1
1
// This file is part of Eigen, a lightweight C++ template library
2
2
// for linear algebra.
4
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
5
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
7
// Eigen is free software; you can redistribute it and/or
8
// modify it under the terms of the GNU Lesser General Public
9
// License as published by the Free Software Foundation; either
10
// version 3 of the License, or (at your option) any later version.
12
// Alternatively, you can redistribute it and/or
13
// modify it under the terms of the GNU General Public License as
14
// published by the Free Software Foundation; either version 2 of
15
// the License, or (at your option) any later version.
17
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
18
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
19
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
20
// GNU General Public License for more details.
22
// You should have received a copy of the GNU Lesser General Public
23
// License and a copy of the GNU General Public License along with
24
// Eigen. If not, see <http://www.gnu.org/licenses/>.
4
// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
6
// This Source Code Form is subject to the terms of the Mozilla Public
7
// License, v. 2.0. If a copy of the MPL was not distributed with this
8
// file, You can obtain one at http://mozilla.org/MPL/2.0/.
26
10
#ifndef EIGEN_PRODUCT_H
27
11
#define EIGEN_PRODUCT_H
29
/** \class GeneralProduct
30
* \ingroup Core_Module
32
* \brief Expression of the product of two general matrices or vectors
34
* \param LhsNested the type used to store the left-hand side
35
* \param RhsNested the type used to store the right-hand side
36
* \param ProductMode the type of the product
38
* This class represents an expression of the product of two general matrices.
39
* We call a general matrix, a dense matrix with full storage. For instance,
40
* This excludes triangular, selfadjoint, and sparse matrices.
41
* It is the return type of the operator* between general matrices. Its template
42
* arguments are determined automatically by ProductReturnType. Therefore,
43
* GeneralProduct should never be used direclty. To determine the result type of a
44
* function which involves a matrix product, use ProductReturnType::Type.
46
* \sa ProductReturnType, MatrixBase::operator*(const MatrixBase<OtherDerived>&)
48
template<typename Lhs, typename Rhs, int ProductType = internal::product_type<Lhs,Rhs>::value>
58
template<int Rows, int Cols, int Depth> struct product_type_selector;
60
template<int Size, int MaxSize> struct product_size_category
62
enum { is_large = MaxSize == Dynamic ||
63
Size >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD,
64
value = is_large ? Large
70
template<typename Lhs, typename Rhs> struct product_type
72
typedef typename remove_all<Lhs>::type _Lhs;
73
typedef typename remove_all<Rhs>::type _Rhs;
75
MaxRows = _Lhs::MaxRowsAtCompileTime,
76
Rows = _Lhs::RowsAtCompileTime,
77
MaxCols = _Rhs::MaxColsAtCompileTime,
78
Cols = _Rhs::ColsAtCompileTime,
79
MaxDepth = EIGEN_SIZE_MIN_PREFER_FIXED(_Lhs::MaxColsAtCompileTime,
80
_Rhs::MaxRowsAtCompileTime),
81
Depth = EIGEN_SIZE_MIN_PREFER_FIXED(_Lhs::ColsAtCompileTime,
82
_Rhs::RowsAtCompileTime),
83
LargeThreshold = EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
86
// the splitting into different lines of code here, introducing the _select enums and the typedef below,
87
// is to work around an internal compiler error with gcc 4.1 and 4.2.
90
rows_select = product_size_category<Rows,MaxRows>::value,
91
cols_select = product_size_category<Cols,MaxCols>::value,
92
depth_select = product_size_category<Depth,MaxDepth>::value
94
typedef product_type_selector<rows_select, cols_select, depth_select> selector;
100
#ifdef EIGEN_DEBUG_PRODUCT
103
EIGEN_DEBUG_VAR(Rows);
104
EIGEN_DEBUG_VAR(Cols);
105
EIGEN_DEBUG_VAR(Depth);
106
EIGEN_DEBUG_VAR(rows_select);
107
EIGEN_DEBUG_VAR(cols_select);
108
EIGEN_DEBUG_VAR(depth_select);
109
EIGEN_DEBUG_VAR(value);
115
/* The following allows to select the kind of product at compile time
116
* based on the three dimensions of the product.
