xref: /aosp_15_r20/external/eigen/Eigen/src/Core/ProductEvaluators.h (revision bf2c37156dfe67e5dfebd6d394bad8b2ab5804d4)
1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2006-2008 Benoit Jacob <[email protected]>
5 // Copyright (C) 2008-2010 Gael Guennebaud <[email protected]>
6 // Copyright (C) 2011 Jitse Niesen <[email protected]>
7 //
8 // This Source Code Form is subject to the terms of the Mozilla
9 // Public License v. 2.0. If a copy of the MPL was not distributed
10 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
11 
12 
13 #ifndef EIGEN_PRODUCTEVALUATORS_H
14 #define EIGEN_PRODUCTEVALUATORS_H
15 
16 namespace Eigen {
17 
18 namespace internal {
19 
20 /** \internal
21   * Evaluator of a product expression.
22   * Since products require special treatments to handle all possible cases,
23   * we simply defer the evaluation logic to a product_evaluator class
24   * which offers more partial specialization possibilities.
25   *
26   * \sa class product_evaluator
27   */
28 template<typename Lhs, typename Rhs, int Options>
29 struct evaluator<Product<Lhs, Rhs, Options> >
30  : public product_evaluator<Product<Lhs, Rhs, Options> >
31 {
32   typedef Product<Lhs, Rhs, Options> XprType;
33   typedef product_evaluator<XprType> Base;
34 
35   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const XprType& xpr) : Base(xpr) {}
36 };
37 
38 // Catch "scalar * ( A * B )" and transform it to "(A*scalar) * B"
39 // TODO we should apply that rule only if that's really helpful
40 template<typename Lhs, typename Rhs, typename Scalar1, typename Scalar2, typename Plain1>
41 struct evaluator_assume_aliasing<CwiseBinaryOp<internal::scalar_product_op<Scalar1,Scalar2>,
42                                                const CwiseNullaryOp<internal::scalar_constant_op<Scalar1>, Plain1>,
43                                                const Product<Lhs, Rhs, DefaultProduct> > >
44 {
45   static const bool value = true;
46 };
47 template<typename Lhs, typename Rhs, typename Scalar1, typename Scalar2, typename Plain1>
48 struct evaluator<CwiseBinaryOp<internal::scalar_product_op<Scalar1,Scalar2>,
49                                const CwiseNullaryOp<internal::scalar_constant_op<Scalar1>, Plain1>,
50                                const Product<Lhs, Rhs, DefaultProduct> > >
51  : public evaluator<Product<EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar1,Lhs,product), Rhs, DefaultProduct> >
52 {
53   typedef CwiseBinaryOp<internal::scalar_product_op<Scalar1,Scalar2>,
54                                const CwiseNullaryOp<internal::scalar_constant_op<Scalar1>, Plain1>,
55                                const Product<Lhs, Rhs, DefaultProduct> > XprType;
56   typedef evaluator<Product<EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar1,Lhs,product), Rhs, DefaultProduct> > Base;
57 
58   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const XprType& xpr)
59     : Base(xpr.lhs().functor().m_other * xpr.rhs().lhs() * xpr.rhs().rhs())
60   {}
61 };
62 
63 
64 template<typename Lhs, typename Rhs, int DiagIndex>
65 struct evaluator<Diagonal<const Product<Lhs, Rhs, DefaultProduct>, DiagIndex> >
66  : public evaluator<Diagonal<const Product<Lhs, Rhs, LazyProduct>, DiagIndex> >
67 {
68   typedef Diagonal<const Product<Lhs, Rhs, DefaultProduct>, DiagIndex> XprType;
69   typedef evaluator<Diagonal<const Product<Lhs, Rhs, LazyProduct>, DiagIndex> > Base;
70 
71   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const XprType& xpr)
72     : Base(Diagonal<const Product<Lhs, Rhs, LazyProduct>, DiagIndex>(
73         Product<Lhs, Rhs, LazyProduct>(xpr.nestedExpression().lhs(), xpr.nestedExpression().rhs()),
74         xpr.index() ))
75   {}
76 };
77 
78 
79 // Helper class to perform a matrix product with the destination at hand.
80 // Depending on the sizes of the factors, there are different evaluation strategies
81 // as controlled by internal::product_type.
82 template< typename Lhs, typename Rhs,
83           typename LhsShape = typename evaluator_traits<Lhs>::Shape,
84           typename RhsShape = typename evaluator_traits<Rhs>::Shape,
85           int ProductType = internal::product_type<Lhs,Rhs>::value>
86 struct generic_product_impl;
87 
88 template<typename Lhs, typename Rhs>
89 struct evaluator_assume_aliasing<Product<Lhs, Rhs, DefaultProduct> > {
90   static const bool value = true;
91 };
92 
93 // This is the default evaluator implementation for products:
94 // It creates a temporary and call generic_product_impl
95 template<typename Lhs, typename Rhs, int Options, int ProductTag, typename LhsShape, typename RhsShape>
96 struct product_evaluator<Product<Lhs, Rhs, Options>, ProductTag, LhsShape, RhsShape>
97   : public evaluator<typename Product<Lhs, Rhs, Options>::PlainObject>
98 {
99   typedef Product<Lhs, Rhs, Options> XprType;
100   typedef typename XprType::PlainObject PlainObject;
101   typedef evaluator<PlainObject> Base;
102   enum {
103     Flags = Base::Flags | EvalBeforeNestingBit
104   };
105 
106   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
107   explicit product_evaluator(const XprType& xpr)
108     : m_result(xpr.rows(), xpr.cols())
109   {
110     ::new (static_cast<Base*>(this)) Base(m_result);
111 
112 // FIXME shall we handle nested_eval here?,
113 // if so, then we must take care at removing the call to nested_eval in the specializations (e.g., in permutation_matrix_product, transposition_matrix_product, etc.)
114 //     typedef typename internal::nested_eval<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;
115 //     typedef typename internal::nested_eval<Rhs,Lhs::RowsAtCompileTime>::type RhsNested;
116 //     typedef typename internal::remove_all<LhsNested>::type LhsNestedCleaned;
117 //     typedef typename internal::remove_all<RhsNested>::type RhsNestedCleaned;
118 //
119 //     const LhsNested lhs(xpr.lhs());
120 //     const RhsNested rhs(xpr.rhs());
121 //
122 //     generic_product_impl<LhsNestedCleaned, RhsNestedCleaned>::evalTo(m_result, lhs, rhs);
123 
124     generic_product_impl<Lhs, Rhs, LhsShape, RhsShape, ProductTag>::evalTo(m_result, xpr.lhs(), xpr.rhs());
125   }
126 
127 protected:
128   PlainObject m_result;
129 };
130 
131 // The following three shortcuts are enabled only if the scalar types match exactly.
132 // TODO: we could enable them for different scalar types when the product is not vectorized.
133 
134 // Dense = Product
135 template< typename DstXprType, typename Lhs, typename Rhs, int Options, typename Scalar>
136 struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::assign_op<Scalar,Scalar>, Dense2Dense,
137   typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct)>::type>
138 {
139   typedef Product<Lhs,Rhs,Options> SrcXprType;
140   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
141   void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,Scalar> &)
142   {
143     Index dstRows = src.rows();
144     Index dstCols = src.cols();
145     if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
146       dst.resize(dstRows, dstCols);
147     // FIXME shall we handle nested_eval here?
