xref: /aosp_15_r20/external/eigen/Eigen/src/Core/GeneralProduct.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) 2008-2011 Gael Guennebaud <[email protected]>
6 //
7 // This Source Code Form is subject to the terms of the Mozilla
8 // Public License v. 2.0. If a copy of the MPL was not distributed
9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10 
11 #ifndef EIGEN_GENERAL_PRODUCT_H
12 #define EIGEN_GENERAL_PRODUCT_H
13 
14 namespace Eigen {
15 
16 enum {
17   Large = 2,
18   Small = 3
19 };
20 
21 // Define the threshold value to fallback from the generic matrix-matrix product
22 // implementation (heavy) to the lightweight coeff-based product one.
23 // See generic_product_impl<Lhs,Rhs,DenseShape,DenseShape,GemmProduct>
24 // in products/GeneralMatrixMatrix.h for more details.
25 // TODO This threshold should also be used in the compile-time selector below.
26 #ifndef EIGEN_GEMM_TO_COEFFBASED_THRESHOLD
27 // This default value has been obtained on a Haswell architecture.
28 #define EIGEN_GEMM_TO_COEFFBASED_THRESHOLD 20
29 #endif
30 
31 namespace internal {
32 
33 template<int Rows, int Cols, int Depth> struct product_type_selector;
34 
35 template<int Size, int MaxSize> struct product_size_category
36 {
37   enum {
38     #ifndef EIGEN_GPU_COMPILE_PHASE
39     is_large = MaxSize == Dynamic ||
40                Size >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD ||
41                (Size==Dynamic && MaxSize>=EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD),
42     #else
43     is_large = 0,
44     #endif
45     value = is_large  ? Large
46           : Size == 1 ? 1
47                       : Small
48   };
49 };
50 
51 template<typename Lhs, typename Rhs> struct product_type
52 {
53   typedef typename remove_all<Lhs>::type _Lhs;
54   typedef typename remove_all<Rhs>::type _Rhs;
55   enum {
56     MaxRows = traits<_Lhs>::MaxRowsAtCompileTime,
57     Rows    = traits<_Lhs>::RowsAtCompileTime,
58     MaxCols = traits<_Rhs>::MaxColsAtCompileTime,
59     Cols    = traits<_Rhs>::ColsAtCompileTime,
60     MaxDepth = EIGEN_SIZE_MIN_PREFER_FIXED(traits<_Lhs>::MaxColsAtCompileTime,
61                                            traits<_Rhs>::MaxRowsAtCompileTime),
62     Depth = EIGEN_SIZE_MIN_PREFER_FIXED(traits<_Lhs>::ColsAtCompileTime,
63                                         traits<_Rhs>::RowsAtCompileTime)
64   };
65 
66   // the splitting into different lines of code here, introducing the _select enums and the typedef below,
67   // is to work around an internal compiler error with gcc 4.1 and 4.2.
68 private:
69   enum {
70     rows_select = product_size_category<Rows,MaxRows>::value,
71     cols_select = product_size_category<Cols,MaxCols>::value,
72     depth_select = product_size_category<Depth,MaxDepth>::value
73   };
74   typedef product_type_selector<rows_select, cols_select, depth_select> selector;
75 
76 public:
77   enum {
78     value = selector::ret,
79     ret = selector::ret
80   };
81 #ifdef EIGEN_DEBUG_PRODUCT
debugproduct_type82   static void debug()
83   {
84       EIGEN_DEBUG_VAR(Rows);
85       EIGEN_DEBUG_VAR(Cols);
86       EIGEN_DEBUG_VAR(Depth);
87       EIGEN_DEBUG_VAR(rows_select);
88       EIGEN_DEBUG_VAR(cols_select);
89       EIGEN_DEBUG_VAR(depth_select);
90       EIGEN_DEBUG_VAR(value);
91   }
92 #endif
93 };
94 
95 /* The following allows to select the kind of product at compile time
96  * based on the three dimensions of the product.
97  * This is a compile time mapping from {1,Small,Large}^3 -> {product types} */
98 // FIXME I'm not sure the current mapping is the ideal one.
