```/* <![CDATA[ */
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
12
13namespace Eigen {
14
15namespace internal {
16
17// pack a selfadjoint block diagonal for use with the gebp_kernel
18template<typename Scalar, typename Index, int Pack1, int Pack2, int StorageOrder>
19struct symm_pack_lhs
20{
21  template<int BlockRows> inline
22  void pack(Scalar* blockA, const const_blas_data_mapper<Scalar,Index,StorageOrder>& lhs, Index cols, Index i, Index& count)
23  {
24    // normal copy
25    for(Index k=0; k<i; k++)
26      for(Index w=0; w<BlockRows; w++)
27        blockA[count++] = lhs(i+w,k);           // normal
28    // symmetric copy
29    Index h = 0;
30    for(Index k=i; k<i+BlockRows; k++)
31    {
32      for(Index w=0; w<h; w++)
33        blockA[count++] = numext::conj(lhs(k, i+w)); // transposed
34
35      blockA[count++] = numext::real(lhs(k,k));   // real (diagonal)
36
37      for(Index w=h+1; w<BlockRows; w++)
38        blockA[count++] = lhs(i+w, k);          // normal
39      ++h;
40    }
41    // transposed copy
42    for(Index k=i+BlockRows; k<cols; k++)
43      for(Index w=0; w<BlockRows; w++)
44        blockA[count++] = numext::conj(lhs(k, i+w)); // transposed
45  }
46  void operator()(Scalar* blockA, const Scalar* _lhs, Index lhsStride, Index cols, Index rows)
47  {
48    const_blas_data_mapper<Scalar,Index,StorageOrder> lhs(_lhs,lhsStride);
49    Index count = 0;
50    Index peeled_mc = (rows/Pack1)*Pack1;
51    for(Index i=0; i<peeled_mc; i+=Pack1)
52    {
53      pack<Pack1>(blockA, lhs, cols, i, count);
54    }
55
56    if(rows-peeled_mc>=Pack2)
57    {
58      pack<Pack2>(blockA, lhs, cols, peeled_mc, count);
59      peeled_mc += Pack2;
60    }
61
62    // do the same with mr==1
63    for(Index i=peeled_mc; i<rows; i++)
64    {
65      for(Index k=0; k<i; k++)
66        blockA[count++] = lhs(i, k);              // normal
67
68      blockA[count++] = numext::real(lhs(i, i));       // real (diagonal)
69
70      for(Index k=i+1; k<cols; k++)
71        blockA[count++] = numext::conj(lhs(k, i));     // transposed
72    }
73  }
74};
75
76template<typename Scalar, typename Index, int nr, int StorageOrder>
77struct symm_pack_rhs
78{
79  enum { PacketSize = packet_traits<Scalar>::size };
80  void operator()(Scalar* blockB, const Scalar* _rhs, Index rhsStride, Index rows, Index cols, Index k2)
81  {
82    Index end_k = k2 + rows;
83    Index count = 0;
84    const_blas_data_mapper<Scalar,Index,StorageOrder> rhs(_rhs,rhsStride);
85    Index packet_cols = (cols/nr)*nr;
86
87    // first part: normal case
88    for(Index j2=0; j2<k2; j2+=nr)
89    {
90      for(Index k=k2; k<end_k; k++)
91      {
92        blockB[count+0] = rhs(k,j2+0);
93        blockB[count+1] = rhs(k,j2+1);
94        if (nr==4)
95        {
96          blockB[count+2] = rhs(k,j2+2);
97          blockB[count+3] = rhs(k,j2+3);
98        }
99        count += nr;
100      }
101    }
102
103    // second part: diagonal block
104    for(Index j2=k2; j2<(std::min)(k2+rows,packet_cols); j2+=nr)
105    {
106      // again we can split vertically in three different parts (transpose, symmetric, normal)
107      // transpose
108      for(Index k=k2; k<j2; k++)
109      {
110        blockB[count+0] = numext::conj(rhs(j2+0,k));
111        blockB[count+1] = numext::conj(rhs(j2+1,k));
112        if (nr==4)
113        {
114          blockB[count+2] = numext::conj(rhs(j2+2,k));
115          blockB[count+3] = numext::conj(rhs(j2+3,k));
116        }
117        count += nr;
118      }
119      // symmetric
120      Index h = 0;
121      for(Index k=j2; k<j2+nr; k++)
122      {
123        // normal
124        for (Index w=0 ; w<h; ++w)
125          blockB[count+w] = rhs(k,j2+w);