148     generic_product_impl<Lhs, Rhs>::evalTo(dst, src.lhs(), src.rhs());
149   }
150 };
151 
152 // Dense += Product
153 template< typename DstXprType, typename Lhs, typename Rhs, int Options, typename Scalar>
154 struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::add_assign_op<Scalar,Scalar>, Dense2Dense,
155   typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct)>::type>
156 {
157   typedef Product<Lhs,Rhs,Options> SrcXprType;
158   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
159   void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<Scalar,Scalar> &)
160   {
161     eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());
162     // FIXME shall we handle nested_eval here?
163     generic_product_impl<Lhs, Rhs>::addTo(dst, src.lhs(), src.rhs());
164   }
165 };
166 
167 // Dense -= Product
168 template< typename DstXprType, typename Lhs, typename Rhs, int Options, typename Scalar>
169 struct Assignment<DstXprType, Product<Lhs,Rhs,Options>, internal::sub_assign_op<Scalar,Scalar>, Dense2Dense,
170   typename enable_if<(Options==DefaultProduct || Options==AliasFreeProduct)>::type>
171 {
172   typedef Product<Lhs,Rhs,Options> SrcXprType;
173   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
174   void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<Scalar,Scalar> &)
175   {
176     eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());
177     // FIXME shall we handle nested_eval here?
178     generic_product_impl<Lhs, Rhs>::subTo(dst, src.lhs(), src.rhs());
179   }
180 };
181 
182 
183 // Dense ?= scalar * Product
184 // TODO we should apply that rule if that's really helpful
185 // for instance, this is not good for inner products
186 template< typename DstXprType, typename Lhs, typename Rhs, typename AssignFunc, typename Scalar, typename ScalarBis, typename Plain>
187 struct Assignment<DstXprType, CwiseBinaryOp<internal::scalar_product_op<ScalarBis,Scalar>, const CwiseNullaryOp<internal::scalar_constant_op<ScalarBis>,Plain>,
188                                            const Product<Lhs,Rhs,DefaultProduct> >, AssignFunc, Dense2Dense>
189 {
190   typedef CwiseBinaryOp<internal::scalar_product_op<ScalarBis,Scalar>,
191                         const CwiseNullaryOp<internal::scalar_constant_op<ScalarBis>,Plain>,
192                         const Product<Lhs,Rhs,DefaultProduct> > SrcXprType;
193   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
194   void run(DstXprType &dst, const SrcXprType &src, const AssignFunc& func)
195   {
196     call_assignment_no_alias(dst, (src.lhs().functor().m_other * src.rhs().lhs())*src.rhs().rhs(), func);
197   }
198 };
199 
200 //----------------------------------------
201 // Catch "Dense ?= xpr + Product<>" expression to save one temporary
202 // FIXME we could probably enable these rules for any product, i.e., not only Dense and DefaultProduct
203 
204 template<typename OtherXpr, typename Lhs, typename Rhs>
205 struct evaluator_assume_aliasing<CwiseBinaryOp<internal::scalar_sum_op<typename OtherXpr::Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, const OtherXpr,
206                                                const Product<Lhs,Rhs,DefaultProduct> >, DenseShape > {
207   static const bool value = true;
208 };
209 
210 template<typename OtherXpr, typename Lhs, typename Rhs>
211 struct evaluator_assume_aliasing<CwiseBinaryOp<internal::scalar_difference_op<typename OtherXpr::Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, const OtherXpr,
212                                                const Product<Lhs,Rhs,DefaultProduct> >, DenseShape > {
213   static const bool value = true;
214 };
215 
216 template<typename DstXprType, typename OtherXpr, typename ProductType, typename Func1, typename Func2>
217 struct assignment_from_xpr_op_product
218 {
219   template<typename SrcXprType, typename InitialFunc>
220   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
221   void run(DstXprType &dst, const SrcXprType &src, const InitialFunc& /*func*/)
222   {
223     call_assignment_no_alias(dst, src.lhs(), Func1());
224     call_assignment_no_alias(dst, src.rhs(), Func2());
225   }
226 };
227 
228 #define EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(ASSIGN_OP,BINOP,ASSIGN_OP2) \
229   template< typename DstXprType, typename OtherXpr, typename Lhs, typename Rhs, typename DstScalar, typename SrcScalar, typename OtherScalar,typename ProdScalar> \
230   struct Assignment<DstXprType, CwiseBinaryOp<internal::BINOP<OtherScalar,ProdScalar>, const OtherXpr, \
231                                             const Product<Lhs,Rhs,DefaultProduct> >, internal::ASSIGN_OP<DstScalar,SrcScalar>, Dense2Dense> \
232     : assignment_from_xpr_op_product<DstXprType, OtherXpr, Product<Lhs,Rhs,DefaultProduct>, internal::ASSIGN_OP<DstScalar,OtherScalar>, internal::ASSIGN_OP2<DstScalar,ProdScalar> > \
233   {}
234 
235 EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(assign_op,    scalar_sum_op,add_assign_op);
236 EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(add_assign_op,scalar_sum_op,add_assign_op);
237 EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(sub_assign_op,scalar_sum_op,sub_assign_op);
238 
239 EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(assign_op,    scalar_difference_op,sub_assign_op);
240 EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(add_assign_op,scalar_difference_op,sub_assign_op);
241 EIGEN_CATCH_ASSIGN_XPR_OP_PRODUCT(sub_assign_op,scalar_difference_op,add_assign_op);
242 
243 //----------------------------------------
244 
245 template<typename Lhs, typename Rhs>
246 struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,InnerProduct>
247 {
248   template<typename Dst>
249   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
250   {
251     dst.coeffRef(0,0) = (lhs.transpose().cwiseProduct(rhs)).sum();
252   }
253 
254   template<typename Dst>
255   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
256   {
257     dst.coeffRef(0,0) += (lhs.transpose().cwiseProduct(rhs)).sum();
258   }
259 
260   template<typename Dst>
261   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
262   { dst.coeffRef(0,0) -= (lhs.transpose().cwiseProduct(rhs)).sum(); }
263 };
264 
265 
266 /***********************************************************************
267 *  Implementation of outer dense * dense vector product
268 ***********************************************************************/
269 
270 // Column major result
271 template<typename Dst, typename Lhs, typename Rhs, typename Func>
272 void EIGEN_DEVICE_FUNC outer_product_selector_run(Dst& dst, const Lhs &lhs, const Rhs &rhs, const Func& func, const false_type&)
273 {
274   evaluator<Rhs> rhsEval(rhs);
275   ei_declare_local_nested_eval(Lhs,lhs,Rhs::SizeAtCompileTime,actual_lhs);
276   // FIXME if cols is large enough, then it might be useful to make sure that lhs is sequentially stored
277   // FIXME not very good if rhs is real and lhs complex while alpha is real too
278   const Index cols = dst.cols();
279   for (Index j=0; j<cols; ++j)
280     func(dst.col(j), rhsEval.coeff(Index(0),j) * actual_lhs);
281 }
282 
283 // Row major result
284 template<typename Dst, typename Lhs, typename Rhs, typename Func>
