Eigen  3.3.0
 
Loading...
Searching...
No Matches
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
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 value = is_large ? Large
30 : Size == 1 ? 1
31 : Small
32 };
33};
34
35template<typename Lhs, typename Rhs> struct product_type
36{
37 typedef typename remove_all<Lhs>::type _Lhs;
38 typedef typename remove_all<Rhs>::type _Rhs;
39 enum {
40 MaxRows = traits<_Lhs>::MaxRowsAtCompileTime,
41 Rows = traits<_Lhs>::RowsAtCompileTime,
42 MaxCols = traits<_Rhs>::MaxColsAtCompileTime,
43 Cols = traits<_Rhs>::ColsAtCompileTime,
44 MaxDepth = EIGEN_SIZE_MIN_PREFER_FIXED(traits<_Lhs>::MaxColsAtCompileTime,
45 traits<_Rhs>::MaxRowsAtCompileTime),
46 Depth = EIGEN_SIZE_MIN_PREFER_FIXED(traits<_Lhs>::ColsAtCompileTime,
47 traits<_Rhs>::RowsAtCompileTime)
48 };
49
50 // the splitting into different lines of code here, introducing the _select enums and the typedef below,
51 // is to work around an internal compiler error with gcc 4.1 and 4.2.
52private:
53 enum {
54 rows_select = product_size_category<Rows,MaxRows>::value,
55 cols_select = product_size_category<Cols,MaxCols>::value,
56 depth_select = product_size_category<Depth,MaxDepth>::value
57 };
58 typedef product_type_selector<rows_select, cols_select, depth_select> selector;
59
60public:
61 enum {
62 value = selector::ret,
63 ret = selector::ret
64 };
65#ifdef EIGEN_DEBUG_PRODUCT
66 static void debug()
67 {
68 EIGEN_DEBUG_VAR(Rows);
69 EIGEN_DEBUG_VAR(Cols);
70 EIGEN_DEBUG_VAR(Depth);
71 EIGEN_DEBUG_VAR(rows_select);
72 EIGEN_DEBUG_VAR(cols_select);
73 EIGEN_DEBUG_VAR(depth_select);
74 EIGEN_DEBUG_VAR(value);
75 }
76#endif
77};
78
79/* The following allows to select the kind of product at compile time
80 * based on the three dimensions of the product.
81 * This is a compile time mapping from {1,Small,Large}^3 -> {product types} */
82// FIXME I'm not sure the current mapping is the ideal one.
83template<int M, int N> struct product_type_selector<M,N,1> { enum { ret = OuterProduct }; };
84template<int M> struct product_type_selector<M, 1, 1> { enum { ret = LazyCoeffBasedProductMode }; };
85template<int N> struct product_type_selector<1, N, 1> { enum { ret = LazyCoeffBasedProductMode }; };
86template<int Depth> struct product_type_selector<1, 1, Depth> { enum { ret = InnerProduct }; };
87template<> struct product_type_selector<1, 1, 1> { enum { ret = InnerProduct }; };
88template<> struct product_type_selector<Small,1, Small> { enum { ret = CoeffBasedProductMode }; };
89template<> struct product_type_selector<1, Small,Small> { enum { ret = CoeffBasedProductMode }; };
90template<> struct product_type_selector<Small,Small,Small> { enum { ret = CoeffBasedProductMode }; };
91template<> struct product_type_selector<Small, Small, 1> { enum { ret = LazyCoeffBasedProductMode }; };
92template<> struct product_type_selector<Small, Large, 1> { enum { ret = LazyCoeffBasedProductMode }; };
93template<> struct product_type_selector<Large, Small, 1> { enum { ret = LazyCoeffBasedProductMode }; };
94template<> struct product_type_selector<1, Large,Small> { enum { ret = CoeffBasedProductMode }; };
95template<> struct product_type_selector<1, Large,Large> { enum { ret = GemvProduct }; };
96template<> struct product_type_selector<1, Small,Large> { enum { ret = CoeffBasedProductMode }; };
97template<> struct product_type_selector<Large,1, Small> { enum { ret = CoeffBasedProductMode }; };
98template<> struct product_type_selector<Large,1, Large> { enum { ret = GemvProduct }; };
99template<> struct product_type_selector<Small,1, Large> { enum { ret = CoeffBasedProductMode }; };
100template<> struct product_type_selector<Small,Small,Large> { enum { ret = GemmProduct }; };
101template<> struct product_type_selector<Large,Small,Large> { enum { ret = GemmProduct }; };
102template<> struct product_type_selector<Small,Large,Large> { enum { ret = GemmProduct }; };
103template<> struct product_type_selector<Large,Large,Large> { enum { ret = GemmProduct }; };
104template<> struct product_type_selector<Large,Small,Small> { enum { ret = CoeffBasedProductMode }; };
105template<> struct product_type_selector<Small,Large,Small> { enum { ret = CoeffBasedProductMode }; };
106template<> struct product_type_selector<Large,Large,Small> { enum { ret = GemmProduct }; };
107
108} // end namespace internal
109
110/***********************************************************************
111* Implementation of Inner Vector Vector Product
112***********************************************************************/
113
114// FIXME : maybe the "inner product" could return a Scalar
115// instead of a 1x1 matrix ??
