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GeneralProduct.h
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 // 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
82  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 = alpha * LhsBlasTraits::extractScalarFactor(lhs)
232  * RhsBlasTraits::extractScalarFactor(rhs);
233 
234  // make sure Dest is a compile-time vector type (bug 1166)
235  typedef typename conditional<Dest::IsVectorAtCompileTime, Dest, typename Dest::ColXpr>::type ActualDest;
236 
237  enum {
238  // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
239  // on, the other hand it is good for the cache to pack the vector anyways...
240  EvalToDestAtCompileTime = (ActualDest::InnerStrideAtCompileTime==1),
241  ComplexByReal = (NumTraits<LhsScalar>::IsComplex) && (!NumTraits<RhsScalar>::IsComplex),
242  MightCannotUseDest = ((!EvalToDestAtCompileTime) || ComplexByReal) && (ActualDest::MaxSizeAtCompileTime!=0)
243  };
244 
245  typedef const_blas_data_mapper<LhsScalar,Index,ColMajor> LhsMapper;
246  typedef const_blas_data_mapper<RhsScalar,Index,RowMajor> RhsMapper;
247  RhsScalar compatibleAlpha = get_factor<ResScalar,RhsScalar>::run(actualAlpha);
248 
249  if(!MightCannotUseDest)
250  {
251  // shortcut if we are sure to be able to use dest directly,
252  // this ease the compiler to generate cleaner and more optimzized code for most common cases
253  general_matrix_vector_product
254  <Index,LhsScalar,LhsMapper,ColMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(
255  actualLhs.rows(), actualLhs.cols(),
256  LhsMapper(actualLhs.data(), actualLhs.outerStride()),
257  RhsMapper(actualRhs.data(), actualRhs.innerStride()),
258  dest.data(), 1,
259  compatibleAlpha);
260  }
261  else
262  {
263  gemv_static_vector_if<ResScalar,ActualDest::SizeAtCompileTime,ActualDest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;
264 
265  const bool alphaIsCompatible = (!ComplexByReal) || (numext::imag(actualAlpha)==RealScalar(0));
266  const bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;
267 
268  ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),
269  evalToDest ? dest.data() : static_dest.data());
270 
271  if(!evalToDest)
272  {
273  #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
274  Index size = dest.size();
275  EIGEN_DENSE_STORAGE_CTOR_PLUGIN
276  #endif
277  if(!alphaIsCompatible)
278  {
279  MappedDest(actualDestPtr, dest.size()).setZero();
280  compatibleAlpha = RhsScalar(1);
281  }
282  else
283  MappedDest(actualDestPtr, dest.size()) = dest;
284  }
285 
286  general_matrix_vector_product
287  <Index,LhsScalar,LhsMapper,ColMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(
288  actualLhs.rows(), actualLhs.cols(),
289  LhsMapper(actualLhs.data(), actualLhs.outerStride()),
290  RhsMapper(actualRhs.data(), actualRhs.innerStride()),
291  actualDestPtr, 1,
292  compatibleAlpha);
293 
294  if (!evalToDest)
295  {
296  if(!alphaIsCompatible)
297  dest.matrix() += actualAlpha * MappedDest(actualDestPtr, dest.size());
298  else
299  dest = MappedDest(actualDestPtr, dest.size());
300  }
301  }
302  }
303 };
304 
305 template<> struct gemv_dense_selector<OnTheRight,RowMajor,true>
306 {
307  template<typename Lhs, typename Rhs, typename Dest>
308  static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
309  {
310  typedef typename Lhs::Scalar LhsScalar;
311  typedef typename Rhs::Scalar RhsScalar;
312  typedef typename Dest::Scalar ResScalar;
313 
314  typedef internal::blas_traits<Lhs> LhsBlasTraits;
315  typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
316  typedef internal::blas_traits<Rhs> RhsBlasTraits;
317  typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
318  typedef typename internal::remove_all<ActualRhsType>::type ActualRhsTypeCleaned;
319 
320  typename add_const<ActualLhsType>::type actualLhs = LhsBlasTraits::extract(lhs);
321  typename add_const<ActualRhsType>::type actualRhs = RhsBlasTraits::extract(rhs);
322 
323  ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(lhs)
324  * RhsBlasTraits::extractScalarFactor(rhs);
325 
326  enum {
327  // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
328  // on, the other hand it is good for the cache to pack the vector anyways...
