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
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
31namespace internal {
32
33template<int Rows, int Cols, int Depth> struct product_type_selector;
34
35template<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
51template<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.
68private:
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
76public:
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.
99template<int M, int N> struct product_type_selector<M,N,1> { enum { ret = OuterProduct }; };
100template<int M> struct product_type_selector<M, 1, 1> { enum { ret = LazyCoeffBasedProductMode }; };
101template<int N> struct product_type_selector<1, N, 1> { enum { ret = LazyCoeffBasedProductMode }; };
102template<int Depth> struct product_type_selector<1, 1, Depth> { enum { ret = InnerProduct }; };
103template<> struct product_type_selector<1, 1, 1> { enum { ret = InnerProduct }; };
104template<> struct product_type_selector<Small,1, Small> { enum { ret = CoeffBasedProductMode }; };
105template<> struct product_type_selector<1, Small,Small> { enum { ret = CoeffBasedProductMode }; };
106template<> struct product_type_selector<Small,Small,Small> { enum { ret = CoeffBasedProductMode }; };
107template<> struct product_type_selector<Small, Small, 1> { enum { ret = LazyCoeffBasedProductMode }; };
108template<> struct product_type_selector<Small, Large, 1> { enum { ret = LazyCoeffBasedProductMode }; };
109template<> struct product_type_selector<Large, Small, 1> { enum { ret = LazyCoeffBasedProductMode }; };
110template<> struct product_type_selector<1, Large,Small> { enum { ret = CoeffBasedProductMode }; };
111template<> struct product_type_selector<1, Large,Large> { enum { ret = GemvProduct }; };
112template<> struct product_type_selector<1, Small,Large> { enum { ret = CoeffBasedProductMode }; };
113template<> struct product_type_selector<Large,1, Small> { enum { ret = CoeffBasedProductMode }; };
114template<> struct product_type_selector<Large,1, Large> { enum { ret = GemvProduct }; };
115template<> struct product_type_selector<Small,1, Large> { enum { ret = CoeffBasedProductMode }; };
116template<> struct product_type_selector<Small,Small,Large> { enum { ret = GemmProduct }; };
117template<> struct product_type_selector<Large,Small,Large> { enum { ret = GemmProduct }; };
118template<> struct product_type_selector<Small,Large,Large> { enum { ret = GemmProduct }; };
119template<> struct product_type_selector<Large,Large,Large> { enum { ret = GemmProduct }; };
120template<> struct product_type_selector<Large,Small,Small> { enum { ret = CoeffBasedProductMode }; };
121template<> struct product_type_selector<Small,Large,Small> { enum { ret = CoeffBasedProductMode }; };
122template<> 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 */
152namespace internal {
153
154template<int Side, int StorageOrder, bool BlasCompatible>
155struct gemv_dense_selector;
156
157} // end namespace internal
158
159namespace internal {
160
161template<typename Scalar,int Size,int MaxSize,bool Cond> struct gemv_static_vector_if;
162
163template<typename Scalar,int Size,int MaxSize>
164struct 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
169template<typename Scalar,int Size>
170struct gemv_static_vector_if<Scalar,Size,Dynamic,true>
171{
172 EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Scalar* data() { return 0; }
173};
174
175template<typename Scalar,int Size,int MaxSize>
176struct 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
198template<int StorageOrder, bool BlasCompatible>
199struct 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
211template<> 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
304template<> 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
356template<> 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
370template<> 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 */
395template<typename Derived>
396template<typename OtherDerived>
397EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
398const Product<Derived, OtherDerived>
399MatrixBase<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 */
438template<typename Derived>
439template<typename OtherDerived>
440EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
441const Product<Derived,OtherDerived,LazyProduct>
442MatrixBase<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

source code of qtmultimedia/src/3rdparty/eigen/Eigen/src/Core/GeneralProduct.h