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1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9 
10 #ifndef EIGEN_PRODUCTBASE_H
11 #define EIGEN_PRODUCTBASE_H
12 
13 namespace Eigen {
14 
15 /** \class ProductBase
16   * \ingroup Core_Module
17   *
18   */
19 
20 namespace internal {
21 template<typename Derived, typename _Lhs, typename _Rhs>
22 struct traits<ProductBase<Derived,_Lhs,_Rhs> >
23 {
24   typedef MatrixXpr XprKind;
25   typedef typename remove_all<_Lhs>::type Lhs;
26   typedef typename remove_all<_Rhs>::type Rhs;
27   typedef typename scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
28   typedef typename promote_storage_type<typename traits<Lhs>::StorageKind,
29                                            typename traits<Rhs>::StorageKind>::ret StorageKind;
30   typedef typename promote_index_type<typename traits<Lhs>::Index,
31                                          typename traits<Rhs>::Index>::type Index;
32   enum {
33     RowsAtCompileTime = traits<Lhs>::RowsAtCompileTime,
34     ColsAtCompileTime = traits<Rhs>::ColsAtCompileTime,
35     MaxRowsAtCompileTime = traits<Lhs>::MaxRowsAtCompileTime,
36     MaxColsAtCompileTime = traits<Rhs>::MaxColsAtCompileTime,
37     Flags = (MaxRowsAtCompileTime==1 ? RowMajorBit : 0)
38           | EvalBeforeNestingBit | EvalBeforeAssigningBit | NestByRefBit,
39                   // Note that EvalBeforeNestingBit and NestByRefBit
40                   // are not used in practice because nested is overloaded for products
41     CoeffReadCost = 0 // FIXME why is it needed ?
42   };
43 };
44 }
45 
46 #define EIGEN_PRODUCT_PUBLIC_INTERFACE(Derived) \
47   typedef ProductBase<Derived, Lhs, Rhs > Base; \
48   EIGEN_DENSE_PUBLIC_INTERFACE(Derived) \
49   typedef typename Base::LhsNested LhsNested; \
50   typedef typename Base::_LhsNested _LhsNested; \
51   typedef typename Base::LhsBlasTraits LhsBlasTraits; \
52   typedef typename Base::ActualLhsType ActualLhsType; \
53   typedef typename Base::_ActualLhsType _ActualLhsType; \
54   typedef typename Base::RhsNested RhsNested; \
55   typedef typename Base::_RhsNested _RhsNested; \
56   typedef typename Base::RhsBlasTraits RhsBlasTraits; \
57   typedef typename Base::ActualRhsType ActualRhsType; \
58   typedef typename Base::_ActualRhsType _ActualRhsType; \
59   using Base::m_lhs; \
60   using Base::m_rhs;
61 
62 template<typename Derived, typename Lhs, typename Rhs>
63 class ProductBase : public MatrixBase<Derived>
64 {
65   public:
66     typedef MatrixBase<Derived> Base;
67     EIGEN_DENSE_PUBLIC_INTERFACE(ProductBase)
68 
69     typedef typename Lhs::Nested LhsNested;
70     typedef typename internal::remove_all<LhsNested>::type _LhsNested;
71     typedef internal::blas_traits<_LhsNested> LhsBlasTraits;
72     typedef typename LhsBlasTraits::DirectLinearAccessType ActualLhsType;
73     typedef typename internal::remove_all<ActualLhsType>::type _ActualLhsType;
74     typedef typename internal::traits<Lhs>::Scalar LhsScalar;
75 
76     typedef typename Rhs::Nested RhsNested;
77     typedef typename internal::remove_all<RhsNested>::type _RhsNested;
78     typedef internal::blas_traits<_RhsNested> RhsBlasTraits;
79     typedef typename RhsBlasTraits::DirectLinearAccessType ActualRhsType;
80     typedef typename internal::remove_all<ActualRhsType>::type _ActualRhsType;
81     typedef typename internal::traits<Rhs>::Scalar RhsScalar;
82 
83     // Diagonal of a product: no need to evaluate the arguments because they are going to be evaluated only once
84     typedef CoeffBasedProduct<LhsNested, RhsNested, 0> FullyLazyCoeffBaseProductType;
85 
86   public:
87 
88 #ifndef EIGEN_NO_MALLOC
