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source: branches/HeuristicLab.Problems.GaussianProcessTuning/HeuristicLab.Eigen/Eigen/src/Core/products/TriangularMatrixMatrix.h @ 9562

Last change on this file since 9562 was 9562, checked in by gkronber, 11 years ago

#1967 worked on Gaussian process evolution.
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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
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    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    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)
209template <typename Scalar, typename Index, int Mode,
210          int LhsStorageOrder, bool ConjugateLhs,
211          int RhsStorageOrder, bool ConjugateRhs, int Version>
212struct 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
352template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
353struct 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
359template<int Mode, bool LhsIsTriangular, typename Lhs, typename Rhs>
360struct 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
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