1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
5 // Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
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 namespace internal {
22 
23 template<int Rows, int Cols, int Depth> struct product_type_selector;
24 
25 template<int Size, int MaxSize> struct product_size_category
26 {
27   enum {
28     #ifndef EIGEN_CUDA_ARCH
29     is_large = MaxSize == Dynamic ||
30                Size >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD ||
31                (Size==Dynamic && MaxSize>=EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD),
32     #else
33     is_large = 0,
34     #endif
35     value = is_large  ? Large
36           : Size == 1 ? 1
37                       : Small
38   };
39 };
40 
41 template<typename Lhs, typename Rhs> struct product_type
42 {
43   typedef typename remove_all<Lhs>::type _Lhs;
44   typedef typename remove_all<Rhs>::type _Rhs;
45   enum {
46     MaxRows = traits<_Lhs>::MaxRowsAtCompileTime,
47     Rows    = traits<_Lhs>::RowsAtCompileTime,
48     MaxCols = traits<_Rhs>::MaxColsAtCompileTime,
49     Cols    = traits<_Rhs>::ColsAtCompileTime,
50     MaxDepth = EIGEN_SIZE_MIN_PREFER_FIXED(traits<_Lhs>::MaxColsAtCompileTime,
51                                            traits<_Rhs>::MaxRowsAtCompileTime),
52     Depth = EIGEN_SIZE_MIN_PREFER_FIXED(traits<_Lhs>::ColsAtCompileTime,
53                                         traits<_Rhs>::RowsAtCompileTime)
54   };
55 
56   // the splitting into different lines of code here, introducing the _select enums and the typedef below,
57   // is to work around an internal compiler error with gcc 4.1 and 4.2.
58 private:
59   enum {
60     rows_select = product_size_category<Rows,MaxRows>::value,
61     cols_select = product_size_category<Cols,MaxCols>::value,
62     depth_select = product_size_category<Depth,MaxDepth>::value
63   };
64   typedef product_type_selector<rows_select, cols_select, depth_select> selector;
65 
66 public:
67   enum {
68     value = selector::ret,
69     ret = selector::ret
70   };
71 #ifdef EIGEN_DEBUG_PRODUCT
debugproduct_type72   static void debug()
73   {
74       EIGEN_DEBUG_VAR(Rows);
75       EIGEN_DEBUG_VAR(Cols);
76       EIGEN_DEBUG_VAR(Depth);
77       EIGEN_DEBUG_VAR(rows_select);
78       EIGEN_DEBUG_VAR(cols_select);
79       EIGEN_DEBUG_VAR(depth_select);
80       EIGEN_DEBUG_VAR(value);
81   }
82 #endif
83 };
84 
85 /* The following allows to select the kind of product at compile time
86  * based on the three dimensions of the product.
87  * This is a compile time mapping from {1,Small,Large}^3 -> {product types} */
88 // FIXME I'm not sure the current mapping is the ideal one.