117
* This is a compile time mapping from {1,Small,Large}^3 -> {product types} */
118
// FIXME I'm not sure the current mapping is the ideal one.
119
template<int M, int N> struct product_type_selector<M,N,1> { enum { ret = OuterProduct }; };
120
template<int Depth> struct product_type_selector<1, 1, Depth> { enum { ret = InnerProduct }; };
121
template<> struct product_type_selector<1, 1, 1> { enum { ret = InnerProduct }; };
122
template<> struct product_type_selector<Small,1, Small> { enum { ret = CoeffBasedProductMode }; };
123
template<> struct product_type_selector<1, Small,Small> { enum { ret = CoeffBasedProductMode }; };
124
template<> struct product_type_selector<Small,Small,Small> { enum { ret = CoeffBasedProductMode }; };
125
template<> struct product_type_selector<Small, Small, 1> { enum { ret = LazyCoeffBasedProductMode }; };
126
template<> struct product_type_selector<Small, Large, 1> { enum { ret = LazyCoeffBasedProductMode }; };
127
template<> struct product_type_selector<Large, Small, 1> { enum { ret = LazyCoeffBasedProductMode }; };
128
template<> struct product_type_selector<1, Large,Small> { enum { ret = CoeffBasedProductMode }; };
129
template<> struct product_type_selector<1, Large,Large> { enum { ret = GemvProduct }; };
130
template<> struct product_type_selector<1, Small,Large> { enum { ret = CoeffBasedProductMode }; };
131
template<> struct product_type_selector<Large,1, Small> { enum { ret = CoeffBasedProductMode }; };
132
template<> struct product_type_selector<Large,1, Large> { enum { ret = GemvProduct }; };
133
template<> struct product_type_selector<Small,1, Large> { enum { ret = CoeffBasedProductMode }; };
134
template<> struct product_type_selector<Small,Small,Large> { enum { ret = GemmProduct }; };
135
template<> struct product_type_selector<Large,Small,Large> { enum { ret = GemmProduct }; };
136
template<> struct product_type_selector<Small,Large,Large> { enum { ret = GemmProduct }; };
137
template<> struct product_type_selector<Large,Large,Large> { enum { ret = GemmProduct }; };
138
template<> struct product_type_selector<Large,Small,Small> { enum { ret = GemmProduct }; };
139
template<> struct product_type_selector<Small,Large,Small> { enum { ret = GemmProduct }; };
140
template<> struct product_type_selector<Large,Large,Small> { enum { ret = GemmProduct }; };
142
} // end namespace internal
144
/** \class ProductReturnType
145
* \ingroup Core_Module
147
* \brief Helper class to get the correct and optimized returned type of operator*
149
* \param Lhs the type of the left-hand side
150
* \param Rhs the type of the right-hand side
151
* \param ProductMode the type of the product (determined automatically by internal::product_mode)
153
* This class defines the typename Type representing the optimized product expression
154
* between two matrix expressions. In practice, using ProductReturnType<Lhs,Rhs>::Type
155
* is the recommended way to define the result type of a function returning an expression
156
* which involve a matrix product. The class Product should never be
159
* \sa class Product, MatrixBase::operator*(const MatrixBase<OtherDerived>&)
161
template<typename Lhs, typename Rhs, int ProductType>
162
struct ProductReturnType
164
// TODO use the nested type to reduce instanciations ????
165
// typedef typename internal::nested<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;
166
// typedef typename internal::nested<Rhs,Lhs::RowsAtCompileTime>::type RhsNested;
168
typedef GeneralProduct<Lhs/*Nested*/, Rhs/*Nested*/, ProductType> Type;
171
template<typename Lhs, typename Rhs>
172
struct ProductReturnType<Lhs,Rhs,CoeffBasedProductMode>
174
typedef typename internal::nested<Lhs, Rhs::ColsAtCompileTime, typename internal::plain_matrix_type<Lhs>::type >::type LhsNested;
175
typedef typename internal::nested<Rhs, Lhs::RowsAtCompileTime, typename internal::plain_matrix_type<Rhs>::type >::type RhsNested;
176
typedef CoeffBasedProduct<LhsNested, RhsNested, EvalBeforeAssigningBit | EvalBeforeNestingBit> Type;
179
template<typename Lhs, typename Rhs>
180
struct ProductReturnType<Lhs,Rhs,LazyCoeffBasedProductMode>
182
typedef typename internal::nested<Lhs, Rhs::ColsAtCompileTime, typename internal::plain_matrix_type<Lhs>::type >::type LhsNested;
183
typedef typename internal::nested<Rhs, Lhs::RowsAtCompileTime, typename internal::plain_matrix_type<Rhs>::type >::type RhsNested;
184
typedef CoeffBasedProduct<LhsNested, RhsNested, NestByRefBit> Type;
187
// this is a workaround for sun CC
188
template<typename Lhs, typename Rhs>
189
struct LazyProductReturnType : public ProductReturnType<Lhs,Rhs,LazyCoeffBasedProductMode>
192
/***********************************************************************
193
* Implementation of Inner Vector Vector Product
194
***********************************************************************/
196
// FIXME : maybe the "inner product" could return a Scalar
197
// instead of a 1x1 matrix ??