116// Pro: more natural for the user
117// Cons: this could be a problem if in a meta unrolled algorithm a matrix-matrix
118// product ends up to a row-vector times col-vector product... To tackle this use
119// case, we could have a specialization for Block<MatrixType,1,1> with: operator=(Scalar x);
120
121/***********************************************************************
122* Implementation of Outer Vector Vector Product
123***********************************************************************/
124
125/***********************************************************************
126* Implementation of General Matrix Vector Product
127***********************************************************************/
128
129/* According to the shape/flags of the matrix we have to distinghish 3 different cases:
130 * 1 - the matrix is col-major, BLAS compatible and M is large => call fast BLAS-like colmajor routine
131 * 2 - the matrix is row-major, BLAS compatible and N is large => call fast BLAS-like rowmajor routine
132 * 3 - all other cases are handled using a simple loop along the outer-storage direction.
133 * Therefore we need a lower level meta selector.
134 * Furthermore, if the matrix is the rhs, then the product has to be transposed.
135 */
136namespace internal {
137
138template<int Side, int StorageOrder, bool BlasCompatible>
139struct gemv_dense_selector;
140
141} // end namespace internal
142
143namespace internal {
144
145template<typename Scalar,int Size,int MaxSize,bool Cond> struct gemv_static_vector_if;
146
147template<typename Scalar,int Size,int MaxSize>
148struct gemv_static_vector_if<Scalar,Size,MaxSize,false>
149{
150 EIGEN_STRONG_INLINE Scalar* data() { eigen_internal_assert(false && "should never be called"); return 0; }
151};
152
153template<typename Scalar,int Size>
154struct gemv_static_vector_if<Scalar,Size,Dynamic,true>
155{
156 EIGEN_STRONG_INLINE Scalar* data() { return 0; }
157};
158
159template<typename Scalar,int Size,int MaxSize>
160struct gemv_static_vector_if<Scalar,Size,MaxSize,true>
161{
162 enum {
163 ForceAlignment = internal::packet_traits<Scalar>::Vectorizable,
164 PacketSize = internal::packet_traits<Scalar>::size
165 };
166 #if EIGEN_MAX_STATIC_ALIGN_BYTES!=0
167 internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize),0,EIGEN_PLAIN_ENUM_MIN(AlignedMax,PacketSize)> m_data;
168 EIGEN_STRONG_INLINE Scalar* data() { return m_data.array; }
169 #else
170 // Some architectures cannot align on the stack,
171 // => let's manually enforce alignment by allocating more data and return the address of the first aligned element.
172 internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize)+(ForceAlignment?EIGEN_MAX_ALIGN_BYTES:0),0> m_data;
173 EIGEN_STRONG_INLINE Scalar* data() {
174 return ForceAlignment
175 ? reinterpret_cast<Scalar*>((internal::UIntPtr(m_data.array) & ~(std::size_t(EIGEN_MAX_ALIGN_BYTES-1))) + EIGEN_MAX_ALIGN_BYTES)
176 : m_data.array;
177 }
178 #endif
179};
181// The vector is on the left => transposition
182template<int StorageOrder, bool BlasCompatible>
183struct gemv_dense_selector<OnTheLeft,StorageOrder,BlasCompatible>
184{
185 template<typename Lhs, typename Rhs, typename Dest>
186 static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
187 {
188 Transpose<Dest> destT(dest);
189 enum { OtherStorageOrder = StorageOrder == RowMajor ? ColMajor : RowMajor };
190 gemv_dense_selector<OnTheRight,OtherStorageOrder,BlasCompatible>
191 ::run(rhs.transpose(), lhs.transpose(), destT, alpha);
192 }
193};
194
195template<> struct gemv_dense_selector<OnTheRight,ColMajor,true>
196{
197 template<typename Lhs, typename Rhs, typename Dest>
198 static inline void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
199 {
200 typedef typename Lhs::Scalar LhsScalar;
201 typedef typename Rhs::Scalar RhsScalar;
202 typedef typename Dest::Scalar ResScalar;
203 typedef typename Dest::RealScalar RealScalar;
204
205 typedef internal::blas_traits<Lhs> LhsBlasTraits;
206 typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
207 typedef internal::blas_traits<Rhs> RhsBlasTraits;
208 typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
209
210 typedef Map<Matrix<ResScalar,Dynamic,1>, EIGEN_PLAIN_ENUM_MIN(AlignedMax,internal::packet_traits<ResScalar>::size)> MappedDest;
211
212 ActualLhsType actualLhs = LhsBlasTraits::extract(lhs);
213 ActualRhsType actualRhs = RhsBlasTraits::extract(rhs);
214
215 ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(lhs)
216 * RhsBlasTraits::extractScalarFactor(rhs);
217
218 // make sure Dest is a compile-time vector type (bug 1166)
219 typedef typename conditional<Dest::IsVectorAtCompileTime, Dest, typename Dest::ColXpr>::type ActualDest;
220
221 enum {
222 // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
223 // on, the other hand it is good for the cache to pack the vector anyways...