99 template<int M, int N>  struct product_type_selector<M,N,1>              { enum { ret = OuterProduct }; };
100 template<int M>         struct product_type_selector<M, 1, 1>            { enum { ret = LazyCoeffBasedProductMode }; };
101 template<int N>         struct product_type_selector<1, N, 1>            { enum { ret = LazyCoeffBasedProductMode }; };
102 template<int Depth>     struct product_type_selector<1,    1,    Depth>  { enum { ret = InnerProduct }; };
103 template<>              struct product_type_selector<1,    1,    1>      { enum { ret = InnerProduct }; };
104 template<>              struct product_type_selector<Small,1,    Small>  { enum { ret = CoeffBasedProductMode }; };
105 template<>              struct product_type_selector<1,    Small,Small>  { enum { ret = CoeffBasedProductMode }; };
106 template<>              struct product_type_selector<Small,Small,Small>  { enum { ret = CoeffBasedProductMode }; };
107 template<>              struct product_type_selector<Small, Small, 1>    { enum { ret = LazyCoeffBasedProductMode }; };
108 template<>              struct product_type_selector<Small, Large, 1>    { enum { ret = LazyCoeffBasedProductMode }; };
109 template<>              struct product_type_selector<Large, Small, 1>    { enum { ret = LazyCoeffBasedProductMode }; };
110 template<>              struct product_type_selector<1,    Large,Small>  { enum { ret = CoeffBasedProductMode }; };
111 template<>              struct product_type_selector<1,    Large,Large>  { enum { ret = GemvProduct }; };
112 template<>              struct product_type_selector<1,    Small,Large>  { enum { ret = CoeffBasedProductMode }; };
113 template<>              struct product_type_selector<Large,1,    Small>  { enum { ret = CoeffBasedProductMode }; };
114 template<>              struct product_type_selector<Large,1,    Large>  { enum { ret = GemvProduct }; };
115 template<>              struct product_type_selector<Small,1,    Large>  { enum { ret = CoeffBasedProductMode }; };
116 template<>              struct product_type_selector<Small,Small,Large>  { enum { ret = GemmProduct }; };
117 template<>              struct product_type_selector<Large,Small,Large>  { enum { ret = GemmProduct }; };
118 template<>              struct product_type_selector<Small,Large,Large>  { enum { ret = GemmProduct }; };
119 template<>              struct product_type_selector<Large,Large,Large>  { enum { ret = GemmProduct }; };
120 template<>              struct product_type_selector<Large,Small,Small>  { enum { ret = CoeffBasedProductMode }; };
121 template<>              struct product_type_selector<Small,Large,Small>  { enum { ret = CoeffBasedProductMode }; };
122 template<>              struct product_type_selector<Large,Large,Small>  { enum { ret = GemmProduct }; };
123 
124 } // end namespace internal
125 
126 /***********************************************************************
127 *  Implementation of Inner Vector Vector Product
128 ***********************************************************************/
129 
130 // FIXME : maybe the "inner product" could return a Scalar
131 // instead of a 1x1 matrix ??
132 // Pro: more natural for the user
133 // Cons: this could be a problem if in a meta unrolled algorithm a matrix-matrix
134 // product ends up to a row-vector times col-vector product... To tackle this use
135 // case, we could have a specialization for Block<MatrixType,1,1> with: operator=(Scalar x);
136 
137 /***********************************************************************
138 *  Implementation of Outer Vector Vector Product
139 ***********************************************************************/
140 
141 /***********************************************************************
142 *  Implementation of General Matrix Vector Product
143 ***********************************************************************/
144 
145 /*  According to the shape/flags of the matrix we have to distinghish 3 different cases:
146  *   1 - the matrix is col-major, BLAS compatible and M is large => call fast BLAS-like colmajor routine
147  *   2 - the matrix is row-major, BLAS compatible and N is large => call fast BLAS-like rowmajor routine
148  *   3 - all other cases are handled using a simple loop along the outer-storage direction.
149  *  Therefore we need a lower level meta selector.
150  *  Furthermore, if the matrix is the rhs, then the product has to be transposed.
