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