198
// Pro: more natural for the user
199
// Cons: this could be a problem if in a meta unrolled algorithm a matrix-matrix
200
// product ends up to a row-vector times col-vector product... To tackle this use
201
// case, we could have a specialization for Block<MatrixType,1,1> with: operator=(Scalar x);
205
template<typename Lhs, typename Rhs>
206
struct traits<GeneralProduct<Lhs,Rhs,InnerProduct> >
207
: traits<Matrix<typename scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType,1,1> >
212
template<typename Lhs, typename Rhs>
213
class GeneralProduct<Lhs, Rhs, InnerProduct>
214
: internal::no_assignment_operator,
215
public Matrix<typename internal::scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType,1,1>
217
typedef Matrix<typename internal::scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType,1,1> Base;
219
GeneralProduct(const Lhs& lhs, const Rhs& rhs)
221
EIGEN_STATIC_ASSERT((internal::is_same<typename Lhs::RealScalar, typename Rhs::RealScalar>::value),
222
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
224
Base::coeffRef(0,0) = (lhs.transpose().cwiseProduct(rhs)).sum();
227
/** Convertion to scalar */
228
operator const typename Base::Scalar() const {
229
return Base::coeff(0,0);
233
/***********************************************************************
234
* Implementation of Outer Vector Vector Product
235
***********************************************************************/
238
template<int StorageOrder> struct outer_product_selector;
240
template<typename Lhs, typename Rhs>
241
struct traits<GeneralProduct<Lhs,Rhs,OuterProduct> >
242
: traits<ProductBase<GeneralProduct<Lhs,Rhs,OuterProduct>, Lhs, Rhs> >
247
template<typename Lhs, typename Rhs>
248
class GeneralProduct<Lhs, Rhs, OuterProduct>
249
: public ProductBase<GeneralProduct<Lhs,Rhs,OuterProduct>, Lhs, Rhs>
252
EIGEN_PRODUCT_PUBLIC_INTERFACE(GeneralProduct)
254
GeneralProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
256
EIGEN_STATIC_ASSERT((internal::is_same<typename Lhs::RealScalar, typename Rhs::RealScalar>::value),
257
YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
260
template<typename Dest> void scaleAndAddTo(Dest& dest, Scalar alpha) const
262
internal::outer_product_selector<(int(Dest::Flags)&RowMajorBit) ? RowMajor : ColMajor>::run(*this, dest, alpha);
268
template<> struct outer_product_selector<ColMajor> {
269
template<typename ProductType, typename Dest>
270
static EIGEN_DONT_INLINE void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha) {
271
typedef typename Dest::Index Index;
272
// FIXME make sure lhs is sequentially stored
273
// FIXME not very good if rhs is real and lhs complex while alpha is real too
274
const Index cols = dest.cols();
275
for (Index j=0; j<cols; ++j)
276
dest.col(j) += (alpha * prod.rhs().coeff(j)) * prod.lhs();
280
template<> struct outer_product_selector<RowMajor> {
281
template<typename ProductType, typename Dest>
282
static EIGEN_DONT_INLINE void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha) {
283
typedef typename Dest::Index Index;
284
// FIXME make sure rhs is sequentially stored
285
// FIXME not very good if lhs is real and rhs complex while alpha is real too
286
const Index rows = dest.rows();
287
for (Index i=0; i<rows; ++i)
288
dest.row(i) += (alpha * prod.lhs().coeff(i)) * prod.rhs();
292
} // end namespace internal
294
/***********************************************************************
295
* Implementation of General Matrix Vector Product
296
***********************************************************************/
298
/* According to the shape/flags of the matrix we have to distinghish 3 different cases:
299
* 1 - the matrix is col-major, BLAS compatible and M is large => call fast BLAS-like colmajor routine
300
* 2 - the matrix is row-major, BLAS compatible and N is large => call fast BLAS-like rowmajor routine
301
* 3 - all other cases are handled using a simple loop along the outer-storage direction.