285 void EIGEN_DEVICE_FUNC outer_product_selector_run(Dst& dst, const Lhs &lhs, const Rhs &rhs, const Func& func, const true_type&)
286 {
287   evaluator<Lhs> lhsEval(lhs);
288   ei_declare_local_nested_eval(Rhs,rhs,Lhs::SizeAtCompileTime,actual_rhs);
289   // FIXME if rows is large enough, then it might be useful to make sure that rhs is sequentially stored
290   // FIXME not very good if lhs is real and rhs complex while alpha is real too
291   const Index rows = dst.rows();
292   for (Index i=0; i<rows; ++i)
293     func(dst.row(i), lhsEval.coeff(i,Index(0)) * actual_rhs);
294 }
295 
296 template<typename Lhs, typename Rhs>
297 struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,OuterProduct>
298 {
299   template<typename T> struct is_row_major : internal::conditional<(int(T::Flags)&RowMajorBit), internal::true_type, internal::false_type>::type {};
300   typedef typename Product<Lhs,Rhs>::Scalar Scalar;
301 
302   // TODO it would be nice to be able to exploit our *_assign_op functors for that purpose
303   struct set  { template<typename Dst, typename Src> EIGEN_DEVICE_FUNC void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived()  = src; } };
304   struct add  { template<typename Dst, typename Src> EIGEN_DEVICE_FUNC void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() += src; } };
305   struct sub  { template<typename Dst, typename Src> EIGEN_DEVICE_FUNC void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() -= src; } };
306   struct adds {
307     Scalar m_scale;
308     explicit adds(const Scalar& s) : m_scale(s) {}
309     template<typename Dst, typename Src> void EIGEN_DEVICE_FUNC operator()(const Dst& dst, const Src& src) const {
310       dst.const_cast_derived() += m_scale * src;
311     }
312   };
313 
314   template<typename Dst>
315   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
316   {
317     internal::outer_product_selector_run(dst, lhs, rhs, set(), is_row_major<Dst>());
318   }
319 
320   template<typename Dst>
321   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
322   {
323     internal::outer_product_selector_run(dst, lhs, rhs, add(), is_row_major<Dst>());
324   }
325 
326   template<typename Dst>
327   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
328   {
329     internal::outer_product_selector_run(dst, lhs, rhs, sub(), is_row_major<Dst>());
330   }
331 
332   template<typename Dst>
333   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void scaleAndAddTo(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
334   {
335     internal::outer_product_selector_run(dst, lhs, rhs, adds(alpha), is_row_major<Dst>());
336   }
337 
338 };
339 
340 
341 // This base class provides default implementations for evalTo, addTo, subTo, in terms of scaleAndAddTo
342 template<typename Lhs, typename Rhs, typename Derived>
343 struct generic_product_impl_base
344 {
345   typedef typename Product<Lhs,Rhs>::Scalar Scalar;
346 
347   template<typename Dst>
348   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
349   { dst.setZero(); scaleAndAddTo(dst, lhs, rhs, Scalar(1)); }
350 
351   template<typename Dst>
352   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
353   { scaleAndAddTo(dst,lhs, rhs, Scalar(1)); }
354 
355   template<typename Dst>
356   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
357   { scaleAndAddTo(dst, lhs, rhs, Scalar(-1)); }
358 
359   template<typename Dst>
360   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void scaleAndAddTo(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
361   { Derived::scaleAndAddTo(dst,lhs,rhs,alpha); }
362 
363 };
364 
365 template<typename Lhs, typename Rhs>
366 struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,GemvProduct>
367   : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,GemvProduct> >
368 {
369   typedef typename nested_eval<Lhs,1>::type LhsNested;
370   typedef typename nested_eval<Rhs,1>::type RhsNested;
371   typedef typename Product<Lhs,Rhs>::Scalar Scalar;
372   enum { Side = Lhs::IsVectorAtCompileTime ? OnTheLeft : OnTheRight };
373   typedef typename internal::remove_all<typename internal::conditional<int(Side)==OnTheRight,LhsNested,RhsNested>::type>::type MatrixType;
374 
375   template<typename Dest>
376   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
377   {
378     // Fallback to inner product if both the lhs and rhs is a runtime vector.
379     if (lhs.rows() == 1 && rhs.cols() == 1) {
380       dst.coeffRef(0,0) += alpha * lhs.row(0).conjugate().dot(rhs.col(0));
381       return;
382     }
383     LhsNested actual_lhs(lhs);
384     RhsNested actual_rhs(rhs);
385     internal::gemv_dense_selector<Side,
386                             (int(MatrixType::Flags)&RowMajorBit) ? RowMajor : ColMajor,
387                             bool(internal::blas_traits<MatrixType>::HasUsableDirectAccess)
388                            >::run(actual_lhs, actual_rhs, dst, alpha);
389   }
390 };
391 
392 template<typename Lhs, typename Rhs>
393 struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,CoeffBasedProductMode>
394 {
395   typedef typename Product<Lhs,Rhs>::Scalar Scalar;
396 
397   template<typename Dst>
398   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
399   {
400     // Same as: dst.noalias() = lhs.lazyProduct(rhs);
401     // but easier on the compiler side
402     call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::assign_op<typename Dst::Scalar,Scalar>());
403   }
404 
405   template<typename Dst>
406   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void addTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
407   {
408     // dst.noalias() += lhs.lazyProduct(rhs);
409     call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::add_assign_op<typename Dst::Scalar,Scalar>());
410   }
411 
412   template<typename Dst>
413   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void subTo(Dst& dst, const Lhs& lhs, const Rhs& rhs)
414   {
415     // dst.noalias() -= lhs.lazyProduct(rhs);
416     call_assignment_no_alias(dst, lhs.lazyProduct(rhs), internal::sub_assign_op<typename Dst::Scalar,Scalar>());
417   }
418 
419   // This is a special evaluation path called from generic_product_impl<...,GemmProduct> in file GeneralMatrixMatrix.h
420   // This variant tries to extract scalar multiples from both the LHS and RHS and factor them out. For instance:
421   //   dst {,+,-}= (s1*A)*(B*s2)
422   // will be rewritten as:
423   //   dst {,+,-}= (s1*s2) * (A.lazyProduct(B))
424   // There are at least four benefits of doing so:
425   //  1 - huge performance gain for heap-allocated matrix types as it save costly allocations.
426   //  2 - it is faster than simply by-passing the heap allocation through stack allocation.
427   //  3 - it makes this fallback consistent with the heavy GEMM routine.
428   //  4 - it fully by-passes huge stack allocation attempts when multiplying huge fixed-size matrices.
429   //      (see https://stackoverflow.com/questions/54738495)
430   // For small fixed sizes matrices, howver, the gains are less obvious, it is sometimes x2 faster, but sometimes x3 slower,
431   // and the behavior depends also a lot on the compiler... This is why this re-writting strategy is currently
432   // enabled only when falling back from the main GEMM.
