TriangularMatrixMatrix.h
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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 
13 namespace Eigen {
14 
15 namespace 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  */
44 template <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>
50 
51 template <typename Scalar, typename Index,
52  int Mode, bool LhsIsTriangular,
53  int LhsStorageOrder, bool ConjugateLhs,
54  int RhsStorageOrder, bool ConjugateRhs, int Version>
55 struct 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  {
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)
79 template <typename Scalar, typename Index, int Mode,
80  int LhsStorageOrder, bool ConjugateLhs,
81  int RhsStorageOrder, bool ConjugateRhs, int Version>
82 struct product_triangular_matrix_matrix<Scalar,Index,Mode,true,
83  LhsStorageOrder,ConjugateLhs,
84  RhsStorageOrder,ConjugateRhs,ColMajor,Version>
85 {
86 
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 
102 template <typename Scalar, typename Index, int Mode,
103  int LhsStorageOrder, bool ConjugateLhs,
104  int RhsStorageOrder, bool ConjugateRhs, int Version>
105 EIGEN_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 
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 
135  triangularBuffer.setZero();
136  if((Mode&ZeroDiag)==ZeroDiag)
137  triangularBuffer.diagonal().setZero();
138  else
139  triangularBuffer.diagonal().setOnes();
140 
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;
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)
221 template <typename Scalar, typename Index, int Mode,
222  int LhsStorageOrder, bool ConjugateLhs,
223  int RhsStorageOrder, bool ConjugateRhs, int Version>
224 struct product_triangular_matrix_matrix<Scalar,Index,Mode,false,
225  LhsStorageOrder,ConjugateLhs,
226  RhsStorageOrder,ConjugateRhs,ColMajor,Version>
227 {
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 
243 template <typename Scalar, typename Index, int Mode,
244  int LhsStorageOrder, bool ConjugateLhs,
245  int RhsStorageOrder, bool ConjugateRhs, int Version>
246 EIGEN_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 
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 
276  triangularBuffer.setZero();
277  if((Mode&ZeroDiag)==ZeroDiag)
278  triangularBuffer.diagonal().setZero();
279  else
280  triangularBuffer.diagonal().setOnes();
281 
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 
376 template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
377 struct 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 
383 template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
384 struct TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>
385  : public ProductBase<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>, Lhs, Rhs >
386 {
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 
411  Mode, LhsIsTriangular,
412  (internal::traits<_ActualLhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
413  (internal::traits<_ActualRhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
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
#define EIGEN_PRODUCT_PUBLIC_INTERFACE(Derived)
Definition: ProductBase.h:46
#define EIGEN_STRONG_INLINE
#define ei_declare_aligned_stack_constructed_variable(TYPE, NAME, SIZE, BUFFER)
iterative scaling algorithm to equilibrate rows and column norms in matrices
Definition: matrix.hpp:471
const unsigned int RowMajorBit
static EIGEN_STRONG_INLINE void run(Index rows, Index cols, Index depth, const Scalar *lhs, Index lhsStride, const Scalar *rhs, Index rhsStride, Scalar *res, Index resStride, const Scalar &alpha, level3_blocking< Scalar, Scalar > &blocking)
Derived & setZero(Index size)
void rhs(const real_t *x, real_t *f)
#define EIGEN_DONT_INLINE
The matrix class, also used for vectors and row-vectors.
Definition: Matrix.h:127
#define EIGEN_PLAIN_ENUM_MAX(a, b)


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Author(s): Milan Vukov, Rien Quirynen
autogenerated on Mon Jun 10 2019 12:35:14