126
127        blockB[count+h] = numext::real(rhs(k,k));
128
129        // transpose
130        for (Index w=h+1 ; w<nr; ++w)
131          blockB[count+w] = numext::conj(rhs(j2+w,k));
132        count += nr;
133        ++h;
134      }
135      // normal
136      for(Index k=j2+nr; k<end_k; k++)
137      {
138        blockB[count+0] = rhs(k,j2+0);
139        blockB[count+1] = rhs(k,j2+1);
140        if (nr==4)
141        {
142          blockB[count+2] = rhs(k,j2+2);
143          blockB[count+3] = rhs(k,j2+3);
144        }
145        count += nr;
146      }
147    }
148
149    // third part: transposed
150    for(Index j2=k2+rows; j2<packet_cols; j2+=nr)
151    {
152      for(Index k=k2; k<end_k; k++)
153      {
154        blockB[count+0] = numext::conj(rhs(j2+0,k));
155        blockB[count+1] = numext::conj(rhs(j2+1,k));
156        if (nr==4)
157        {
158          blockB[count+2] = numext::conj(rhs(j2+2,k));
159          blockB[count+3] = numext::conj(rhs(j2+3,k));
160        }
161        count += nr;
162      }
163    }
164
165    // copy the remaining columns one at a time (=> the same with nr==1)
166    for(Index j2=packet_cols; j2<cols; ++j2)
167    {
168      // transpose
169      Index half = (std::min)(end_k,j2);
170      for(Index k=k2; k<half; k++)
171      {
172        blockB[count] = numext::conj(rhs(j2,k));
173        count += 1;
174      }
175
176      if(half==j2 && half<k2+rows)
177      {
178        blockB[count] = numext::real(rhs(j2,j2));
179        count += 1;
180      }
181      else
182        half--;
183
184      // normal
185      for(Index k=half+1; k<k2+rows; k++)
186      {
187        blockB[count] = rhs(k,j2);
188        count += 1;
189      }
190    }
191  }
192};
193
194/* Optimized selfadjoint matrix * matrix (_SYMM) product built on top of
195 * the general matrix matrix product.
196 */
197template <typename Scalar, typename Index,
198          int LhsStorageOrder, bool LhsSelfAdjoint, bool ConjugateLhs,
199          int RhsStorageOrder, bool RhsSelfAdjoint, bool ConjugateRhs,
200          int ResStorageOrder>
202
203template <typename Scalar, typename Index,
204          int LhsStorageOrder, bool LhsSelfAdjoint, bool ConjugateLhs,
205          int RhsStorageOrder, bool RhsSelfAdjoint, bool ConjugateRhs>
207{
208
209  static EIGEN_STRONG_INLINE void run(
210    Index rows, Index cols,
211    const Scalar* lhs, Index lhsStride,
212    const Scalar* rhs, Index rhsStride,
213    Scalar* res,       Index resStride,
214    const Scalar& alpha)
215  {
217      EIGEN_LOGICAL_XOR(RhsSelfAdjoint,RhsStorageOrder==RowMajor) ? ColMajor : RowMajor,
219      EIGEN_LOGICAL_XOR(LhsSelfAdjoint,LhsStorageOrder==RowMajor) ? ColMajor : RowMajor,
221      ColMajor>
222      ::run(cols, rows,  rhs, rhsStride,  lhs, lhsStride,  res, resStride,  alpha);
223  }
224};
225
226template <typename Scalar, typename Index,
227          int LhsStorageOrder, bool ConjugateLhs,
228          int RhsStorageOrder, bool ConjugateRhs>
230{
231
232  static EIGEN_DONT_INLINE void run(
233    Index rows, Index cols,
234    const Scalar* _lhs, Index lhsStride,
235    const Scalar* _rhs, Index rhsStride,
236    Scalar* res,        Index resStride,
237    const Scalar& alpha);
238};
239
240template <typename Scalar, typename Index,
241          int LhsStorageOrder, bool ConjugateLhs,
242          int RhsStorageOrder, bool ConjugateRhs>
244    Index rows, Index cols,
245    const Scalar* _lhs, Index lhsStride,
246    const Scalar* _rhs, Index rhsStride,
247    Scalar* res,        Index resStride,
248    const Scalar& alpha)
249  {
250    Index size = rows;
251
252    const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