151  */
152 namespace internal {
153 
154 template<int Side, int StorageOrder, bool BlasCompatible>
155 struct gemv_dense_selector;
156 
157 } // end namespace internal
158 
159 namespace internal {
160 
161 template<typename Scalar,int Size,int MaxSize,bool Cond> struct gemv_static_vector_if;
162 
163 template<typename Scalar,int Size,int MaxSize>
164 struct gemv_static_vector_if<Scalar,Size,MaxSize,false>
165 {
166   EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Scalar* data() { eigen_internal_assert(false && "should never be called"); return 0; }
167 };
168 
169 template<typename Scalar,int Size>
170 struct gemv_static_vector_if<Scalar,Size,Dynamic,true>
171 {
172   EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Scalar* data() { return 0; }
173 };
174 
175 template<typename Scalar,int Size,int MaxSize>
176 struct gemv_static_vector_if<Scalar,Size,MaxSize,true>
177 {
178   enum {
179     ForceAlignment  = internal::packet_traits<Scalar>::Vectorizable,
180     PacketSize      = internal::packet_traits<Scalar>::size
181   };
182   #if EIGEN_MAX_STATIC_ALIGN_BYTES!=0
183   internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize),0,EIGEN_PLAIN_ENUM_MIN(AlignedMax,PacketSize)> m_data;
184   EIGEN_STRONG_INLINE Scalar* data() { return m_data.array; }
185   #else
186   // Some architectures cannot align on the stack,
187   // => let's manually enforce alignment by allocating more data and return the address of the first aligned element.
188   internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize)+(ForceAlignment?EIGEN_MAX_ALIGN_BYTES:0),0> m_data;
189   EIGEN_STRONG_INLINE Scalar* data() {
190     return ForceAlignment
191             ? reinterpret_cast<Scalar*>((internal::UIntPtr(m_data.array) & ~(std::size_t(EIGEN_MAX_ALIGN_BYTES-1))) + EIGEN_MAX_ALIGN_BYTES)
192             : m_data.array;
193   }
194   #endif
195 };
196 
197 // The vector is on the left => transposition
198 template<int StorageOrder, bool BlasCompatible>
199 struct gemv_dense_selector<OnTheLeft,StorageOrder,BlasCompatible>
200 {
201   template<typename Lhs, typename Rhs, typename Dest>
202   static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
203   {
204     Transpose<Dest> destT(dest);
205     enum { OtherStorageOrder = StorageOrder == RowMajor ? ColMajor : RowMajor };
206     gemv_dense_selector<OnTheRight,OtherStorageOrder,BlasCompatible>
207       ::run(rhs.transpose(), lhs.transpose(), destT, alpha);
208   }
209 };
210 
211 template<> struct gemv_dense_selector<OnTheRight,ColMajor,true>
212 {
213   template<typename Lhs, typename Rhs, typename Dest>
214   static inline void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
215   {
216     typedef typename Lhs::Scalar   LhsScalar;
217     typedef typename Rhs::Scalar   RhsScalar;
218     typedef typename Dest::Scalar  ResScalar;
219     typedef typename Dest::RealScalar  RealScalar;
220 
221     typedef internal::blas_traits<Lhs> LhsBlasTraits;
222     typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
223     typedef internal::blas_traits<Rhs> RhsBlasTraits;
224     typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
225 
226     typedef Map<Matrix<ResScalar,Dynamic,1>, EIGEN_PLAIN_ENUM_MIN(AlignedMax,internal::packet_traits<ResScalar>::size)> MappedDest;
227 
228     ActualLhsType actualLhs = LhsBlasTraits::extract(lhs);
229     ActualRhsType actualRhs = RhsBlasTraits::extract(rhs);
230 
231     ResScalar actualAlpha = combine_scalar_factors(alpha, lhs, rhs);
232 
233     // make sure Dest is a compile-time vector type (bug 1166)
234     typedef typename conditional<Dest::IsVectorAtCompileTime, Dest, typename Dest::ColXpr>::type ActualDest;
235 
236     enum {
237       // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
238       // on, the other hand it is good for the cache to pack the vector anyways...