89 template<int M, int N>  struct product_type_selector<M,N,1>              { enum { ret = OuterProduct }; };
90 template<int M>         struct product_type_selector<M, 1, 1>            { enum { ret = LazyCoeffBasedProductMode }; };
91 template<int N>         struct product_type_selector<1, N, 1>            { enum { ret = LazyCoeffBasedProductMode }; };
92 template<int Depth>     struct product_type_selector<1,    1,    Depth>  { enum { ret = InnerProduct }; };
93 template<>              struct product_type_selector<1,    1,    1>      { enum { ret = InnerProduct }; };
94 template<>              struct product_type_selector<Small,1,    Small>  { enum { ret = CoeffBasedProductMode }; };
95 template<>              struct product_type_selector<1,    Small,Small>  { enum { ret = CoeffBasedProductMode }; };
96 template<>              struct product_type_selector<Small,Small,Small>  { enum { ret = CoeffBasedProductMode }; };
97 template<>              struct product_type_selector<Small, Small, 1>    { enum { ret = LazyCoeffBasedProductMode }; };
98 template<>              struct product_type_selector<Small, Large, 1>    { enum { ret = LazyCoeffBasedProductMode }; };
99 template<>              struct product_type_selector<Large, Small, 1>    { enum { ret = LazyCoeffBasedProductMode }; };
100 template<>              struct product_type_selector<1,    Large,Small>  { enum { ret = CoeffBasedProductMode }; };
101 template<>              struct product_type_selector<1,    Large,Large>  { enum { ret = GemvProduct }; };
102 template<>              struct product_type_selector<1,    Small,Large>  { enum { ret = CoeffBasedProductMode }; };
103 template<>              struct product_type_selector<Large,1,    Small>  { enum { ret = CoeffBasedProductMode }; };
104 template<>              struct product_type_selector<Large,1,    Large>  { enum { ret = GemvProduct }; };
105 template<>              struct product_type_selector<Small,1,    Large>  { enum { ret = CoeffBasedProductMode }; };
106 template<>              struct product_type_selector<Small,Small,Large>  { enum { ret = GemmProduct }; };
107 template<>              struct product_type_selector<Large,Small,Large>  { enum { ret = GemmProduct }; };
108 template<>              struct product_type_selector<Small,Large,Large>  { enum { ret = GemmProduct }; };
109 template<>              struct product_type_selector<Large,Large,Large>  { enum { ret = GemmProduct }; };
110 template<>              struct product_type_selector<Large,Small,Small>  { enum { ret = CoeffBasedProductMode }; };
111 template<>              struct product_type_selector<Small,Large,Small>  { enum { ret = CoeffBasedProductMode }; };
112 template<>              struct product_type_selector<Large,Large,Small>  { enum { ret = GemmProduct }; };
113 
114 } // end namespace internal
115 
116 /***********************************************************************
117 *  Implementation of Inner Vector Vector Product
118 ***********************************************************************/
119 
120 // FIXME : maybe the "inner product" could return a Scalar
121 // instead of a 1x1 matrix ??
122 // Pro: more natural for the user
123 // Cons: this could be a problem if in a meta unrolled algorithm a matrix-matrix
124 // product ends up to a row-vector times col-vector product... To tackle this use
125 // case, we could have a specialization for Block<MatrixType,1,1> with: operator=(Scalar x);
126 
127 /***********************************************************************
128 *  Implementation of Outer Vector Vector Product
129 ***********************************************************************/
130 
131 /***********************************************************************
132 *  Implementation of General Matrix Vector Product
133 ***********************************************************************/
134 
135 /*  According to the shape/flags of the matrix we have to distinghish 3 different cases:
136  *   1 - the matrix is col-major, BLAS compatible and M is large => call fast BLAS-like colmajor routine
137  *   2 - the matrix is row-major, BLAS compatible and N is large => call fast BLAS-like rowmajor routine
138  *   3 - all other cases are handled using a simple loop along the outer-storage direction.
139  *  Therefore we need a lower level meta selector.
140  *  Furthermore, if the matrix is the rhs, then the product has to be transposed.
141  */
142 namespace internal {
143 
144 template<int Side, int StorageOrder, bool BlasCompatible>
145 struct gemv_dense_selector;
146 
147 } // end namespace internal
148 
149 namespace internal {
150 
151 template<typename Scalar,int Size,int MaxSize,bool Cond> struct gemv_static_vector_if;
152 
153 template<typename Scalar,int Size,int MaxSize>
154 struct gemv_static_vector_if<Scalar,Size,MaxSize,false>
155 {
156   EIGEN_STRONG_INLINE  Scalar* data() { eigen_internal_assert(false && "should never be called"); return 0; }
157 };
158 
159 template<typename Scalar,int Size>
160 struct gemv_static_vector_if<Scalar,Size,Dynamic,true>
161 {
162   EIGEN_STRONG_INLINE Scalar* data() { return 0; }
163 };
164 
165 template<typename Scalar,int Size,int MaxSize>
166 struct gemv_static_vector_if<Scalar,Size,MaxSize,true>
167 {
168   enum {
169     ForceAlignment  = internal::packet_traits<Scalar>::Vectorizable,
170     PacketSize      = internal::packet_traits<Scalar>::size
171   };
172   #if EIGEN_MAX_STATIC_ALIGN_BYTES!=0
173   internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize),0,EIGEN_PLAIN_ENUM_MIN(AlignedMax,PacketSize)> m_data;
174   EIGEN_STRONG_INLINE Scalar* data() { return m_data.array; }
175   #else
176   // Some architectures cannot align on the stack,
177   // => let's manually enforce alignment by allocating more data and return the address of the first aligned element.