433   template<typename Dst, typename Func>
434   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
435   void eval_dynamic(Dst& dst, const Lhs& lhs, const Rhs& rhs, const Func &func)
436   {
437     enum {
438       HasScalarFactor = blas_traits<Lhs>::HasScalarFactor || blas_traits<Rhs>::HasScalarFactor,
439       ConjLhs = blas_traits<Lhs>::NeedToConjugate,
440       ConjRhs = blas_traits<Rhs>::NeedToConjugate
441     };
442     // FIXME: in c++11 this should be auto, and extractScalarFactor should also return auto
443     //        this is important for real*complex_mat
444     Scalar actualAlpha = combine_scalar_factors<Scalar>(lhs, rhs);
445 
446     eval_dynamic_impl(dst,
447                       blas_traits<Lhs>::extract(lhs).template conjugateIf<ConjLhs>(),
448                       blas_traits<Rhs>::extract(rhs).template conjugateIf<ConjRhs>(),
449                       func,
450                       actualAlpha,
451                       typename conditional<HasScalarFactor,true_type,false_type>::type());
452   }
453 
454 protected:
455 
456   template<typename Dst, typename LhsT, typename RhsT, typename Func, typename Scalar>
457   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
458   void eval_dynamic_impl(Dst& dst, const LhsT& lhs, const RhsT& rhs, const Func &func, const Scalar&  s /* == 1 */, false_type)
459   {
460     EIGEN_UNUSED_VARIABLE(s);
461     eigen_internal_assert(s==Scalar(1));
462     call_restricted_packet_assignment_no_alias(dst, lhs.lazyProduct(rhs), func);
463   }
464 
465   template<typename Dst, typename LhsT, typename RhsT, typename Func, typename Scalar>
466   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
467   void eval_dynamic_impl(Dst& dst, const LhsT& lhs, const RhsT& rhs, const Func &func, const Scalar& s, true_type)
468   {
469     call_restricted_packet_assignment_no_alias(dst, s * lhs.lazyProduct(rhs), func);
470   }
471 };
472 
473 // This specialization enforces the use of a coefficient-based evaluation strategy
474 template<typename Lhs, typename Rhs>
475 struct generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,LazyCoeffBasedProductMode>
476   : generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,CoeffBasedProductMode> {};
477 
478 // Case 2: Evaluate coeff by coeff
479 //
480 // This is mostly taken from CoeffBasedProduct.h
481 // The main difference is that we add an extra argument to the etor_product_*_impl::run() function
482 // for the inner dimension of the product, because evaluator object do not know their size.
483 
484 template<int Traversal, int UnrollingIndex, typename Lhs, typename Rhs, typename RetScalar>
485 struct etor_product_coeff_impl;
486 
487 template<int StorageOrder, int UnrollingIndex, typename Lhs, typename Rhs, typename Packet, int LoadMode>
488 struct etor_product_packet_impl;
489 
490 template<typename Lhs, typename Rhs, int ProductTag>
491 struct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, DenseShape, DenseShape>
492     : evaluator_base<Product<Lhs, Rhs, LazyProduct> >
493 {
494   typedef Product<Lhs, Rhs, LazyProduct> XprType;
495   typedef typename XprType::Scalar Scalar;
496   typedef typename XprType::CoeffReturnType CoeffReturnType;
497 
498   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
499   explicit product_evaluator(const XprType& xpr)
500     : m_lhs(xpr.lhs()),
501       m_rhs(xpr.rhs()),
502       m_lhsImpl(m_lhs),     // FIXME the creation of the evaluator objects should result in a no-op, but check that!
503       m_rhsImpl(m_rhs),     //       Moreover, they are only useful for the packet path, so we could completely disable them when not needed,
504                             //       or perhaps declare them on the fly on the packet method... We have experiment to check what's best.
505       m_innerDim(xpr.lhs().cols())
506   {
507     EIGEN_INTERNAL_CHECK_COST_VALUE(NumTraits<Scalar>::MulCost);
508     EIGEN_INTERNAL_CHECK_COST_VALUE(NumTraits<Scalar>::AddCost);
509     EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
510 #if 0
511     std::cerr << "LhsOuterStrideBytes=  " << LhsOuterStrideBytes << "\n";
512     std::cerr << "RhsOuterStrideBytes=  " << RhsOuterStrideBytes << "\n";
513     std::cerr << "LhsAlignment=         " << LhsAlignment << "\n";
514     std::cerr << "RhsAlignment=         " << RhsAlignment << "\n";
515     std::cerr << "CanVectorizeLhs=      " << CanVectorizeLhs << "\n";
516     std::cerr << "CanVectorizeRhs=      " << CanVectorizeRhs << "\n";
517     std::cerr << "CanVectorizeInner=    " << CanVectorizeInner << "\n";
518     std::cerr << "EvalToRowMajor=       " << EvalToRowMajor << "\n";
519     std::cerr << "Alignment=            " << Alignment << "\n";
520     std::cerr << "Flags=                " << Flags << "\n";
521 #endif
522   }
523 
524   // Everything below here is taken from CoeffBasedProduct.h
525 
526   typedef typename internal::nested_eval<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;
527   typedef typename internal::nested_eval<Rhs,Lhs::RowsAtCompileTime>::type RhsNested;
528 
529   typedef typename internal::remove_all<LhsNested>::type LhsNestedCleaned;
530   typedef typename internal::remove_all<RhsNested>::type RhsNestedCleaned;
531 
532   typedef evaluator<LhsNestedCleaned> LhsEtorType;
533   typedef evaluator<RhsNestedCleaned> RhsEtorType;
534 
535   enum {
536     RowsAtCompileTime = LhsNestedCleaned::RowsAtCompileTime,
537     ColsAtCompileTime = RhsNestedCleaned::ColsAtCompileTime,
538     InnerSize = EIGEN_SIZE_MIN_PREFER_FIXED(LhsNestedCleaned::ColsAtCompileTime, RhsNestedCleaned::RowsAtCompileTime),
539     MaxRowsAtCompileTime = LhsNestedCleaned::MaxRowsAtCompileTime,
540     MaxColsAtCompileTime = RhsNestedCleaned::MaxColsAtCompileTime
541   };
542 
543   typedef typename find_best_packet<Scalar,RowsAtCompileTime>::type LhsVecPacketType;
544   typedef typename find_best_packet<Scalar,ColsAtCompileTime>::type RhsVecPacketType;
545 
546   enum {
547 
548     LhsCoeffReadCost = LhsEtorType::CoeffReadCost,
549     RhsCoeffReadCost = RhsEtorType::CoeffReadCost,
550     CoeffReadCost = InnerSize==0 ? NumTraits<Scalar>::ReadCost
551                   : InnerSize == Dynamic ? HugeCost
552                     : InnerSize * (NumTraits<Scalar>::MulCost + int(LhsCoeffReadCost) + int(RhsCoeffReadCost))
553                     + (InnerSize - 1) * NumTraits<Scalar>::AddCost,
554 
555     Unroll = CoeffReadCost <= EIGEN_UNROLLING_LIMIT,
556 
557     LhsFlags = LhsEtorType::Flags,
558     RhsFlags = RhsEtorType::Flags,
559 
560     LhsRowMajor = LhsFlags & RowMajorBit,
561     RhsRowMajor = RhsFlags & RowMajorBit,
562 
563     LhsVecPacketSize = unpacket_traits<LhsVecPacketType>::size,
564     RhsVecPacketSize = unpacket_traits<RhsVecPacketType>::size,
565 
566     // Here, we don't care about alignment larger than the usable packet size.