253    const_blas_data_mapper<Scalar, Index, RhsStorageOrder> rhs(_rhs,rhsStride);
254
255    typedef gebp_traits<Scalar,Scalar> Traits;
256
257    Index kc = size;  // cache block size along the K direction
258    Index mc = rows;  // cache block size along the M direction
259    Index nc = cols;  // cache block size along the N direction
260    computeProductBlockingSizes<Scalar,Scalar>(kc, mc, nc);
261    // kc must smaller than mc
262    kc = (std::min)(kc,mc);
263
264    std::size_t sizeW = kc*Traits::WorkSpaceFactor;
265    std::size_t sizeB = sizeW + kc*cols;
266    ei_declare_aligned_stack_constructed_variable(Scalar, blockA, kc*mc, 0);
267    ei_declare_aligned_stack_constructed_variable(Scalar, allocatedBlockB, sizeB, 0);
268    Scalar* blockB = allocatedBlockB + sizeW;
269
270    gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
271    symm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
272    gemm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
273    gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder==RowMajor?ColMajor:RowMajor, true> pack_lhs_transposed;
274
275    for(Index k2=0; k2<size; k2+=kc)
276    {
277      const Index actual_kc = (std::min)(k2+kc,size)-k2;
278
279      // we have selected one row panel of rhs and one column panel of lhs
280      // pack rhs's panel into a sequential chunk of memory
281      // and expand each coeff to a constant packet for further reuse
282      pack_rhs(blockB, &rhs(k2,0), rhsStride, actual_kc, cols);
283
284      // the select lhs's panel has to be split in three different parts:
285      //  1 - the transposed panel above the diagonal block => transposed packed copy
286      //  2 - the diagonal block => special packed copy
287      //  3 - the panel below the diagonal block => generic packed copy
288      for(Index i2=0; i2<k2; i2+=mc)
289      {
290        const Index actual_mc = (std::min)(i2+mc,k2)-i2;
291        // transposed packed copy
292        pack_lhs_transposed(blockA, &lhs(k2, i2), lhsStride, actual_kc, actual_mc);
293
294        gebp_kernel(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha);
295      }
296      // the block diagonal
297      {
298        const Index actual_mc = (std::min)(k2+kc,size)-k2;
299        // symmetric packed copy
300        pack_lhs(blockA, &lhs(k2,k2), lhsStride, actual_kc, actual_mc);
301
302        gebp_kernel(res+k2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha);
303      }
304
305      for(Index i2=k2+kc; i2<size; i2+=mc)
306      {
307        const Index actual_mc = (std::min)(i2+mc,size)-i2;
308        gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder,false>()
309          (blockA, &lhs(i2, k2), lhsStride, actual_kc, actual_mc);
310
311        gebp_kernel(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha);
312      }
313    }
314  }
315
317template <typename Scalar, typename Index,
318          int LhsStorageOrder, bool ConjugateLhs,
319          int RhsStorageOrder, bool ConjugateRhs>
321{
322
323  static EIGEN_DONT_INLINE void run(
324    Index rows, Index cols,
325    const Scalar* _lhs, Index lhsStride,
326    const Scalar* _rhs, Index rhsStride,
327    Scalar* res,        Index resStride,
328    const Scalar& alpha);
329};
330
331template <typename Scalar, typename Index,
332          int LhsStorageOrder, bool ConjugateLhs,
333          int RhsStorageOrder, bool ConjugateRhs>
335    Index rows, Index cols,
336    const Scalar* _lhs, Index lhsStride,
337    const Scalar* _rhs, Index rhsStride,
338    Scalar* res,        Index resStride,
339    const Scalar& alpha)
340  {
341    Index size = cols;
342
343    const_blas_data_mapper<Scalar, Index, LhsStorageOrder> lhs(_lhs,lhsStride);
344