178   internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize)+(ForceAlignment?EIGEN_MAX_ALIGN_BYTES:0),0> m_data;
179   EIGEN_STRONG_INLINE Scalar* data() {
180     return ForceAlignment
181             ? reinterpret_cast<Scalar*>((internal::UIntPtr(m_data.array) & ~(std::size_t(EIGEN_MAX_ALIGN_BYTES-1))) + EIGEN_MAX_ALIGN_BYTES)
182             : m_data.array;
183   }
184   #endif
185 };
186 
187 // The vector is on the left => transposition
188 template<int StorageOrder, bool BlasCompatible>
189 struct gemv_dense_selector<OnTheLeft,StorageOrder,BlasCompatible>
190 {
191   template<typename Lhs, typename Rhs, typename Dest>
192   static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
193   {
194     Transpose<Dest> destT(dest);
195     enum { OtherStorageOrder = StorageOrder == RowMajor ? ColMajor : RowMajor };
196     gemv_dense_selector<OnTheRight,OtherStorageOrder,BlasCompatible>
197       ::run(rhs.transpose(), lhs.transpose(), destT, alpha);
198   }
199 };
200 
201 template<> struct gemv_dense_selector<OnTheRight,ColMajor,true>
202 {
203   template<typename Lhs, typename Rhs, typename Dest>
204   static inline void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
205   {
206     typedef typename Lhs::Scalar   LhsScalar;
207     typedef typename Rhs::Scalar   RhsScalar;
208     typedef typename Dest::Scalar  ResScalar;
209     typedef typename Dest::RealScalar  RealScalar;
210 
211     typedef internal::blas_traits<Lhs> LhsBlasTraits;
212     typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
213     typedef internal::blas_traits<Rhs> RhsBlasTraits;
214     typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
215 
216     typedef Map<Matrix<ResScalar,Dynamic,1>, EIGEN_PLAIN_ENUM_MIN(AlignedMax,internal::packet_traits<ResScalar>::size)> MappedDest;
217 
218     ActualLhsType actualLhs = LhsBlasTraits::extract(lhs);
219     ActualRhsType actualRhs = RhsBlasTraits::extract(rhs);
220 
221     ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(lhs)
222                                   * RhsBlasTraits::extractScalarFactor(rhs);
223 
224     // make sure Dest is a compile-time vector type (bug 1166)
225     typedef typename conditional<Dest::IsVectorAtCompileTime, Dest, typename Dest::ColXpr>::type ActualDest;
226 
227     enum {
228       // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
229       // on, the other hand it is good for the cache to pack the vector anyways...
230       EvalToDestAtCompileTime = (ActualDest::InnerStrideAtCompileTime==1),
231       ComplexByReal = (NumTraits<LhsScalar>::IsComplex) && (!NumTraits<RhsScalar>::IsComplex),
232       MightCannotUseDest = (!EvalToDestAtCompileTime) || ComplexByReal
233     };
234 
235     typedef const_blas_data_mapper<LhsScalar,Index,ColMajor> LhsMapper;
236     typedef const_blas_data_mapper<RhsScalar,Index,RowMajor> RhsMapper;
237     RhsScalar compatibleAlpha = get_factor<ResScalar,RhsScalar>::run(actualAlpha);
238 
239     if(!MightCannotUseDest)
240     {
241       // shortcut if we are sure to be able to use dest directly,
242       // this ease the compiler to generate cleaner and more optimzized code for most common cases
243       general_matrix_vector_product
244           <Index,LhsScalar,LhsMapper,ColMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(
245           actualLhs.rows(), actualLhs.cols(),
246           LhsMapper(actualLhs.data(), actualLhs.outerStride()),
247           RhsMapper(actualRhs.data(), actualRhs.innerStride()),
248           dest.data(), 1,
249           compatibleAlpha);
250     }
251     else
252     {
253       gemv_static_vector_if<ResScalar,ActualDest::SizeAtCompileTime,ActualDest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;
254 
255       const bool alphaIsCompatible = (!ComplexByReal) || (numext::imag(actualAlpha)==RealScalar(0));
256       const bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;
257 
258       ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),
259                                                     evalToDest ? dest.data() : static_dest.data());
260 
261       if(!evalToDest)
262       {
263         #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
264         Index size = dest.size();
265         EIGEN_DENSE_STORAGE_CTOR_PLUGIN
266         #endif
267         if(!alphaIsCompatible)