302
* Therefore we need a lower level meta selector.
303
* Furthermore, if the matrix is the rhs, then the product has to be transposed.
307
template<typename Lhs, typename Rhs>
308
struct traits<GeneralProduct<Lhs,Rhs,GemvProduct> >
309
: traits<ProductBase<GeneralProduct<Lhs,Rhs,GemvProduct>, Lhs, Rhs> >
312
template<int Side, int StorageOrder, bool BlasCompatible>
313
struct gemv_selector;
315
} // end namespace internal
317
template<typename Lhs, typename Rhs>
318
class GeneralProduct<Lhs, Rhs, GemvProduct>
319
: public ProductBase<GeneralProduct<Lhs,Rhs,GemvProduct>, Lhs, Rhs>
322
EIGEN_PRODUCT_PUBLIC_INTERFACE(GeneralProduct)
324
typedef typename Lhs::Scalar LhsScalar;
325
typedef typename Rhs::Scalar RhsScalar;
327
GeneralProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
329
// EIGEN_STATIC_ASSERT((internal::is_same<typename Lhs::Scalar, typename Rhs::Scalar>::value),
330
// YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
333
enum { Side = Lhs::IsVectorAtCompileTime ? OnTheLeft : OnTheRight };
334
typedef typename internal::conditional<int(Side)==OnTheRight,_LhsNested,_RhsNested>::type MatrixType;
336
template<typename Dest> void scaleAndAddTo(Dest& dst, Scalar alpha) const
338
eigen_assert(m_lhs.rows() == dst.rows() && m_rhs.cols() == dst.cols());
339
internal::gemv_selector<Side,(int(MatrixType::Flags)&RowMajorBit) ? RowMajor : ColMajor,
340
bool(internal::blas_traits<MatrixType>::HasUsableDirectAccess)>::run(*this, dst, alpha);
346
// The vector is on the left => transposition
347
template<int StorageOrder, bool BlasCompatible>
348
struct gemv_selector<OnTheLeft,StorageOrder,BlasCompatible>
350
template<typename ProductType, typename Dest>
351
static void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha)
353
Transpose<Dest> destT(dest);
354
enum { OtherStorageOrder = StorageOrder == RowMajor ? ColMajor : RowMajor };
355
gemv_selector<OnTheRight,OtherStorageOrder,BlasCompatible>
356
::run(GeneralProduct<Transpose<const typename ProductType::_RhsNested>,Transpose<const typename ProductType::_LhsNested>, GemvProduct>
357
(prod.rhs().transpose(), prod.lhs().transpose()), destT, alpha);
361
template<typename Scalar,int Size,int MaxSize,bool Cond> struct gemv_static_vector_if;
363
template<typename Scalar,int Size,int MaxSize>
364
struct gemv_static_vector_if<Scalar,Size,MaxSize,false>
366
EIGEN_STRONG_INLINE Scalar* data() { eigen_internal_assert(false && "should never be called"); return 0; }
369
template<typename Scalar,int Size>
370
struct gemv_static_vector_if<Scalar,Size,Dynamic,true>
372
EIGEN_STRONG_INLINE Scalar* data() { return 0; }
375
template<typename Scalar,int Size,int MaxSize>
376
struct gemv_static_vector_if<Scalar,Size,MaxSize,true>
378
#if EIGEN_ALIGN_STATICALLY
379
internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize),0> m_data;
380
EIGEN_STRONG_INLINE Scalar* data() { return m_data.array; }
382
// Some architectures cannot align on the stack,
383
// => let's manually enforce alignment by allocating more data and return the address of the first aligned element.
