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
13namespace Eigen {
14
15namespace 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 */
44template <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>
49struct product_triangular_matrix_matrix;
50
51template <typename Scalar, typename Index,
52          int Mode, bool LhsIsTriangular,
53          int LhsStorageOrder, bool ConjugateLhs,
54          int RhsStorageOrder, bool ConjugateRhs, int Version>
55struct 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)
79template <typename Scalar, typename Index, int Mode,
80          int LhsStorageOrder, bool ConjugateLhs,
81          int RhsStorageOrder, bool ConjugateRhs, int Version>
82struct 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
102template <typename Scalar, typename Index, int Mode,
103          int LhsStorageOrder, bool ConjugateLhs,
104          int RhsStorageOrder, bool ConjugateRhs, int Version>
105EIGEN_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)
221template <typename Scalar, typename Index, int Mode,
222          int LhsStorageOrder, bool ConjugateLhs,
223          int RhsStorageOrder, bool ConjugateRhs, int Version>
224struct 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
243template <typename Scalar, typename Index, int Mode,
244          int LhsStorageOrder, bool ConjugateLhs,
245          int RhsStorageOrder, bool ConjugateRhs, int Version>
246EIGEN_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
376template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
377struct 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
383template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
384struct 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