224 EvalToDestAtCompileTime = (ActualDest::InnerStrideAtCompileTime==1),
226 MightCannotUseDest = (ActualDest::InnerStrideAtCompileTime!=1) || ComplexByReal
227 };
228
229 gemv_static_vector_if<ResScalar,ActualDest::SizeAtCompileTime,ActualDest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;
230
231 const bool alphaIsCompatible = (!ComplexByReal) || (numext::imag(actualAlpha)==RealScalar(0));
232 const bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;
233
234 RhsScalar compatibleAlpha = get_factor<ResScalar,RhsScalar>::run(actualAlpha);
235
236 ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),
237 evalToDest ? dest.data() : static_dest.data());
238
239 if(!evalToDest)
240 {
241 #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
242 Index size = dest.size();
243 EIGEN_DENSE_STORAGE_CTOR_PLUGIN
244 #endif
245 if(!alphaIsCompatible)
246 {
247 MappedDest(actualDestPtr, dest.size()).setZero();
248 compatibleAlpha = RhsScalar(1);
249 }
250 else
251 MappedDest(actualDestPtr, dest.size()) = dest;
252 }
253
254 typedef const_blas_data_mapper<LhsScalar,Index,ColMajor> LhsMapper;
255 typedef const_blas_data_mapper<RhsScalar,Index,RowMajor> RhsMapper;
256 general_matrix_vector_product
257 <Index,LhsScalar,LhsMapper,ColMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(
258 actualLhs.rows(), actualLhs.cols(),
259 LhsMapper(actualLhs.data(), actualLhs.outerStride()),
260 RhsMapper(actualRhs.data(), actualRhs.innerStride()),
261 actualDestPtr, 1,
262 compatibleAlpha);
263
264 if (!evalToDest)
265 {
266 if(!alphaIsCompatible)
267 dest += actualAlpha * MappedDest(actualDestPtr, dest.size());
268 else
269 dest = MappedDest(actualDestPtr, dest.size());
270 }
271 }
272};
273
274template<> struct gemv_dense_selector<OnTheRight,RowMajor,true>
275{
276 template<typename Lhs, typename Rhs, typename Dest>
277 static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
278 {
279 typedef typename Lhs::Scalar LhsScalar;
280 typedef typename Rhs::Scalar RhsScalar;
281 typedef typename Dest::Scalar ResScalar;
282
283 typedef internal::blas_traits<Lhs> LhsBlasTraits;
284 typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
285 typedef internal::blas_traits<Rhs> RhsBlasTraits;
286 typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
287 typedef typename internal::remove_all<ActualRhsType>::type ActualRhsTypeCleaned;
288
289 typename add_const<ActualLhsType>::type actualLhs = LhsBlasTraits::extract(lhs);
290 typename add_const<ActualRhsType>::type actualRhs = RhsBlasTraits::extract(rhs);
291
292 ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(lhs)
293 * RhsBlasTraits::extractScalarFactor(rhs);
294
295 enum {
296 // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
297 // on, the other hand it is good for the cache to pack the vector anyways...