385
ForceAlignment = internal::packet_traits<Scalar>::Vectorizable,
386
PacketSize = internal::packet_traits<Scalar>::size
388
internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize)+(ForceAlignment?PacketSize:0),0> m_data;
389
EIGEN_STRONG_INLINE Scalar* data() {
390
return ForceAlignment
391
? reinterpret_cast<Scalar*>((reinterpret_cast<size_t>(m_data.array) & ~(size_t(15))) + 16)
397
template<> struct gemv_selector<OnTheRight,ColMajor,true>
399
template<typename ProductType, typename Dest>
400
static inline void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha)
402
typedef typename ProductType::Index Index;
403
typedef typename ProductType::LhsScalar LhsScalar;
404
typedef typename ProductType::RhsScalar RhsScalar;
405
typedef typename ProductType::Scalar ResScalar;
406
typedef typename ProductType::RealScalar RealScalar;
407
typedef typename ProductType::ActualLhsType ActualLhsType;
408
typedef typename ProductType::ActualRhsType ActualRhsType;
409
typedef typename ProductType::LhsBlasTraits LhsBlasTraits;
410
typedef typename ProductType::RhsBlasTraits RhsBlasTraits;
411
typedef Map<Matrix<ResScalar,Dynamic,1>, Aligned> MappedDest;
413
const ActualLhsType actualLhs = LhsBlasTraits::extract(prod.lhs());
414
const ActualRhsType actualRhs = RhsBlasTraits::extract(prod.rhs());
416
ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs())
417
* RhsBlasTraits::extractScalarFactor(prod.rhs());
420
// FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
421
// on, the other hand it is good for the cache to pack the vector anyways...
422
EvalToDestAtCompileTime = Dest::InnerStrideAtCompileTime==1,
423
ComplexByReal = (NumTraits<LhsScalar>::IsComplex) && (!NumTraits<RhsScalar>::IsComplex),
424
MightCannotUseDest = (Dest::InnerStrideAtCompileTime!=1) || ComplexByReal
427
gemv_static_vector_if<ResScalar,Dest::SizeAtCompileTime,Dest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;
429
// this is written like this (i.e., with a ?:) to workaround an ICE with ICC 12
430
bool alphaIsCompatible = (!ComplexByReal) ? true : (imag(actualAlpha)==RealScalar(0));
431
bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;
433
RhsScalar compatibleAlpha = get_factor<ResScalar,RhsScalar>::run(actualAlpha);
435
ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),
436
evalToDest ? dest.data() : static_dest.data());
440
#ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
441
int size = dest.size();
442
EIGEN_DENSE_STORAGE_CTOR_PLUGIN
444
if(!alphaIsCompatible)
446
MappedDest(actualDestPtr, dest.size()).setZero();
447
compatibleAlpha = RhsScalar(1);
450
MappedDest(actualDestPtr, dest.size()) = dest;
453
general_matrix_vector_product
454
<Index,LhsScalar,ColMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsBlasTraits::NeedToConjugate>::run(
455
actualLhs.rows(), actualLhs.cols(),
456
&actualLhs.coeffRef(0,0), actualLhs.outerStride(),
457
actualRhs.data(), actualRhs.innerStride(),
463
if(!alphaIsCompatible)
464
dest += actualAlpha * MappedDest(actualDestPtr, dest.size());
466
dest = MappedDest(actualDestPtr, dest.size());
471
template<> struct gemv_selector<OnTheRight,RowMajor,true>
473
template<typename ProductType, typename Dest>
474
static void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha)
476
typedef typename ProductType::LhsScalar LhsScalar;
477
typedef typename ProductType::RhsScalar RhsScalar;
478
typedef typename ProductType::Scalar ResScalar;
479
typedef typename ProductType::Index Index;
480
typedef typename ProductType::ActualLhsType ActualLhsType;
481
typedef typename ProductType::ActualRhsType ActualRhsType;
482
typedef typename ProductType::_ActualRhsType _ActualRhsType;
483
typedef typename ProductType::LhsBlasTraits LhsBlasTraits;
484
typedef typename ProductType::RhsBlasTraits RhsBlasTraits;
486
typename add_const<ActualLhsType>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
487
typename add_const<ActualRhsType>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
489
ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs())
490
* RhsBlasTraits::extractScalarFactor(prod.rhs());
493
// FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
494
// on, the other hand it is good for the cache to pack the vector anyways...