345    typedef gebp_traits<Scalar,Scalar> Traits;
346
347    Index kc = size; // cache block size along the K direction
348    Index mc = rows;  // cache block size along the M direction
349    Index nc = cols;  // cache block size along the N direction
350    computeProductBlockingSizes<Scalar,Scalar>(kc, mc, nc);
351    std::size_t sizeW = kc*Traits::WorkSpaceFactor;
352    std::size_t sizeB = sizeW + kc*cols;
353    ei_declare_aligned_stack_constructed_variable(Scalar, blockA, kc*mc, 0);
354    ei_declare_aligned_stack_constructed_variable(Scalar, allocatedBlockB, sizeB, 0);
355    Scalar* blockB = allocatedBlockB + sizeW;
356
357    gebp_kernel<Scalar, Scalar, Index, Traits::mr, Traits::nr, ConjugateLhs, ConjugateRhs> gebp_kernel;
358    gemm_pack_lhs<Scalar, Index, Traits::mr, Traits::LhsProgress, LhsStorageOrder> pack_lhs;
359    symm_pack_rhs<Scalar, Index, Traits::nr,RhsStorageOrder> pack_rhs;
360
361    for(Index k2=0; k2<size; k2+=kc)
362    {
363      const Index actual_kc = (std::min)(k2+kc,size)-k2;
364
365      pack_rhs(blockB, _rhs, rhsStride, actual_kc, cols, k2);
366
367      // => GEPP
368      for(Index i2=0; i2<rows; i2+=mc)
369      {
370        const Index actual_mc = (std::min)(i2+mc,rows)-i2;
371        pack_lhs(blockA, &lhs(i2, k2), lhsStride, actual_kc, actual_mc);
372
373        gebp_kernel(res+i2, resStride, blockA, blockB, actual_mc, actual_kc, cols, alpha);
374      }
375    }
376  }
377
378} // end namespace internal
379
380/***************************************************************************
382***************************************************************************/
383
384namespace internal {
385template<typename Lhs, int LhsMode, typename Rhs, int RhsMode>
387  : traits<ProductBase<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,RhsMode,false>, Lhs, Rhs> >
388{};
389}
390
391template<typename Lhs, int LhsMode, typename Rhs, int RhsMode>
393  : public ProductBase<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,RhsMode,false>, Lhs, Rhs >
394{
396
397  SelfadjointProductMatrix(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) {}
398
399  enum {
400    LhsIsUpper = (LhsMode&(Upper|Lower))==Upper,
402    RhsIsUpper = (RhsMode&(Upper|Lower))==Upper,
404  };
405
406  template<typename Dest> void scaleAndAddTo(Dest& dst, const Scalar& alpha) const
407  {
408    eigen_assert(dst.rows()==m_lhs.rows() && dst.cols()==m_rhs.cols());
409
410    typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(m_lhs);
411    typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(m_rhs);
412
413    Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs)
414                               * RhsBlasTraits::extractScalarFactor(m_rhs);
415
417      EIGEN_LOGICAL_XOR(LhsIsUpper,
418                        internal::traits<Lhs>::Flags &RowMajorBit) ? RowMajor : ColMajor, LhsIsSelfAdjoint,
419      NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(LhsIsUpper,bool(LhsBlasTraits::NeedToConjugate)),
420      EIGEN_LOGICAL_XOR(RhsIsUpper,
421                        internal::traits<Rhs>::Flags &RowMajorBit) ? RowMajor : ColMajor, RhsIsSelfAdjoint,
422      NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(RhsIsUpper,bool(RhsBlasTraits::NeedToConjugate)),
423      internal::traits<Dest>::Flags&RowMajorBit  ? RowMajor : ColMajor>
424      ::run(
425        lhs.rows(), rhs.cols(),                 // sizes
426        &lhs.coeffRef(0,0),    lhs.outerStride(),  // lhs info
427        &rhs.coeffRef(0,0),    rhs.outerStride(),  // rhs info
428        &dst.coeffRef(0,0), dst.outerStride(),  // result info
429        actualAlpha                             // alpha
430      );
431  }
432};
433
434} // end namespace Eigen
435