }
447 
448  template<typename Dst>
449  static void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
450  {
451  if((rhs.rows()+dst.rows()+dst.cols())<20 && rhs.rows()>0)
452  lazyproduct::subTo(dst, lhs, rhs);
453  else
454  scaleAndAddTo(dst, lhs, rhs, Scalar(-1));
455  }
456 
457  template<typename Dest>
458  static void scaleAndAddTo(Dest& dst, const Lhs& a_lhs, const Rhs& a_rhs, const Scalar& alpha)
459  {
460  eigen_assert(dst.rows()==a_lhs.rows() && dst.cols()==a_rhs.cols());
461  if(a_lhs.cols()==0 || a_lhs.rows()==0 || a_rhs.cols()==0)
462  return;
463 
464  typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(a_lhs);
465  typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(a_rhs);
466 
467  Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(a_lhs)
468  * RhsBlasTraits::extractScalarFactor(a_rhs);
469 
470  typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,LhsScalar,RhsScalar,
471  Dest::MaxRowsAtCompileTime,Dest::MaxColsAtCompileTime,MaxDepthAtCompileTime> BlockingType;
472 
473  typedef internal::gemm_functor<
474  Scalar, Index,
476  Index,
477  LhsScalar, (ActualLhsTypeCleaned::Flags&RowMajorBit) ? RowMajor : ColMajor, bool(LhsBlasTraits::NeedToConjugate),
478  RhsScalar, (ActualRhsTypeCleaned::Flags&RowMajorBit) ? RowMajor : ColMajor, bool(RhsBlasTraits::NeedToConjugate),
479  (Dest::Flags&RowMajorBit) ? RowMajor : ColMajor>,
480  ActualLhsTypeCleaned, ActualRhsTypeCleaned, Dest, BlockingType> GemmFunctor;
481 
482  BlockingType blocking(dst.rows(), dst.cols(), lhs.cols(), 1, true);
483  internal::parallelize_gemm<(Dest::MaxRowsAtCompileTime>32 || Dest::MaxRowsAtCompileTime==Dynamic)>
484  (GemmFunctor(lhs, rhs, dst, actualAlpha, blocking), a_lhs.rows(), a_rhs.cols(), a_lhs.cols(), Dest::Flags&RowMajorBit);
485  }
486 };
487 
488 } // end namespace internal
489 
490 } // end namespace Eigen
491 
492 #endif // EIGEN_GENERAL_MATRIX_MATRIX_H
void initParallel()
Must be call first when calling Eigen from multiple threads.
Definition: Parallelizer.h:48
Definition: BlasUtil.h:269
Storage order is column major (see TopicStorageOrders).
Definition: Constants.h:320
Definition: BlasUtil.h:28
Expression of the product of two arbitrary matrices or vectors.
Definition: Product.h:71
Definition: GeneralBlockPanelKernel.h:19
Expression of the transpose of a matrix.
Definition: Transpose.h:52
Namespace containing all symbols from the Eigen library.
Definition: bench_norm.cpp:85
Definition: Half.h:529
const unsigned int RowMajorBit
for a matrix, this means that the storage order is row-major.
Definition: Constants.h:61
Definition: Constants.h:512
Definition: ProductEvaluators.h:343
Definition: GeneralMatrixMatrix.h:17
Definition: ProductEvaluators.h:86
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:33
Definition: BlasUtil.h:256
Definition: GeneralBlockPanelKernel.h:859
Definition: BlasUtil.h:192
Definition: BandTriangularSolver.h:13
Storage order is row major (see TopicStorageOrders).
Definition: Constants.h:322
Determines whether the given binary operation of two numeric types is allowed and what the scalar ret...
Definition: XprHelper.h:757
const int Dynamic
This value means that a positive quantity (e.g., a size) is not known at compile-time, and that instead the value is stored in some runtime variable.
Definition: Constants.h:21
Generic expression where a coefficient-wise unary operator is applied to an expression.
Definition: CwiseUnaryOp.h:55
Definition: GeneralMatrixMatrix.h:209
Definition: GeneralMatrixMatrix.h:244
Definition: Parallelizer.h:74
Definition: BlasUtil.h:25