567     LhsAlignment = EIGEN_PLAIN_ENUM_MIN(LhsEtorType::Alignment,LhsVecPacketSize*int(sizeof(typename LhsNestedCleaned::Scalar))),
568     RhsAlignment = EIGEN_PLAIN_ENUM_MIN(RhsEtorType::Alignment,RhsVecPacketSize*int(sizeof(typename RhsNestedCleaned::Scalar))),
569 
570     SameType = is_same<typename LhsNestedCleaned::Scalar,typename RhsNestedCleaned::Scalar>::value,
571 
572     CanVectorizeRhs = bool(RhsRowMajor) && (RhsFlags & PacketAccessBit) && (ColsAtCompileTime!=1),
573     CanVectorizeLhs = (!LhsRowMajor) && (LhsFlags & PacketAccessBit) && (RowsAtCompileTime!=1),
574 
575     EvalToRowMajor = (MaxRowsAtCompileTime==1&&MaxColsAtCompileTime!=1) ? 1
576                     : (MaxColsAtCompileTime==1&&MaxRowsAtCompileTime!=1) ? 0
577                     : (bool(RhsRowMajor) && !CanVectorizeLhs),
578 
579     Flags = ((int(LhsFlags) | int(RhsFlags)) & HereditaryBits & ~RowMajorBit)
580           | (EvalToRowMajor ? RowMajorBit : 0)
581           // TODO enable vectorization for mixed types
582           | (SameType && (CanVectorizeLhs || CanVectorizeRhs) ? PacketAccessBit : 0)
583           | (XprType::IsVectorAtCompileTime ? LinearAccessBit : 0),
584 
585     LhsOuterStrideBytes = int(LhsNestedCleaned::OuterStrideAtCompileTime) * int(sizeof(typename LhsNestedCleaned::Scalar)),
586     RhsOuterStrideBytes = int(RhsNestedCleaned::OuterStrideAtCompileTime) * int(sizeof(typename RhsNestedCleaned::Scalar)),
587 
588     Alignment = bool(CanVectorizeLhs) ? (LhsOuterStrideBytes<=0 || (int(LhsOuterStrideBytes) % EIGEN_PLAIN_ENUM_MAX(1,LhsAlignment))!=0 ? 0 : LhsAlignment)
589               : bool(CanVectorizeRhs) ? (RhsOuterStrideBytes<=0 || (int(RhsOuterStrideBytes) % EIGEN_PLAIN_ENUM_MAX(1,RhsAlignment))!=0 ? 0 : RhsAlignment)
590               : 0,
591 
592     /* CanVectorizeInner deserves special explanation. It does not affect the product flags. It is not used outside
593      * of Product. If the Product itself is not a packet-access expression, there is still a chance that the inner
594      * loop of the product might be vectorized. This is the meaning of CanVectorizeInner. Since it doesn't affect
595      * the Flags, it is safe to make this value depend on ActualPacketAccessBit, that doesn't affect the ABI.
596      */
597     CanVectorizeInner =    SameType
598                         && LhsRowMajor
599                         && (!RhsRowMajor)
600                         && (int(LhsFlags) & int(RhsFlags) & ActualPacketAccessBit)
601                         && (int(InnerSize) % packet_traits<Scalar>::size == 0)
602   };
603 
604   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CoeffReturnType coeff(Index row, Index col) const
605   {
606     return (m_lhs.row(row).transpose().cwiseProduct( m_rhs.col(col) )).sum();
607   }
608 
609   /* Allow index-based non-packet access. It is impossible though to allow index-based packed access,
610    * which is why we don't set the LinearAccessBit.
611    * TODO: this seems possible when the result is a vector
612    */
613   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
614   const CoeffReturnType coeff(Index index) const
615   {
616     const Index row = (RowsAtCompileTime == 1 || MaxRowsAtCompileTime==1) ? 0 : index;
617     const Index col = (RowsAtCompileTime == 1 || MaxRowsAtCompileTime==1) ? index : 0;
618     return (m_lhs.row(row).transpose().cwiseProduct( m_rhs.col(col) )).sum();
619   }
620 
621   template<int LoadMode, typename PacketType>
622   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
623   const PacketType packet(Index row, Index col) const
624   {
625     PacketType res;
626     typedef etor_product_packet_impl<bool(int(Flags)&RowMajorBit) ? RowMajor : ColMajor,
627                                      Unroll ? int(InnerSize) : Dynamic,
628                                      LhsEtorType, RhsEtorType, PacketType, LoadMode> PacketImpl;
629     PacketImpl::run(row, col, m_lhsImpl, m_rhsImpl, m_innerDim, res);
630     return res;
631   }
632 
633   template<int LoadMode, typename PacketType>
634   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
635   const PacketType packet(Index index) const
636   {
637     const Index row = (RowsAtCompileTime == 1 || MaxRowsAtCompileTime==1) ? 0 : index;
638     const Index col = (RowsAtCompileTime == 1 || MaxRowsAtCompileTime==1) ? index : 0;
639     return packet<LoadMode,PacketType>(row,col);
640   }
641 
642 protected:
643   typename internal::add_const_on_value_type<LhsNested>::type m_lhs;
644   typename internal::add_const_on_value_type<RhsNested>::type m_rhs;
645 
646   LhsEtorType m_lhsImpl;
647   RhsEtorType m_rhsImpl;
648 
649   // TODO: Get rid of m_innerDim if known at compile time
650   Index m_innerDim;
651 };
652 
653 template<typename Lhs, typename Rhs>
654 struct product_evaluator<Product<Lhs, Rhs, DefaultProduct>, LazyCoeffBasedProductMode, DenseShape, DenseShape>
655   : product_evaluator<Product<Lhs, Rhs, LazyProduct>, CoeffBasedProductMode, DenseShape, DenseShape>
656 {
657   typedef Product<Lhs, Rhs, DefaultProduct> XprType;
658   typedef Product<Lhs, Rhs, LazyProduct> BaseProduct;
659   typedef product_evaluator<BaseProduct, CoeffBasedProductMode, DenseShape, DenseShape> Base;
660   enum {
661     Flags = Base::Flags | EvalBeforeNestingBit
662   };
663   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
664   explicit product_evaluator(const XprType& xpr)
665     : Base(BaseProduct(xpr.lhs(),xpr.rhs()))
666   {}
667 };
668 
669 /****************************************
670 *** Coeff based product, Packet path  ***
671 ****************************************/
672 
673 template<int UnrollingIndex, typename Lhs, typename Rhs, typename Packet, int LoadMode>
674 struct etor_product_packet_impl<RowMajor, UnrollingIndex, Lhs, Rhs, Packet, LoadMode>
675 {
676   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet &res)
677   {
678     etor_product_packet_impl<RowMajor, UnrollingIndex-1, Lhs, Rhs, Packet, LoadMode>::run(row, col, lhs, rhs, innerDim, res);
679     res =  pmadd(pset1<Packet>(lhs.coeff(row, Index(UnrollingIndex-1))), rhs.template packet<LoadMode,Packet>(Index(UnrollingIndex-1), col), res);
680   }
681 };
682 
683 template<int UnrollingIndex, typename Lhs, typename Rhs, typename Packet, int LoadMode>
684 struct etor_product_packet_impl<ColMajor, UnrollingIndex, Lhs, Rhs, Packet, LoadMode>
685 {
686   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet &res)
687   {
688     etor_product_packet_impl<ColMajor, UnrollingIndex-1, Lhs, Rhs, Packet, LoadMode>::run(row, col, lhs, rhs, innerDim, res);
689     res =  pmadd(lhs.template packet<LoadMode,Packet>(row, Index(UnrollingIndex-1)), pset1<Packet>(rhs.coeff(Index(UnrollingIndex-1), col)), res);
690   }
691 };
692 
693 template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
694 struct etor_product_packet_impl<RowMajor, 1, Lhs, Rhs, Packet, LoadMode>
695 {
696   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index /*innerDim*/, Packet &res)