268         {
269           MappedDest(actualDestPtr, dest.size()).setZero();
270           compatibleAlpha = RhsScalar(1);
271         }
272         else
273           MappedDest(actualDestPtr, dest.size()) = dest;
274       }
275 
276       general_matrix_vector_product
277           <Index,LhsScalar,LhsMapper,ColMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(
278           actualLhs.rows(), actualLhs.cols(),
279           LhsMapper(actualLhs.data(), actualLhs.outerStride()),
280           RhsMapper(actualRhs.data(), actualRhs.innerStride()),
281           actualDestPtr, 1,
282           compatibleAlpha);
283 
284       if (!evalToDest)
285       {
286         if(!alphaIsCompatible)
287           dest.matrix() += actualAlpha * MappedDest(actualDestPtr, dest.size());
288         else
289           dest = MappedDest(actualDestPtr, dest.size());
290       }
291     }
292   }
293 };
294 
295 template<> struct gemv_dense_selector<OnTheRight,RowMajor,true>
296 {
297   template<typename Lhs, typename Rhs, typename Dest>
298   static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
299   {
300     typedef typename Lhs::Scalar   LhsScalar;
301     typedef typename Rhs::Scalar   RhsScalar;
302     typedef typename Dest::Scalar  ResScalar;
303 
304     typedef internal::blas_traits<Lhs> LhsBlasTraits;
305     typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
306     typedef internal::blas_traits<Rhs> RhsBlasTraits;
307     typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
308     typedef typename internal::remove_all<ActualRhsType>::type ActualRhsTypeCleaned;
309 
310     typename add_const<ActualLhsType>::type actualLhs = LhsBlasTraits::extract(lhs);
311     typename add_const<ActualRhsType>::type actualRhs = RhsBlasTraits::extract(rhs);
312 
313     ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(lhs)
314                                   * RhsBlasTraits::extractScalarFactor(rhs);
315 
316     enum {
317       // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
318       // on, the other hand it is good for the cache to pack the vector anyways...
319       DirectlyUseRhs = ActualRhsTypeCleaned::InnerStrideAtCompileTime==1
320     };
321 
322     gemv_static_vector_if<RhsScalar,ActualRhsTypeCleaned::SizeAtCompileTime,ActualRhsTypeCleaned::MaxSizeAtCompileTime,!DirectlyUseRhs> static_rhs;
323 
324     ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,actualRhs.size(),
325         DirectlyUseRhs ? const_cast<RhsScalar*>(actualRhs.data()) : static_rhs.data());
326 
327     if(!DirectlyUseRhs)
328     {
329       #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
330       Index size = actualRhs.size();
331       EIGEN_DENSE_STORAGE_CTOR_PLUGIN
332       #endif
333       Map<typename ActualRhsTypeCleaned::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
334     }
335 
336     typedef const_blas_data_mapper<LhsScalar,Index,RowMajor> LhsMapper;
337     typedef const_blas_data_mapper<RhsScalar,Index,ColMajor> RhsMapper;
338     general_matrix_vector_product
339         <Index,LhsScalar,LhsMapper,RowMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(
340         actualLhs.rows(), actualLhs.cols(),
341         LhsMapper(actualLhs.data(), actualLhs.outerStride()),
342         RhsMapper(actualRhsPtr, 1),
343         dest.data(), dest.col(0).innerStride(), //NOTE  if dest is not a vector at compile-time, then dest.innerStride() might be wrong. (bug 1166)
344         actualAlpha);
345   }
346 };
347 
348 template<> struct gemv_dense_selector<OnTheRight,ColMajor,false>
349 {
350   template<typename Lhs, typename Rhs, typename Dest>
351   static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
352   {
353     EIGEN_STATIC_ASSERT((!nested_eval<Lhs,1>::Evaluate),EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE);
354     // TODO if rhs is large enough it might be beneficial to make sure that dest is sequentially stored in memory, otherwise use a temp
355     typename nested_eval<Rhs,1>::type actual_rhs(rhs);
356     const Index size = rhs.rows();
357     for(Index k=0; k<size; ++k)
358       dest += (alpha*actual_rhs.coeff(k)) * lhs.col(k);
359   }
360 };
361 
362 template<> struct gemv_dense_selector<OnTheRight,RowMajor,false>
363 {
364   template<typename Lhs, typename Rhs, typename Dest>