495
DirectlyUseRhs = _ActualRhsType::InnerStrideAtCompileTime==1
498
gemv_static_vector_if<RhsScalar,_ActualRhsType::SizeAtCompileTime,_ActualRhsType::MaxSizeAtCompileTime,!DirectlyUseRhs> static_rhs;
500
ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,actualRhs.size(),
501
DirectlyUseRhs ? const_cast<RhsScalar*>(actualRhs.data()) : static_rhs.data());
505
#ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
506
int size = actualRhs.size();
507
EIGEN_DENSE_STORAGE_CTOR_PLUGIN
509
Map<typename _ActualRhsType::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
512
general_matrix_vector_product
513
<Index,LhsScalar,RowMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsBlasTraits::NeedToConjugate>::run(
514
actualLhs.rows(), actualLhs.cols(),
515
&actualLhs.coeffRef(0,0), actualLhs.outerStride(),
517
&dest.coeffRef(0,0), dest.innerStride(),
522
template<> struct gemv_selector<OnTheRight,ColMajor,false>
524
template<typename ProductType, typename Dest>
525
static void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha)
527
typedef typename Dest::Index Index;
528
// TODO makes sure dest is sequentially stored in memory, otherwise use a temp
529
const Index size = prod.rhs().rows();
530
for(Index k=0; k<size; ++k)
531
dest += (alpha*prod.rhs().coeff(k)) * prod.lhs().col(k);
535
template<> struct gemv_selector<OnTheRight,RowMajor,false>
537
template<typename ProductType, typename Dest>
538
static void run(const ProductType& prod, Dest& dest, typename ProductType::Scalar alpha)
540
typedef typename Dest::Index Index;
541
// TODO makes sure rhs is sequentially stored in memory, otherwise use a temp
542
const Index rows = prod.rows();
543
for(Index i=0; i<rows; ++i)
544
dest.coeffRef(i) += alpha * (prod.lhs().row(i).cwiseProduct(prod.rhs().transpose())).sum();
548
} // end namespace internal
550
/***************************************************************************
551
* Implementation of matrix base methods
552
***************************************************************************/
554
/** \returns the matrix product of \c *this and \a other.
556
* \note If instead of the matrix product you want the coefficient-wise product, see Cwise::operator*().
558
* \sa lazyProduct(), operator*=(const MatrixBase&), Cwise::operator*()
560
template<typename Derived>
561
template<typename OtherDerived>
562
inline const typename ProductReturnType<Derived,OtherDerived>::Type
563
MatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const
565
// A note regarding the function declaration: In MSVC, this function will sometimes
566
// not be inlined since DenseStorage is an unwindable object for dynamic
567
// matrices and product types are holding a member to store the result.
568
// Thus it does not help tagging this function with EIGEN_STRONG_INLINE.
570
ProductIsValid = Derived::ColsAtCompileTime==Dynamic
571
|| OtherDerived::RowsAtCompileTime==Dynamic
572
|| int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
573
AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
574
SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
576
// note to the lost user:
577
// * for a dot product use: v1.dot(v2)
578
// * for a coeff-wise product use: v1.cwiseProduct(v2)
579
EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
580
INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
581
EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
582
INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
583
EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
584
#ifdef EIGEN_DEBUG_PRODUCT
585
internal::product_type<Derived,OtherDerived>::debug();
587
return typename ProductReturnType<Derived,OtherDerived>::Type(derived(), other.derived());
590
/** \returns an expression of the matrix product of \c *this and \a other without implicit evaluation.
592
* The returned product will behave like any other expressions: the coefficients of the product will be
593
* computed once at a time as requested. This might be useful in some extremely rare cases when only
594
* a small and no coherent fraction of the result's coefficients have to be computed.
596
* \warning This version of the matrix product can be much much slower. So use it only if you know
597
* what you are doing and that you measured a true speed improvement.