239       EvalToDestAtCompileTime = (ActualDest::InnerStrideAtCompileTime==1),
240       ComplexByReal = (NumTraits<LhsScalar>::IsComplex) && (!NumTraits<RhsScalar>::IsComplex),
241       MightCannotUseDest = ((!EvalToDestAtCompileTime) || ComplexByReal) && (ActualDest::MaxSizeAtCompileTime!=0)
242     };
243 
244     typedef const_blas_data_mapper<LhsScalar,Index,ColMajor> LhsMapper;
245     typedef const_blas_data_mapper<RhsScalar,Index,RowMajor> RhsMapper;
246     RhsScalar compatibleAlpha = get_factor<ResScalar,RhsScalar>::run(actualAlpha);
247 
248     if(!MightCannotUseDest)
249     {
250       // shortcut if we are sure to be able to use dest directly,
251       // this ease the compiler to generate cleaner and more optimzized code for most common cases
252       general_matrix_vector_product
253           <Index,LhsScalar,LhsMapper,ColMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(
254           actualLhs.rows(), actualLhs.cols(),
255           LhsMapper(actualLhs.data(), actualLhs.outerStride()),
256           RhsMapper(actualRhs.data(), actualRhs.innerStride()),
257           dest.data(), 1,
258           compatibleAlpha);
259     }
260     else
261     {
262       gemv_static_vector_if<ResScalar,ActualDest::SizeAtCompileTime,ActualDest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;
263 
264       const bool alphaIsCompatible = (!ComplexByReal) || (numext::imag(actualAlpha)==RealScalar(0));
265       const bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;
266 
267       ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),
268                                                     evalToDest ? dest.data() : static_dest.data());
269 
270       if(!evalToDest)
271       {
272         #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
273         Index size = dest.size();
274         EIGEN_DENSE_STORAGE_CTOR_PLUGIN
275         #endif
276         if(!alphaIsCompatible)
277         {
278           MappedDest(actualDestPtr, dest.size()).setZero();
279           compatibleAlpha = RhsScalar(1);
280         }
281         else
282           MappedDest(actualDestPtr, dest.size()) = dest;
283       }
284 
285       general_matrix_vector_product
286           <Index,LhsScalar,LhsMapper,ColMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(
287           actualLhs.rows(), actualLhs.cols(),
288           LhsMapper(actualLhs.data(), actualLhs.outerStride()),
289           RhsMapper(actualRhs.data(), actualRhs.innerStride()),
290           actualDestPtr, 1,
291           compatibleAlpha);
292 
293       if (!evalToDest)
294       {
295         if(!alphaIsCompatible)
296           dest.matrix() += actualAlpha * MappedDest(actualDestPtr, dest.size());
297         else
298           dest = MappedDest(actualDestPtr, dest.size());
299       }
300     }
301   }
302 };
303 
304 template<> struct gemv_dense_selector<OnTheRight,RowMajor,true>
305 {
306   template<typename Lhs, typename Rhs, typename Dest>
307   static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
308   {
309     typedef typename Lhs::Scalar   LhsScalar;
310     typedef typename Rhs::Scalar   RhsScalar;
311     typedef typename Dest::Scalar  ResScalar;
312 
313     typedef internal::blas_traits<Lhs> LhsBlasTraits;
314     typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
315     typedef internal::blas_traits<Rhs> RhsBlasTraits;
316     typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
317     typedef typename internal::remove_all<ActualRhsType>::type ActualRhsTypeCleaned;
318 
319     typename add_const<ActualLhsType>::type actualLhs = LhsBlasTraits::extract(lhs);
320     typename add_const<ActualRhsType>::type actualRhs = RhsBlasTraits::extract(rhs);
321 
322     ResScalar actualAlpha = combine_scalar_factors(alpha, lhs, rhs);
323 
324     enum {
325       // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
326       // on, the other hand it is good for the cache to pack the vector anyways...
327       DirectlyUseRhs = ActualRhsTypeCleaned::InnerStrideAtCompileTime==1 || ActualRhsTypeCleaned::MaxSizeAtCompileTime==0
328     };
329 
330     gemv_static_vector_if<RhsScalar,ActualRhsTypeCleaned::SizeAtCompileTime,ActualRhsTypeCleaned::MaxSizeAtCompileTime,!DirectlyUseRhs> static_rhs;
331 
332     ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,actualRhs.size(),
333         DirectlyUseRhs ? const_cast<RhsScalar*>(actualRhs.data()) : static_rhs.data());
334 
335     if(!DirectlyUseRhs)
336     {
337       #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
338       Index size = actualRhs.size();
339       EIGEN_DENSE_STORAGE_CTOR_PLUGIN
340       #endif
341       Map<typename ActualRhsTypeCleaned::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
342     }
343 
344     typedef const_blas_data_mapper<LhsScalar,Index,RowMajor> LhsMapper;
345     typedef const_blas_data_mapper<RhsScalar,Index,ColMajor> RhsMapper;
346     general_matrix_vector_product
347         <Index,LhsScalar,LhsMapper,RowMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(
348         actualLhs.rows(), actualLhs.cols(),
349         LhsMapper(actualLhs.data(), actualLhs.outerStride()),
350         RhsMapper(actualRhsPtr, 1),
351         dest.data(), dest.col(0).innerStride(), //NOTE  if dest is not a vector at compile-time, then dest.innerStride() might be wrong. (bug 1166)