697   {
698     res = pmul(pset1<Packet>(lhs.coeff(row, Index(0))),rhs.template packet<LoadMode,Packet>(Index(0), col));
699   }
700 };
701 
702 template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
703 struct etor_product_packet_impl<ColMajor, 1, Lhs, Rhs, Packet, LoadMode>
704 {
705   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index /*innerDim*/, Packet &res)
706   {
707     res = pmul(lhs.template packet<LoadMode,Packet>(row, Index(0)), pset1<Packet>(rhs.coeff(Index(0), col)));
708   }
709 };
710 
711 template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
712 struct etor_product_packet_impl<RowMajor, 0, Lhs, Rhs, Packet, LoadMode>
713 {
714   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, Index /*innerDim*/, Packet &res)
715   {
716     res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));
717   }
718 };
719 
720 template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
721 struct etor_product_packet_impl<ColMajor, 0, Lhs, Rhs, Packet, LoadMode>
722 {
723   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index /*row*/, Index /*col*/, const Lhs& /*lhs*/, const Rhs& /*rhs*/, Index /*innerDim*/, Packet &res)
724   {
725     res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));
726   }
727 };
728 
729 template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
730 struct etor_product_packet_impl<RowMajor, Dynamic, Lhs, Rhs, Packet, LoadMode>
731 {
732   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet& res)
733   {
734     res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));
735     for(Index i = 0; i < innerDim; ++i)
736       res =  pmadd(pset1<Packet>(lhs.coeff(row, i)), rhs.template packet<LoadMode,Packet>(i, col), res);
737   }
738 };
739 
740 template<typename Lhs, typename Rhs, typename Packet, int LoadMode>
741 struct etor_product_packet_impl<ColMajor, Dynamic, Lhs, Rhs, Packet, LoadMode>
742 {
743   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Index row, Index col, const Lhs& lhs, const Rhs& rhs, Index innerDim, Packet& res)
744   {
745     res = pset1<Packet>(typename unpacket_traits<Packet>::type(0));
746     for(Index i = 0; i < innerDim; ++i)
747       res =  pmadd(lhs.template packet<LoadMode,Packet>(row, i), pset1<Packet>(rhs.coeff(i, col)), res);
748   }
749 };
750 
751 
752 /***************************************************************************
753 * Triangular products
754 ***************************************************************************/
755 template<int Mode, bool LhsIsTriangular,
756          typename Lhs, bool LhsIsVector,
757          typename Rhs, bool RhsIsVector>
758 struct triangular_product_impl;
759 
760 template<typename Lhs, typename Rhs, int ProductTag>
761 struct generic_product_impl<Lhs,Rhs,TriangularShape,DenseShape,ProductTag>
762   : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,TriangularShape,DenseShape,ProductTag> >
763 {
764   typedef typename Product<Lhs,Rhs>::Scalar Scalar;
765 
766   template<typename Dest>
767   static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
768   {
769     triangular_product_impl<Lhs::Mode,true,typename Lhs::MatrixType,false,Rhs, Rhs::ColsAtCompileTime==1>
770         ::run(dst, lhs.nestedExpression(), rhs, alpha);
771   }
772 };
773 
774 template<typename Lhs, typename Rhs, int ProductTag>
775 struct generic_product_impl<Lhs,Rhs,DenseShape,TriangularShape,ProductTag>
776 : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,DenseShape,TriangularShape,ProductTag> >
777 {
778   typedef typename Product<Lhs,Rhs>::Scalar Scalar;
779 
780   template<typename Dest>
781   static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
782   {
783     triangular_product_impl<Rhs::Mode,false,Lhs,Lhs::RowsAtCompileTime==1, typename Rhs::MatrixType, false>::run(dst, lhs, rhs.nestedExpression(), alpha);
784   }
785 };
786 
787 
788 /***************************************************************************
789 * SelfAdjoint products
790 ***************************************************************************/
791 template <typename Lhs, int LhsMode, bool LhsIsVector,
792           typename Rhs, int RhsMode, bool RhsIsVector>
793 struct selfadjoint_product_impl;
794 
795 template<typename Lhs, typename Rhs, int ProductTag>
796 struct generic_product_impl<Lhs,Rhs,SelfAdjointShape,DenseShape,ProductTag>
797   : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,SelfAdjointShape,DenseShape,ProductTag> >
798 {
799   typedef typename Product<Lhs,Rhs>::Scalar Scalar;
800 
801   template<typename Dest>
802   static EIGEN_DEVICE_FUNC
803   void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
804   {
805     selfadjoint_product_impl<typename Lhs::MatrixType,Lhs::Mode,false,Rhs,0,Rhs::IsVectorAtCompileTime>::run(dst, lhs.nestedExpression(), rhs, alpha);
806   }
807 };
808 
809 template<typename Lhs, typename Rhs, int ProductTag>
810 struct generic_product_impl<Lhs,Rhs,DenseShape,SelfAdjointShape,ProductTag>
811 : generic_product_impl_base<Lhs,Rhs,generic_product_impl<Lhs,Rhs,DenseShape,SelfAdjointShape,ProductTag> >
812 {
813   typedef typename Product<Lhs,Rhs>::Scalar Scalar;
814 
815   template<typename Dest>
816   static void scaleAndAddTo(Dest& dst, const Lhs& lhs, const Rhs& rhs, const Scalar& alpha)
817   {
818     selfadjoint_product_impl<Lhs,0,Lhs::IsVectorAtCompileTime,typename Rhs::MatrixType,Rhs::Mode,false>::run(dst, lhs, rhs.nestedExpression(), alpha);
819   }
820 };
821 
822 
823 /***************************************************************************
824 * Diagonal products
825 ***************************************************************************/
826 
827 template<typename MatrixType, typename DiagonalType, typename Derived, int ProductOrder>
828 struct diagonal_product_evaluator_base
829   : evaluator_base<Derived>
830 {
831    typedef typename ScalarBinaryOpTraits<typename MatrixType::Scalar, typename DiagonalType::Scalar>::ReturnType Scalar;
832 public:
833   enum {
834     CoeffReadCost = int(NumTraits<Scalar>::MulCost) + int(evaluator<MatrixType>::CoeffReadCost) + int(evaluator<DiagonalType>::CoeffReadCost),
835 
836     MatrixFlags = evaluator<MatrixType>::Flags,
837     DiagFlags = evaluator<DiagonalType>::Flags,
838 
839     _StorageOrder = (Derived::MaxRowsAtCompileTime==1 && Derived::MaxColsAtCompileTime!=1) ? RowMajor
840                   : (Derived::MaxColsAtCompileTime==1 && Derived::MaxRowsAtCompileTime!=1) ? ColMajor
841                   : MatrixFlags & RowMajorBit ? RowMajor : ColMajor,
842     _SameStorageOrder = _StorageOrder == (MatrixFlags & RowMajorBit ? RowMajor : ColMajor),
843 
844     _ScalarAccessOnDiag =  !((int(_StorageOrder) == ColMajor && int(ProductOrder) == OnTheLeft)
845                            ||(int(_StorageOrder) == RowMajor && int(ProductOrder) == OnTheRight)),
846     _SameTypes = is_same<typename MatrixType::Scalar, typename DiagonalType::Scalar>::value,
