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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>
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     const 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     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 
120     const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
121     const_blas_data_mapper<Scalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
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 
134     Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,LhsStorageOrder> triangularBuffer;
135     triangularBuffer.setZero();
136     if((Mode&ZeroDiag)==ZeroDiag)
137       triangularBuffer.diagonal().setZero();
138     else
139       triangularBuffer.diagonal().setOnes();
140 
141     gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
142     gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
143     gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
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;
211           gemm_pack_lhs<Scalar, Index, Traits::mr,Traits::LhsProgress, LhsStorageOrder,false>()
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 {
228   typedef gebp_traits<Scalar,Scalar> Traits;
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 
261     const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
262     const_blas_data_mapper<Scalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
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 
275     Matrix<Scalar,SmallPanelWidth,SmallPanelWidth,RhsStorageOrder> triangularBuffer;
276     triangularBuffer.setZero();
277     if((Mode&ZeroDiag)==ZeroDiag)
278       triangularBuffer.diagonal().setZero();
279     else
280       triangularBuffer.diagonal().setOnes();
281 
282     gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
283     gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
284     gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
285     gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder,false,true> pack_rhs_panel;
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 {
387   EIGEN_PRODUCT_PUBLIC_INTERFACE(TriangularProduct)
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 
410     internal::product_triangular_matrix_matrix<Scalar, Index,
411       Mode, LhsIsTriangular,
412       (internal::traits<_ActualLhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, LhsBlasTraits::NeedToConjugate,
413       (internal::traits<_ActualRhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, RhsBlasTraits::NeedToConjugate,
414       (internal::traits<Dest          >::Flags&RowMajorBit) ? RowMajor : ColMajor>
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
428