TriangularMatrixMatrix.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_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>
49 struct product_triangular_matrix_matrix;
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  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)
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 
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  Scalar alpha, level3_blocking<Scalar,Scalar>& blocking)
100  {
101  // strip zeros
102  Index diagSize = (std::min)(_rows,_depth);
103  Index rows = IsLower ? _rows : diagSize;
104  Index depth = IsLower ? diagSize : _depth;
105  Index cols = _cols;
106 
107  const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
108  const_blas_data_mapper<Scalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
109 
110  Index kc = blocking.kc(); // cache block size along the K direction
111  Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction
112 
113  std::size_t sizeA = kc*mc;
114  std::size_t sizeB = kc*cols;
115  std::size_t sizeW = kc*Traits::WorkSpaceFactor;
116 
117  ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
118  ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
119  ei_declare_aligned_stack_constructed_variable(Scalar, blockW, sizeW, blocking.blockW());
120 
121  Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,LhsStorageOrder> triangularBuffer;
122  triangularBuffer.setZero();
123  if((Mode&ZeroDiag)==ZeroDiag)
124  triangularBuffer.diagonal().setZero();
125  else
126  triangularBuffer.diagonal().setOnes();
127 
128  gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
129  gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
130  gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
131 
132  for(Index k2=IsLower ? depth : 0;
133  IsLower ? k2>0 : k2<depth;
134  IsLower ? k2-=kc : k2+=kc)
135  {
136  Index actual_kc = (std::min)(IsLower ? k2 : depth-k2, kc);
137  Index actual_k2 = IsLower ? k2-actual_kc : k2;
138 
139  // align blocks with the end of the triangular part for trapezoidal lhs
140  if((!IsLower)&&(k2<rows)&&(k2+actual_kc>rows))
141  {
142  actual_kc = rows-k2;
143  k2 = k2+actual_kc-kc;
144  }
145 
146  pack_rhs(blockB, &rhs(actual_k2,0), rhsStride, actual_kc, cols);
147 
148  // the selected lhs's panel has to be split in three different parts:
149  // 1 - the part which is zero => skip it
150  // 2 - the diagonal block => special kernel
151  // 3 - the dense panel below (lower case) or above (upper case) the diagonal block => GEPP
152 
153  // the block diagonal, if any:
154  if(IsLower || actual_k2<rows)
155  {
156  // for each small vertical panels of lhs
157  for (Index k1=0; k1<actual_kc; k1+=SmallPanelWidth)
158  {
159  Index actualPanelWidth = std::min<Index>(actual_kc-k1, SmallPanelWidth);
160  Index lengthTarget = IsLower ? actual_kc-k1-actualPanelWidth : k1;
161  Index startBlock = actual_k2+k1;
162  Index blockBOffset = k1;
163 
164  // => GEBP with the micro triangular block
165  // The trick is to pack this micro block while filling the opposite triangular part with zeros.
166  // To this end we do an extra triangular copy to a small temporary buffer
167  for (Index k=0;k<actualPanelWidth;++k)
168  {
169  if (SetDiag)
170  triangularBuffer.coeffRef(k,k) = lhs(startBlock+k,startBlock+k);
171  for (Index i=IsLower ? k+1 : 0; IsLower ? i<actualPanelWidth : i<k; ++i)
172  triangularBuffer.coeffRef(i,k) = lhs(startBlock+i,startBlock+k);
173  }
174  pack_lhs(blockA, triangularBuffer.data(), triangularBuffer.outerStride(), actualPanelWidth, actualPanelWidth);
175 
176  gebp_kernel(res+startBlock, resStride, blockA, blockB, actualPanelWidth, actualPanelWidth, cols, alpha,
177  actualPanelWidth, actual_kc, 0, blockBOffset, blockW);
178 
179  // GEBP with remaining micro panel
180  if (lengthTarget>0)
181  {
182  Index startTarget = IsLower ? actual_k2+k1+actualPanelWidth : actual_k2;
183 
184  pack_lhs(blockA, &lhs(startTarget,startBlock), lhsStride, actualPanelWidth, lengthTarget);
185 
186  gebp_kernel(res+startTarget, resStride, blockA, blockB, lengthTarget, actualPanelWidth, cols, alpha,
187  actualPanelWidth, actual_kc, 0, blockBOffset, blockW);
188  }
189  }
190  }