847     // FIXME currently we need same types, but in the future the next rule should be the one
848     //_Vectorizable = bool(int(MatrixFlags)&PacketAccessBit) && ((!_PacketOnDiag) || (_SameTypes && bool(int(DiagFlags)&PacketAccessBit))),
849     _Vectorizable =   bool(int(MatrixFlags)&PacketAccessBit)
850                   &&  _SameTypes
851                   && (_SameStorageOrder || (MatrixFlags&LinearAccessBit)==LinearAccessBit)
852                   && (_ScalarAccessOnDiag || (bool(int(DiagFlags)&PacketAccessBit))),
853     _LinearAccessMask = (MatrixType::RowsAtCompileTime==1 || MatrixType::ColsAtCompileTime==1) ? LinearAccessBit : 0,
854     Flags = ((HereditaryBits|_LinearAccessMask) & (unsigned int)(MatrixFlags)) | (_Vectorizable ? PacketAccessBit : 0),
855     Alignment = evaluator<MatrixType>::Alignment,
856 
857     AsScalarProduct =     (DiagonalType::SizeAtCompileTime==1)
858                       ||  (DiagonalType::SizeAtCompileTime==Dynamic && MatrixType::RowsAtCompileTime==1 && ProductOrder==OnTheLeft)
859                       ||  (DiagonalType::SizeAtCompileTime==Dynamic && MatrixType::ColsAtCompileTime==1 && ProductOrder==OnTheRight)
860   };
861 
862   EIGEN_DEVICE_FUNC diagonal_product_evaluator_base(const MatrixType &mat, const DiagonalType &diag)
863     : m_diagImpl(diag), m_matImpl(mat)
864   {
865     EIGEN_INTERNAL_CHECK_COST_VALUE(NumTraits<Scalar>::MulCost);
866     EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
867   }
868 
869   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar coeff(Index idx) const
870   {
871     if(AsScalarProduct)
872       return m_diagImpl.coeff(0) * m_matImpl.coeff(idx);
873     else
874       return m_diagImpl.coeff(idx) * m_matImpl.coeff(idx);
875   }
876 
877 protected:
878   template<int LoadMode,typename PacketType>
879   EIGEN_STRONG_INLINE PacketType packet_impl(Index row, Index col, Index id, internal::true_type) const
880   {
881     return internal::pmul(m_matImpl.template packet<LoadMode,PacketType>(row, col),
882                           internal::pset1<PacketType>(m_diagImpl.coeff(id)));
883   }
884 
885   template<int LoadMode,typename PacketType>
886   EIGEN_STRONG_INLINE PacketType packet_impl(Index row, Index col, Index id, internal::false_type) const
887   {
888     enum {
889       InnerSize = (MatrixType::Flags & RowMajorBit) ? MatrixType::ColsAtCompileTime : MatrixType::RowsAtCompileTime,
890       DiagonalPacketLoadMode = EIGEN_PLAIN_ENUM_MIN(LoadMode,((InnerSize%16) == 0) ? int(Aligned16) : int(evaluator<DiagonalType>::Alignment)) // FIXME hardcoded 16!!
891     };
892     return internal::pmul(m_matImpl.template packet<LoadMode,PacketType>(row, col),
893                           m_diagImpl.template packet<DiagonalPacketLoadMode,PacketType>(id));
894   }
895 
896   evaluator<DiagonalType> m_diagImpl;
897   evaluator<MatrixType>   m_matImpl;
898 };
899 
900 // diagonal * dense
901 template<typename Lhs, typename Rhs, int ProductKind, int ProductTag>
902 struct product_evaluator<Product<Lhs, Rhs, ProductKind>, ProductTag, DiagonalShape, DenseShape>
903   : diagonal_product_evaluator_base<Rhs, typename Lhs::DiagonalVectorType, Product<Lhs, Rhs, LazyProduct>, OnTheLeft>
904 {
905   typedef diagonal_product_evaluator_base<Rhs, typename Lhs::DiagonalVectorType, Product<Lhs, Rhs, LazyProduct>, OnTheLeft> Base;
906   using Base::m_diagImpl;
907   using Base::m_matImpl;
908   using Base::coeff;
909   typedef typename Base::Scalar Scalar;
910 
911   typedef Product<Lhs, Rhs, ProductKind> XprType;
912   typedef typename XprType::PlainObject PlainObject;
913   typedef typename Lhs::DiagonalVectorType DiagonalType;
914 
915 
916   enum { StorageOrder = Base::_StorageOrder };
917 
918   EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
919     : Base(xpr.rhs(), xpr.lhs().diagonal())
920   {
921   }
922 
923   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar coeff(Index row, Index col) const
924   {
925     return m_diagImpl.coeff(row) * m_matImpl.coeff(row, col);
926   }
927 
928 #ifndef EIGEN_GPUCC
929   template<int LoadMode,typename PacketType>
930   EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const
931   {
932     // FIXME: NVCC used to complain about the template keyword, but we have to check whether this is still the case.
933     // See also similar calls below.
934     return this->template packet_impl<LoadMode,PacketType>(row,col, row,
935                                  typename internal::conditional<int(StorageOrder)==RowMajor, internal::true_type, internal::false_type>::type());
936   }
937 
938   template<int LoadMode,typename PacketType>
939   EIGEN_STRONG_INLINE PacketType packet(Index idx) const
940   {
941     return packet<LoadMode,PacketType>(int(StorageOrder)==ColMajor?idx:0,int(StorageOrder)==ColMajor?0:idx);
942   }
943 #endif
944 };
945 
946 // dense * diagonal
947 template<typename Lhs, typename Rhs, int ProductKind, int ProductTag>
948 struct product_evaluator<Product<Lhs, Rhs, ProductKind>, ProductTag, DenseShape, DiagonalShape>
949   : diagonal_product_evaluator_base<Lhs, typename Rhs::DiagonalVectorType, Product<Lhs, Rhs, LazyProduct>, OnTheRight>
950 {
951   typedef diagonal_product_evaluator_base<Lhs, typename Rhs::DiagonalVectorType, Product<Lhs, Rhs, LazyProduct>, OnTheRight> Base;
952   using Base::m_diagImpl;
953   using Base::m_matImpl;
954   using Base::coeff;
955   typedef typename Base::Scalar Scalar;
956 
957   typedef Product<Lhs, Rhs, ProductKind> XprType;
958   typedef typename XprType::PlainObject PlainObject;
959 
960   enum { StorageOrder = Base::_StorageOrder };
961 
962   EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
963     : Base(xpr.lhs(), xpr.rhs().diagonal())
964   {
965   }
966 
967   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar coeff(Index row, Index col) const
968   {
969     return m_matImpl.coeff(row, col) * m_diagImpl.coeff(col);
970   }
971 
972 #ifndef EIGEN_GPUCC
973   template<int LoadMode,typename PacketType>
974   EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const
975   {
976     return this->template packet_impl<LoadMode,PacketType>(row,col, col,
977                                  typename internal::conditional<int(StorageOrder)==ColMajor, internal::true_type, internal::false_type>::type());
978   }
979 
980   template<int LoadMode,typename PacketType>
981   EIGEN_STRONG_INLINE PacketType packet(Index idx) const
982   {
983     return packet<LoadMode,PacketType>(int(StorageOrder)==ColMajor?idx:0,int(StorageOrder)==ColMajor?0:idx);
984   }
985 #endif
986 };
987 
988 /***************************************************************************
989 * Products with permutation matrices
990 ***************************************************************************/
991 
992 /** \internal
993   * \class permutation_matrix_product
994   * Internal helper class implementing the product between a permutation matrix and a matrix.