329  DirectlyUseRhs = ActualRhsTypeCleaned::InnerStrideAtCompileTime==1 || ActualRhsTypeCleaned::MaxSizeAtCompileTime==0
330  };
331 
332  gemv_static_vector_if<RhsScalar,ActualRhsTypeCleaned::SizeAtCompileTime,ActualRhsTypeCleaned::MaxSizeAtCompileTime,!DirectlyUseRhs> static_rhs;
333 
334  ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,actualRhs.size(),
335  DirectlyUseRhs ? const_cast<RhsScalar*>(actualRhs.data()) : static_rhs.data());
336 
337  if(!DirectlyUseRhs)
338  {
339  #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
340  Index size = actualRhs.size();
341  EIGEN_DENSE_STORAGE_CTOR_PLUGIN
342  #endif
343  Map<typename ActualRhsTypeCleaned::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
344  }
345 
346  typedef const_blas_data_mapper<LhsScalar,Index,RowMajor> LhsMapper;
347  typedef const_blas_data_mapper<RhsScalar,Index,ColMajor> RhsMapper;
348  general_matrix_vector_product
349  <Index,LhsScalar,LhsMapper,RowMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(
350  actualLhs.rows(), actualLhs.cols(),
351  LhsMapper(actualLhs.data(), actualLhs.outerStride()),
352  RhsMapper(actualRhsPtr, 1),
353  dest.data(), dest.col(0).innerStride(), //NOTE if dest is not a vector at compile-time, then dest.innerStride() might be wrong. (bug 1166)
354  actualAlpha);
355  }
356 };
357 
358 template<> struct gemv_dense_selector<OnTheRight,ColMajor,false>
359 {
360  template<typename Lhs, typename Rhs, typename Dest>
361  static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
362  {
363  EIGEN_STATIC_ASSERT((!nested_eval<Lhs,1>::Evaluate),EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE);
364  // TODO if rhs is large enough it might be beneficial to make sure that dest is sequentially stored in memory, otherwise use a temp
365  typename nested_eval<Rhs,1>::type actual_rhs(rhs);
366  const Index size = rhs.rows();
367  for(Index k=0; k<size; ++k)
368  dest += (alpha*actual_rhs.coeff(k)) * lhs.col(k);
369  }
370 };
371 
372 template<> struct gemv_dense_selector<OnTheRight,RowMajor,false>
373 {
374  template<typename Lhs, typename Rhs, typename Dest>
375  static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
376  {
377  EIGEN_STATIC_ASSERT((!nested_eval<Lhs,1>::Evaluate),EIGEN_INTERNAL_COMPILATION_ERROR_OR_YOU_MADE_A_PROGRAMMING_MISTAKE);
378  typename nested_eval<Rhs,Lhs::RowsAtCompileTime>::type actual_rhs(rhs);
379  const Index rows = dest.rows();
380  for(Index i=0; i<rows; ++i)
381  dest.coeffRef(i) += alpha * (lhs.row(i).cwiseProduct(actual_rhs.transpose())).sum();
382  }
383 };
384 
385 } // end namespace internal
386 
387 /***************************************************************************
388 * Implementation of matrix base methods
389 ***************************************************************************/
390 
397 template<typename Derived>
398 template<typename OtherDerived>
399 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
400 const Product<Derived, OtherDerived>
401 MatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const
402 {
403  // A note regarding the function declaration: In MSVC, this function will sometimes
404  // not be inlined since DenseStorage is an unwindable object for dynamic
405  // matrices and product types are holding a member to store the result.