352         actualAlpha);
353   }
354 };
355 
356 template<> struct gemv_dense_selector<OnTheRight,ColMajor,false>
357 {
358   template<typename Lhs, typename Rhs, typename Dest>
359   static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
360   {
361     EIGEN_STATIC_ASSERT((!nested_eval<Lhs,1>::Evaluate),EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE);
362     // TODO if rhs is large enough it might be beneficial to make sure that dest is sequentially stored in memory, otherwise use a temp
363     typename nested_eval<Rhs,1>::type actual_rhs(rhs);
364     const Index size = rhs.rows();
365     for(Index k=0; k<size; ++k)
366       dest += (alpha*actual_rhs.coeff(k)) * lhs.col(k);
367   }
368 };
369 
370 template<> struct gemv_dense_selector<OnTheRight,RowMajor,false>
371 {
372   template<typename Lhs, typename Rhs, typename Dest>
373   static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
374   {
375     EIGEN_STATIC_ASSERT((!nested_eval<Lhs,1>::Evaluate),EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE);
376     typename nested_eval<Rhs,Lhs::RowsAtCompileTime>::type actual_rhs(rhs);
377     const Index rows = dest.rows();
378     for(Index i=0; i<rows; ++i)
379       dest.coeffRef(i) += alpha * (lhs.row(i).cwiseProduct(actual_rhs.transpose())).sum();
380   }
381 };
382 
383 } // end namespace internal
384 
385 /***************************************************************************
386 * Implementation of matrix base methods
387 ***************************************************************************/
388 
389 /** \returns the matrix product of \c *this and \a other.
390   *
391   * \note If instead of the matrix product you want the coefficient-wise product, see Cwise::operator*().
392   *
393   * \sa lazyProduct(), operator*=(const MatrixBase&), Cwise::operator*()
394   */
395 template<typename Derived>
396 template<typename OtherDerived>
397 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
398 const Product<Derived, OtherDerived>
399 MatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const
400 {
401   // A note regarding the function declaration: In MSVC, this function will sometimes
402   // not be inlined since DenseStorage is an unwindable object for dynamic
403   // matrices and product types are holding a member to store the result.
404   // Thus it does not help tagging this function with EIGEN_STRONG_INLINE.
405   enum {
406     ProductIsValid =  Derived::ColsAtCompileTime==Dynamic
407                    || OtherDerived::RowsAtCompileTime==Dynamic
408                    || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
409     AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
410     SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
411   };
412   // note to the lost user:
413   //    * for a dot product use: v1.dot(v2)
414   //    * for a coeff-wise product use: v1.cwiseProduct(v2)
415   EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
416     INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
417   EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
418     INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
419   EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
420 #ifdef EIGEN_DEBUG_PRODUCT
421   internal::product_type<Derived,OtherDerived>::debug();
422 #endif
423 
424   return Product<Derived, OtherDerived>(derived(), other.derived());
425 }
426 
427 /** \returns an expression of the matrix product of \c *this and \a other without implicit evaluation.
428   *
429   * The returned product will behave like any other expressions: the coefficients of the product will be
430   * computed once at a time as requested. This might be useful in some extremely rare cases when only
431   * a small and no coherent fraction of the result's coefficients have to be computed.
432   *
433   * \warning This version of the matrix product can be much much slower. So use it only if you know
434   * what you are doing and that you measured a true speed improvement.
435   *
436   * \sa operator*(const MatrixBase&)
437   */
438 template<typename Derived>
439 template<typename OtherDerived>
440 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
441 const Product<Derived,OtherDerived,LazyProduct>
442 MatrixBase<Derived>::lazyProduct(const MatrixBase<OtherDerived> &other) const
443 {
444   enum {
445     ProductIsValid =  Derived::ColsAtCompileTime==Dynamic
446                    || OtherDerived::RowsAtCompileTime==Dynamic
447                    || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
448     AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
449     SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
450   };
451   // note to the lost user:
452   //    * for a dot product use: v1.dot(v2)
453   //    * for a coeff-wise product use: v1.cwiseProduct(v2)
454   EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
455     INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
456   EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
457     INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
458   EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
459 
460   return Product<Derived,OtherDerived,LazyProduct>(derived(), other.derived());
461 }
462 
463 } // end namespace Eigen
464 
465 #endif // EIGEN_PRODUCT_H
466