995   * This class is specialized for DenseShape below and for SparseShape in SparseCore/SparsePermutation.h
996   */
997 template<typename ExpressionType, int Side, bool Transposed, typename ExpressionShape>
998 struct permutation_matrix_product;
999 
1000 template<typename ExpressionType, int Side, bool Transposed>
1001 struct permutation_matrix_product<ExpressionType, Side, Transposed, DenseShape>
1002 {
1003     typedef typename nested_eval<ExpressionType, 1>::type MatrixType;
1004     typedef typename remove_all<MatrixType>::type MatrixTypeCleaned;
1005 
1006     template<typename Dest, typename PermutationType>
1007     static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Dest& dst, const PermutationType& perm, const ExpressionType& xpr)
1008     {
1009       MatrixType mat(xpr);
1010       const Index n = Side==OnTheLeft ? mat.rows() : mat.cols();
1011       // FIXME we need an is_same for expression that is not sensitive to constness. For instance
1012       // is_same_xpr<Block<const Matrix>, Block<Matrix> >::value should be true.
1013       //if(is_same<MatrixTypeCleaned,Dest>::value && extract_data(dst) == extract_data(mat))
1014       if(is_same_dense(dst, mat))
1015       {
1016         // apply the permutation inplace
1017         Matrix<bool,PermutationType::RowsAtCompileTime,1,0,PermutationType::MaxRowsAtCompileTime> mask(perm.size());
1018         mask.fill(false);
1019         Index r = 0;
1020         while(r < perm.size())
1021         {
1022           // search for the next seed
1023           while(r<perm.size() && mask[r]) r++;
1024           if(r>=perm.size())
1025             break;
1026           // we got one, let's follow it until we are back to the seed
1027           Index k0 = r++;
1028           Index kPrev = k0;
1029           mask.coeffRef(k0) = true;
1030           for(Index k=perm.indices().coeff(k0); k!=k0; k=perm.indices().coeff(k))
1031           {
1032                   Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>(dst, k)
1033             .swap(Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>
1034                        (dst,((Side==OnTheLeft) ^ Transposed) ? k0 : kPrev));
1035 
1036             mask.coeffRef(k) = true;
1037             kPrev = k;
1038           }
1039         }
1040       }
1041       else
1042       {
1043         for(Index i = 0; i < n; ++i)
1044         {
1045           Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>
1046                (dst, ((Side==OnTheLeft) ^ Transposed) ? perm.indices().coeff(i) : i)
1047 
1048           =
1049 
1050           Block<const MatrixTypeCleaned,Side==OnTheLeft ? 1 : MatrixTypeCleaned::RowsAtCompileTime,Side==OnTheRight ? 1 : MatrixTypeCleaned::ColsAtCompileTime>
1051                (mat, ((Side==OnTheRight) ^ Transposed) ? perm.indices().coeff(i) : i);
1052         }
1053       }
1054     }
1055 };
1056 
1057 template<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>
1058 struct generic_product_impl<Lhs, Rhs, PermutationShape, MatrixShape, ProductTag>
1059 {
1060   template<typename Dest>
1061   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)
1062   {
1063     permutation_matrix_product<Rhs, OnTheLeft, false, MatrixShape>::run(dst, lhs, rhs);
1064   }
1065 };
1066 
1067 template<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>
1068 struct generic_product_impl<Lhs, Rhs, MatrixShape, PermutationShape, ProductTag>
1069 {
1070   template<typename Dest>
1071   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)
1072   {
1073     permutation_matrix_product<Lhs, OnTheRight, false, MatrixShape>::run(dst, rhs, lhs);
1074   }
1075 };
1076 
1077 template<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>
1078 struct generic_product_impl<Inverse<Lhs>, Rhs, PermutationShape, MatrixShape, ProductTag>
1079 {
1080   template<typename Dest>
1081   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Inverse<Lhs>& lhs, const Rhs& rhs)
1082   {
1083     permutation_matrix_product<Rhs, OnTheLeft, true, MatrixShape>::run(dst, lhs.nestedExpression(), rhs);
1084   }
1085 };
1086 
1087 template<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>
1088 struct generic_product_impl<Lhs, Inverse<Rhs>, MatrixShape, PermutationShape, ProductTag>
1089 {
1090   template<typename Dest>
1091   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Inverse<Rhs>& rhs)
1092   {
1093     permutation_matrix_product<Lhs, OnTheRight, true, MatrixShape>::run(dst, rhs.nestedExpression(), lhs);
1094   }
1095 };
1096 
1097 
1098 /***************************************************************************
1099 * Products with transpositions matrices
1100 ***************************************************************************/
1101 
1102 // FIXME could we unify Transpositions and Permutation into a single "shape"??
1103 
1104 /** \internal
1105   * \class transposition_matrix_product
1106   * Internal helper class implementing the product between a permutation matrix and a matrix.
1107   */
1108 template<typename ExpressionType, int Side, bool Transposed, typename ExpressionShape>
1109 struct transposition_matrix_product
1110 {
1111   typedef typename nested_eval<ExpressionType, 1>::type MatrixType;
1112   typedef typename remove_all<MatrixType>::type MatrixTypeCleaned;
1113 
1114   template<typename Dest, typename TranspositionType>
1115   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(Dest& dst, const TranspositionType& tr, const ExpressionType& xpr)
1116   {
1117     MatrixType mat(xpr);
1118     typedef typename TranspositionType::StorageIndex StorageIndex;
1119     const Index size = tr.size();
1120     StorageIndex j = 0;
1121 
1122     if(!is_same_dense(dst,mat))
1123       dst = mat;
1124 
1125     for(Index k=(Transposed?size-1:0) ; Transposed?k>=0:k<size ; Transposed?--k:++k)
1126       if(Index(j=tr.coeff(k))!=k)
1127       {
1128         if(Side==OnTheLeft)        dst.row(k).swap(dst.row(j));
1129         else if(Side==OnTheRight)  dst.col(k).swap(dst.col(j));
1130       }
1131   }
1132 };
1133 
1134 template<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>
1135 struct generic_product_impl<Lhs, Rhs, TranspositionsShape, MatrixShape, ProductTag>
1136 {
1137   template<typename Dest>
1138   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)
1139   {
1140     transposition_matrix_product<Rhs, OnTheLeft, false, MatrixShape>::run(dst, lhs, rhs);
1141   }
1142 };
1143 
1144 template<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>
1145 struct generic_product_impl<Lhs, Rhs, MatrixShape, TranspositionsShape, ProductTag>
1146 {
1147   template<typename Dest>
1148   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Rhs& rhs)
1149   {
1150     transposition_matrix_product<Lhs, OnTheRight, false, MatrixShape>::run(dst, rhs, lhs);
1151   }
1152 };
1153 
1154 
1155 template<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>
1156 struct generic_product_impl<Transpose<Lhs>, Rhs, TranspositionsShape, MatrixShape, ProductTag>
1157 {
1158   template<typename Dest>
1159   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Transpose<Lhs>& lhs, const Rhs& rhs)
1160   {
1161     transposition_matrix_product<Rhs, OnTheLeft, true, MatrixShape>::run(dst, lhs.nestedExpression(), rhs);
1162   }
1163 };
1164 
1165 template<typename Lhs, typename Rhs, int ProductTag, typename MatrixShape>
1166 struct generic_product_impl<Lhs, Transpose<Rhs>, MatrixShape, TranspositionsShape, ProductTag>
1167 {
1168   template<typename Dest>
1169   static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void evalTo(Dest& dst, const Lhs& lhs, const Transpose<Rhs>& rhs)
1170   {
1171     transposition_matrix_product<Lhs, OnTheRight, true, MatrixShape>::run(dst, rhs.nestedExpression(), lhs);
1172   }
1173 };
1174 
1175 } // end namespace internal
1176 
1177 } // end namespace Eigen
1178 
1179 #endif // EIGEN_PRODUCT_EVALUATORS_H
1180