191  // the part below (lower case) or above (upper case) the diagonal => GEPP
192  {
193  Index start = IsLower ? k2 : 0;
194  Index end = IsLower ? rows : (std::min)(actual_k2,rows);
195  for(Index i2=start; i2<end; i2+=mc)
196  {
197  const Index actual_mc = (std::min)(i2+mc,end)-i2;
198  gemm_pack_lhs<Scalar, Index, Traits::mr,Traits::LhsProgress, LhsStorageOrder,false>()
199  (blockA, &lhs(i2, actual_k2), lhsStride, actual_kc, actual_mc);
200 
201  gebp_kernel(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha, -1, -1, 0, 0, blockW);
202  }
203  }
204  }
205  }
206 };
207 
208 // implements col-major += alpha * op(general) * op(triangular)
209 template <typename Scalar, typename Index, int Mode,
210  int LhsStorageOrder, bool ConjugateLhs,
211  int RhsStorageOrder, bool ConjugateRhs, int Version>
212 struct product_triangular_matrix_matrix<Scalar,Index,Mode,false,
213  LhsStorageOrder,ConjugateLhs,
214  RhsStorageOrder,ConjugateRhs,ColMajor,Version>
215 {
216  typedef gebp_traits<Scalar,Scalar> Traits;
217  enum {
218  SmallPanelWidth = EIGEN_PLAIN_ENUM_MAX(Traits::mr,Traits::nr),
219  IsLower = (Mode&Lower) == Lower,
220  SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1
221  };
222 
223  static EIGEN_DONT_INLINE void run(
224  Index _rows, Index _cols, Index _depth,
225  const Scalar* _lhs, Index lhsStride,
226  const Scalar* _rhs, Index rhsStride,
227  Scalar* res, Index resStride,
228  Scalar alpha, level3_blocking<Scalar,Scalar>& blocking)
229  {
230  // strip zeros
231  Index diagSize = (std::min)(_cols,_depth);
232  Index rows = _rows;
233  Index depth = IsLower ? _depth : diagSize;
234  Index cols = IsLower ? diagSize : _cols;
235 
236  const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
237  const_blas_data_mapper<Scalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
238 
239  Index kc = blocking.kc(); // cache block size along the K direction
240  Index mc = (std::min)(rows,blocking.mc()); // cache block size along the M direction
241 
242  std::size_t sizeA = kc*mc;
243  std::size_t sizeB = kc*cols;
244  std::size_t sizeW = kc*Traits::WorkSpaceFactor;
245 
246  ei_declare_aligned_stack_constructed_variable(Scalar, blockA, sizeA, blocking.blockA());
247  ei_declare_aligned_stack_constructed_variable(Scalar, blockB, sizeB, blocking.blockB());
248  ei_declare_aligned_stack_constructed_variable(Scalar, blockW, sizeW, blocking.blockW());
249 
250  Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,RhsStorageOrder> triangularBuffer;
251  triangularBuffer.setZero();
252  if((Mode&ZeroDiag)==ZeroDiag)
253  triangularBuffer.diagonal().setZero();
254  else
255  triangularBuffer.diagonal().setOnes();
256 
257  gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
258  gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
259  gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
260  gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder,false,true> pack_rhs_panel;
261 
262  for(Index k2=IsLower ? 0 : depth;
263  IsLower ? k2<depth : k2>0;
264  IsLower ? k2+=kc : k2-=kc)
265  {
266  Index actual_kc = (std::min)(IsLower ? depth-k2 : k2, kc);
267  Index actual_k2 = IsLower ? k2 : k2-actual_kc;
268 
269  // align blocks with the end of the triangular part for trapezoidal rhs
270  if(IsLower && (k2<cols) && (actual_k2+actual_kc>cols))
271  {
272  actual_kc = cols-k2;
273  k2 = actual_k2 + actual_kc - kc;
274  }
275 
276  // remaining size
277  Index rs = IsLower ? (std::min)(cols,actual_k2) : cols - k2;
278  // size of the triangular part
279  Index ts = (IsLower && actual_k2>=cols) ? 0 : actual_kc;
280 
281  Scalar* geb = blockB+ts*ts;
282 
283  pack_rhs(geb, &rhs(actual_k2,IsLower ? 0 : k2), rhsStride, actual_kc, rs);
284 
285  // pack the triangular part of the rhs padding the unrolled blocks with zeros
286  if(ts>0)
287  {
288  for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
289  {
290  Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
291  Index actual_j2 = actual_k2 + j2;
292  Index panelOffset = IsLower ? j2+actualPanelWidth : 0;
293  Index panelLength = IsLower ? actual_kc-j2-actualPanelWidth : j2;
294  // general part
295  pack_rhs_panel(blockB+j2*actual_kc,
296  &rhs(actual_k2+panelOffset, actual_j2), rhsStride,