406  // Thus it does not help tagging this function with EIGEN_STRONG_INLINE.
407  enum {
408  ProductIsValid = Derived::ColsAtCompileTime==Dynamic
409  || OtherDerived::RowsAtCompileTime==Dynamic
410  || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
411  AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
412  SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
413  };
414  // note to the lost user:
415  // * for a dot product use: v1.dot(v2)
416  // * for a coeff-wise product use: v1.cwiseProduct(v2)
417  EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
418  INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
419  EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
420  INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
421  EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
422 #ifdef EIGEN_DEBUG_PRODUCT
423  internal::product_type<Derived,OtherDerived>::debug();
424 #endif
425 
426  return Product<Derived, OtherDerived>(derived(), other.derived());
427 }
428 
440 template<typename Derived>
441 template<typename OtherDerived>
442 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
443 const Product<Derived,OtherDerived,LazyProduct>
444 MatrixBase<Derived>::lazyProduct(const MatrixBase<OtherDerived> &other) const
445 {
446  enum {
447  ProductIsValid = Derived::ColsAtCompileTime==Dynamic
448  || OtherDerived::RowsAtCompileTime==Dynamic
449  || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
450  AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
451  SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
452  };
453  // note to the lost user:
454  // * for a dot product use: v1.dot(v2)
455  // * for a coeff-wise product use: v1.cwiseProduct(v2)
456  EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
457  INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
458  EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
459  INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
460  EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
461 
462  return Product<Derived,OtherDerived,LazyProduct>(derived(), other.derived());
463 }
464 
465 } // end namespace Eigen
466 
467 #endif // EIGEN_PRODUCT_H
Eigen
Namespace containing all symbols from the Eigen library.
Definition: LDLT.h:16
Eigen::internal::general_matrix_vector_product
Definition: BlasUtil.h:40
Eigen::internal::gemv_static_vector_if
Definition: GeneralProduct.h:161
Eigen::internal::packet_traits
Definition: GenericPacketMath.h:107
Eigen::internal::nested_eval
Definition: XprHelper.h:466
Eigen::RowMajor
@ RowMajor
Definition: Constants.h:320
Eigen::Transpose
Expression of the transpose of a matrix.
Definition: Transpose.h:54
Eigen::OnTheLeft
@ OnTheLeft
Definition: Constants.h:331
Eigen::internal::true_type
Definition: Meta.h:63
Eigen::Dynamic
const int Dynamic
Definition: Constants.h:21
Eigen::Diagonal
Expression of a diagonal/subdiagonal/superdiagonal in a matrix.
Definition: Diagonal.h:65
Eigen::Product
Expression of the product of two arbitrary matrices or vectors.
Definition: Product.h:75
Eigen::internal::get_factor
Definition: BlasUtil.h:126
Eigen::internal::product_type_selector
Definition: GeneralProduct.h:33
Eigen::Map
A matrix or vector expression mapping an existing array of data.
Definition: Map.h:96
Eigen::OnTheRight
@ OnTheRight
Definition: Constants.h:333
Eigen::internal::traits
Definition: ForwardDeclarations.h:17
Eigen::internal::const_blas_data_mapper
Definition: BlasUtil.h:473
Eigen::internal::plain_array
Definition: DenseStorage.h:45
Eigen::internal::product_type
Definition: GeneralProduct.h:52
Eigen::internal::product_size_category
Definition: GeneralProduct.h:36
Eigen::internal::blas_traits
Definition: BlasUtil.h:487
Eigen::MatrixBase
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:50
Eigen::ColMajor
@ ColMajor
Definition: Constants.h:318
Eigen::NumTraits
Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
Definition: NumTraits.h:213
Eigen::internal::gemv_dense_selector
Definition: GeneralProduct.h:161
Eigen::Index
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:42
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