599
* \sa operator*(const MatrixBase&)
601
template<typename Derived>
602
template<typename OtherDerived>
603
const typename LazyProductReturnType<Derived,OtherDerived>::Type
604
MatrixBase<Derived>::lazyProduct(const MatrixBase<OtherDerived> &other) const
607
ProductIsValid = Derived::ColsAtCompileTime==Dynamic
608
|| OtherDerived::RowsAtCompileTime==Dynamic
609
|| int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
610
AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
611
SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
613
// note to the lost user:
614
// * for a dot product use: v1.dot(v2)
615
// * for a coeff-wise product use: v1.cwiseProduct(v2)
616
EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
617
INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
618
EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
619
INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
620
EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
622
return typename LazyProductReturnType<Derived,OtherDerived>::Type(derived(), other.derived());
13
template<typename Lhs, typename Rhs> class Product;
14
template<typename Lhs, typename Rhs, typename StorageKind> class ProductImpl;
17
* \ingroup Core_Module
19
* \brief Expression of the product of two arbitrary matrices or vectors
21
* \param Lhs the type of the left-hand side expression
22
* \param Rhs the type of the right-hand side expression
24
* This class represents an expression of the product of two arbitrary matrices.
29
template<typename Lhs, typename Rhs>
30
struct traits<Product<Lhs, Rhs> >
32
typedef MatrixXpr XprKind;
33
typedef typename remove_all<Lhs>::type LhsCleaned;
34
typedef typename remove_all<Rhs>::type RhsCleaned;
35
typedef typename scalar_product_traits<typename traits<LhsCleaned>::Scalar, typename traits<RhsCleaned>::Scalar>::ReturnType Scalar;
36
typedef typename promote_storage_type<typename traits<LhsCleaned>::StorageKind,
37
typename traits<RhsCleaned>::StorageKind>::ret StorageKind;
38
typedef typename promote_index_type<typename traits<LhsCleaned>::Index,
39
typename traits<RhsCleaned>::Index>::type Index;
41
RowsAtCompileTime = LhsCleaned::RowsAtCompileTime,
42
ColsAtCompileTime = RhsCleaned::ColsAtCompileTime,
43
MaxRowsAtCompileTime = LhsCleaned::MaxRowsAtCompileTime,
44
MaxColsAtCompileTime = RhsCleaned::MaxColsAtCompileTime,
45
Flags = (MaxRowsAtCompileTime==1 ? RowMajorBit : 0), // TODO should be no storage order
46
CoeffReadCost = 0 // TODO CoeffReadCost should not be part of the expression traits
49
} // end namespace internal
52
template<typename Lhs, typename Rhs>
53
class Product : public ProductImpl<Lhs,Rhs,typename internal::promote_storage_type<typename internal::traits<Lhs>::StorageKind,
54
typename internal::traits<Rhs>::StorageKind>::ret>
58
typedef typename ProductImpl<
60
typename internal::promote_storage_type<typename Lhs::StorageKind,
61
typename Rhs::StorageKind>::ret>::Base Base;
62
EIGEN_GENERIC_PUBLIC_INTERFACE(Product)
64
typedef typename Lhs::Nested LhsNested;
65
typedef typename Rhs::Nested RhsNested;
66
typedef typename internal::remove_all<LhsNested>::type LhsNestedCleaned;
67
typedef typename internal::remove_all<RhsNested>::type RhsNestedCleaned;
69
Product(const Lhs& lhs, const Rhs& rhs) : m_lhs(lhs), m_rhs(rhs)
71
eigen_assert(lhs.cols() == rhs.rows()
72
&& "invalid matrix product"
73
&& "if you wanted a coeff-wise or a dot product use the respective explicit functions");
76
inline Index rows() const { return m_lhs.rows(); }
77
inline Index cols() const { return m_rhs.cols(); }
79
const LhsNestedCleaned& lhs() const { return m_lhs; }
80
const RhsNestedCleaned& rhs() const { return m_rhs; }
84
const LhsNested m_lhs;
85
const RhsNested m_rhs;
88
template<typename Lhs, typename Rhs>
89
class ProductImpl<Lhs,Rhs,Dense> : public internal::dense_xpr_base<Product<Lhs,Rhs> >::type
91
typedef Product<Lhs, Rhs> Derived;
94
typedef typename internal::dense_xpr_base<Product<Lhs, Rhs> >::type Base;
95
EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
625
98
#endif // EIGEN_PRODUCT_H
added
removed
extern/Eigen3/Eigen/src/Core/Product.h