297  panelLength, actualPanelWidth,
298  actual_kc, panelOffset);
299 
300  // append the triangular part via a temporary buffer
301  for (Index j=0;j<actualPanelWidth;++j)
302  {
303  if (SetDiag)
304  triangularBuffer.coeffRef(j,j) = rhs(actual_j2+j,actual_j2+j);
305  for (Index k=IsLower ? j+1 : 0; IsLower ? k<actualPanelWidth : k<j; ++k)
306  triangularBuffer.coeffRef(k,j) = rhs(actual_j2+k,actual_j2+j);
307  }
308 
309  pack_rhs_panel(blockB+j2*actual_kc,
310  triangularBuffer.data(), triangularBuffer.outerStride(),
311  actualPanelWidth, actualPanelWidth,
312  actual_kc, j2);
313  }
314  }
315 
316  for (Index i2=0; i2<rows; i2+=mc)
317  {
318  const Index actual_mc = (std::min)(mc,rows-i2);
319  pack_lhs(blockA, &lhs(i2, actual_k2), lhsStride, actual_kc, actual_mc);
320 
321  // triangular kernel
322  if(ts>0)
323  {
324  for (Index j2=0; j2<actual_kc; j2+=SmallPanelWidth)
325  {
326  Index actualPanelWidth = std::min<Index>(actual_kc-j2, SmallPanelWidth);
327  Index panelLength = IsLower ? actual_kc-j2 : j2+actualPanelWidth;
328  Index blockOffset = IsLower ? j2 : 0;
329 
330  gebp_kernel(res+i2+(actual_k2+j2)*resStride, resStride,
331  blockA, blockB+j2*actual_kc,
332  actual_mc, panelLength, actualPanelWidth,
333  alpha,
334  actual_kc, actual_kc, // strides
335  blockOffset, blockOffset,// offsets
336  blockW); // workspace
337  }
338  }
339  gebp_kernel(res+i2+(IsLower ? 0 : k2)*resStride, resStride,
340  blockA, geb, actual_mc, actual_kc, rs,
341  alpha,
342  -1, -1, 0, 0, blockW);
343  }
344  }
345  }
346 };
347 
348 /***************************************************************************
349 * Wrapper to product_triangular_matrix_matrix
350 ***************************************************************************/
351 
352 template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
353 struct traits<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false> >
354  : traits<ProductBase<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>, Lhs, Rhs> >
355 {};
356 
357 } // end namespace internal
358 
359 template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
360 struct TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>
361  : public ProductBase<TriangularProduct<Mode,LhsIsTriangular,Lhs,false,Rhs,false>, Lhs, Rhs >
362 {
363  EIGEN_PRODUCT_PUBLIC_INTERFACE(TriangularProduct)
364 
365  TriangularProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) {}
366 
367  template<typename Dest> void scaleAndAddTo(Dest& dst, Scalar alpha) const
368  {
369  typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(m_lhs);
370  typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(m_rhs);
371 
372  Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs)
373  * RhsBlasTraits::extractScalarFactor(m_rhs);
374 
375  typedef internal::gemm_blocking_space<(Dest::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar,
376  Lhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxColsAtCompileTime,4> BlockingType;
377 
378  enum { IsLower = (Mode&Lower) == Lower };
379  Index stripedRows = ((!LhsIsTriangular) || (IsLower)) ? lhs.rows() : (std::min)(lhs.rows(),lhs.cols());
380  Index stripedCols = ((LhsIsTriangular) || (!IsLower)) ? rhs.cols() : (std::min)(rhs.cols(),rhs.rows());
381  Index stripedDepth = LhsIsTriangular ? ((!IsLower) ? lhs.cols() : (std::min)(lhs.cols(),lhs.rows()))
382  : ((IsLower) ? rhs.rows() : (std::min)(rhs.rows(),rhs.cols()));
383 
384  BlockingType blocking(stripedRows, stripedCols, stripedDepth);
385 
386  internal::product_triangular_matrix_matrix<Scalar, Index,
387  Mode, LhsIsTriangular,
388  (internal::traits<_ActualLhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
389  (internal::traits<_ActualRhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
390  (internal::traits<Dest >::Flags&RowMajorBit) ? RowMajor : ColMajor>
391  ::run(
392  stripedRows, stripedCols, stripedDepth, // sizes
393  &lhs.coeffRef(0,0), lhs.outerStride(), // lhs info
394  &rhs.coeffRef(0,0), rhs.outerStride(), // rhs info
395  &dst.coeffRef(0,0), dst.outerStride(), // result info
396  actualAlpha, blocking
397  );
398  }
399 };
400 
401 } // end namespace Eigen
402 
403 #endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_H