298 DirectlyUseRhs = ActualRhsTypeCleaned::InnerStrideAtCompileTime==1
299 };
300
301 gemv_static_vector_if<RhsScalar,ActualRhsTypeCleaned::SizeAtCompileTime,ActualRhsTypeCleaned::MaxSizeAtCompileTime,!DirectlyUseRhs> static_rhs;
302
303 ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,actualRhs.size(),
304 DirectlyUseRhs ? const_cast<RhsScalar*>(actualRhs.data()) : static_rhs.data());
305
306 if(!DirectlyUseRhs)
307 {
308 #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
309 Index size = actualRhs.size();
310 EIGEN_DENSE_STORAGE_CTOR_PLUGIN
311 #endif
312 Map<typename ActualRhsTypeCleaned::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
313 }
314
315 typedef const_blas_data_mapper<LhsScalar,Index,RowMajor> LhsMapper;
316 typedef const_blas_data_mapper<RhsScalar,Index,ColMajor> RhsMapper;
317 general_matrix_vector_product
318 <Index,LhsScalar,LhsMapper,RowMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsMapper,RhsBlasTraits::NeedToConjugate>::run(
319 actualLhs.rows(), actualLhs.cols(),
320 LhsMapper(actualLhs.data(), actualLhs.outerStride()),
321 RhsMapper(actualRhsPtr, 1),
322 dest.data(), dest.col(0).innerStride(), //NOTE if dest is not a vector at compile-time, then dest.innerStride() might be wrong. (bug 1166)
323 actualAlpha);
324 }
325};
326
327template<> struct gemv_dense_selector<OnTheRight,ColMajor,false>
328{
329 template<typename Lhs, typename Rhs, typename Dest>
330 static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
331 {
332 // TODO if rhs is large enough it might be beneficial to make sure that dest is sequentially stored in memory, otherwise use a temp
333 typename nested_eval<Rhs,1>::type actual_rhs(rhs);
334 const Index size = rhs.rows();
335 for(Index k=0; k<size; ++k)
336 dest += (alpha*actual_rhs.coeff(k)) * lhs.col(k);
337 }
338};
339
340template<> struct gemv_dense_selector<OnTheRight,RowMajor,false>
341{
342 template<typename Lhs, typename Rhs, typename Dest>
343 static void run(const Lhs &lhs, const Rhs &rhs, Dest& dest, const typename Dest::Scalar& alpha)
344 {
345 typename nested_eval<Rhs,Lhs::RowsAtCompileTime>::type actual_rhs(rhs);
346 const Index rows = dest.rows();
347 for(Index i=0; i<rows; ++i)
348 dest.coeffRef(i) += alpha * (lhs.row(i).cwiseProduct(actual_rhs.transpose())).sum();
349 }
350};
351
352} // end namespace internal
353
354/***************************************************************************
355* Implementation of matrix base methods
356***************************************************************************/
357
364#ifndef __CUDACC__
365
366template<typename Derived>
367template<typename OtherDerived>
368inline const Product<Derived, OtherDerived>
370{
371 // A note regarding the function declaration: In MSVC, this function will sometimes
372 // not be inlined since DenseStorage is an unwindable object for dynamic
373 // matrices and product types are holding a member to store the result.
374 // Thus it does not help tagging this function with EIGEN_STRONG_INLINE.
375 enum {
376 ProductIsValid = Derived::ColsAtCompileTime==Dynamic
377 || OtherDerived::RowsAtCompileTime==Dynamic
378 || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
379 AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
380 SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
381 };
382 // note to the lost user:
383 // * for a dot product use: v1.dot(v2)
384 // * for a coeff-wise product use: v1.cwiseProduct(v2)
385 EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
386 INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
387 EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
388 INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
389 EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
390#ifdef EIGEN_DEBUG_PRODUCT
391 internal::product_type<Derived,OtherDerived>::debug();
392#endif
393
394 return Product<Derived, OtherDerived>(derived(), other.derived());
395}
396
397#endif // __CUDACC__
398
410template<typename Derived>
411template<typename OtherDerived>
414{
415 enum {
416 ProductIsValid = Derived::ColsAtCompileTime==Dynamic
417 || OtherDerived::RowsAtCompileTime==Dynamic
418 || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
419 AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
420 SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
421 };
422 // note to the lost user:
423 // * for a dot product use: v1.dot(v2)
424 // * for a coeff-wise product use: v1.cwiseProduct(v2)
425 EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
426 INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
427 EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
428 INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
429 EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
430
431 return Product<Derived,OtherDerived,LazyProduct>(derived(), other.derived());
432}
433
434} // end namespace Eigen
435
436#endif // EIGEN_PRODUCT_H
internal::traits< Derived >::Scalar Scalar
Definition: DenseBase.h:66
Derived & derived()
Definition: EigenBase.h:44
A matrix or vector expression mapping an existing array of data.
Definition: Map.h:90
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:50
Expression of the product of two arbitrary matrices or vectors.
Definition: Product.h:75
Expression of the transpose of a matrix.
Definition: Transpose.h:54
@ ColMajor
Definition: Constants.h:320
@ RowMajor
Definition: Constants.h:322
@ OnTheLeft
Definition: Constants.h:333
@ OnTheRight
Definition: Constants.h:335
Namespace containing all symbols from the Eigen library.
Definition: Core:287
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:33
const int Dynamic
Definition: Constants.h:21
Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
Definition: NumTraits.h:151