365   static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
366   {
367     EIGEN_STATIC_ASSERT((!nested_eval<Lhs,1>::Evaluate),EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE);
368     typename nested_eval<Rhs,Lhs::RowsAtCompileTime>::type actual_rhs(rhs);
369     const Index rows = dest.rows();
370     for(Index i=0; i<rows; ++i)
371       dest.coeffRef(i) += alpha * (lhs.row(i).cwiseProduct(actual_rhs.transpose())).sum();
372   }
373 };
374 
375 } // end namespace internal
376 
377 /***************************************************************************
378 * Implementation of matrix base methods
379 ***************************************************************************/
380 
381 /** \returns the matrix product of \c *this and \a other.
382   *
383   * \note If instead of the matrix product you want the coefficient-wise product, see Cwise::operator*().
384   *
385   * \sa lazyProduct(), operator*=(const MatrixBase&), Cwise::operator*()
386   */
387 template<typename Derived>
388 template<typename OtherDerived>
389 inline const Product<Derived, OtherDerived>
390 MatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const
391 {
392   // A note regarding the function declaration: In MSVC, this function will sometimes
393   // not be inlined since DenseStorage is an unwindable object for dynamic
394   // matrices and product types are holding a member to store the result.
395   // Thus it does not help tagging this function with EIGEN_STRONG_INLINE.
396   enum {
397     ProductIsValid =  Derived::ColsAtCompileTime==Dynamic
398                    || OtherDerived::RowsAtCompileTime==Dynamic
399                    || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
400     AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
401     SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
402   };
403   // note to the lost user:
404   //    * for a dot product use: v1.dot(v2)
405   //    * for a coeff-wise product use: v1.cwiseProduct(v2)
406   EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
407     INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
408   EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
409     INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
410   EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
411 #ifdef EIGEN_DEBUG_PRODUCT
412   internal::product_type<Derived,OtherDerived>::debug();
413 #endif
414 
415   return Product<Derived, OtherDerived>(derived(), other.derived());
416 }
417 
418 /** \returns an expression of the matrix product of \c *this and \a other without implicit evaluation.
419   *
420   * The returned product will behave like any other expressions: the coefficients of the product will be
421   * computed once at a time as requested. This might be useful in some extremely rare cases when only
422   * a small and no coherent fraction of the result's coefficients have to be computed.
423   *
424   * \warning This version of the matrix product can be much much slower. So use it only if you know
425   * what you are doing and that you measured a true speed improvement.
426   *
427   * \sa operator*(const MatrixBase&)
428   */
429 template<typename Derived>
430 template<typename OtherDerived>
431 const Product<Derived,OtherDerived,LazyProduct>
432 MatrixBase<Derived>::lazyProduct(const MatrixBase<OtherDerived> &other) const
433 {
434   enum {
435     ProductIsValid =  Derived::ColsAtCompileTime==Dynamic
436                    || OtherDerived::RowsAtCompileTime==Dynamic
437                    || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
438     AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
439     SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
440   };
441   // note to the lost user:
442   //    * for a dot product use: v1.dot(v2)
443   //    * for a coeff-wise product use: v1.cwiseProduct(v2)
444   EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
445     INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
446   EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
447     INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
448   EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
449 
450   return Product<Derived,OtherDerived,LazyProduct>(derived(), other.derived());
451 }
452 
453 } // end namespace Eigen
454 
455 #endif // EIGEN_PRODUCT_H
456