89     typedef typename Base::PlainObject BasePlainObject;
90     typedef Matrix<Scalar,RowsAtCompileTime==1?1:Dynamic,ColsAtCompileTime==1?1:Dynamic,BasePlainObject::Options> DynPlainObject;
91     typedef typename internal::conditional<(BasePlainObject::SizeAtCompileTime==Dynamic) || (BasePlainObject::SizeAtCompileTime*int(sizeof(Scalar)) < int(EIGEN_STACK_ALLOCATION_LIMIT)),
92                                            BasePlainObject, DynPlainObject>::type PlainObject;
93 #else
94     typedef typename Base::PlainObject PlainObject;
95 #endif
96 
97     ProductBase(const Lhs& a_lhs, const Rhs& a_rhs)
98       : m_lhs(a_lhs), m_rhs(a_rhs)
99     {
100       eigen_assert(a_lhs.cols() == a_rhs.rows()
101         && "invalid matrix product"
102         && "if you wanted a coeff-wise or a dot product use the respective explicit functions");
103     }
104 
105     inline Index rows() const { return m_lhs.rows(); }
106     inline Index cols() const { return m_rhs.cols(); }
107 
108     template<typename Dest>
109     inline void evalTo(Dest& dst) const { dst.setZero(); scaleAndAddTo(dst,Scalar(1)); }
110 
111     template<typename Dest>
112     inline void addTo(Dest& dst) const { scaleAndAddTo(dst,Scalar(1)); }
113 
114     template<typename Dest>
115     inline void subTo(Dest& dst) const { scaleAndAddTo(dst,Scalar(-1)); }
116 
117     template<typename Dest>
118     inline void scaleAndAddTo(Dest& dst, const Scalar& alpha) const { derived().scaleAndAddTo(dst,alpha); }
119 
120     const _LhsNested& lhs() const { return m_lhs; }
121     const _RhsNested& rhs() const { return m_rhs; }
122 
123     // Implicit conversion to the nested type (trigger the evaluation of the product)
124     operator const PlainObject& () const
125     {
126       m_result.resize(m_lhs.rows(), m_rhs.cols());
127       derived().evalTo(m_result);
128       return m_result;
129     }
130 
131     const Diagonal<const FullyLazyCoeffBaseProductType,0> diagonal() const
132     { return FullyLazyCoeffBaseProductType(m_lhs, m_rhs); }
133 
134     template<int Index>
135     const Diagonal<FullyLazyCoeffBaseProductType,Index> diagonal() const
136     { return FullyLazyCoeffBaseProductType(m_lhs, m_rhs); }
137 
138     const Diagonal<FullyLazyCoeffBaseProductType,Dynamic> diagonal(Index index) const
139     { return FullyLazyCoeffBaseProductType(m_lhs, m_rhs).diagonal(index); }
140 
141     // restrict coeff accessors to 1x1 expressions. No need to care about mutators here since this isnt a Lvalue expression
142     typename Base::CoeffReturnType coeff(Index row, Index col) const
143     {
144 #ifdef EIGEN2_SUPPORT
145       return lhs().row(row).cwiseProduct(rhs().col(col).transpose()).sum();
146 #else
147       EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
148       eigen_assert(this->rows() == 1 && this->cols() == 1);
149       Matrix<Scalar,1,1> result = *this;
150       return result.coeff(row,col);
151 #endif
152     }
153 
154     typename Base::CoeffReturnType coeff(Index i) const
155     {
156       EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
157       eigen_assert(this->rows() == 1 && this->cols() == 1);
158       Matrix<Scalar,1,1> result = *this;
159       return result.coeff(i);
160     }
161 
162     const Scalar& coeffRef(Index row, Index col) const
163     {
164       EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
165       eigen_assert(this->rows() == 1 && this->cols() == 1);
166       return derived().coeffRef(row,col);
167     }
168 
169     const Scalar& coeffRef(Index i) const
170     {
171       EIGEN_STATIC_ASSERT_SIZE_1x1(Derived)
172       eigen_assert(this->rows() == 1 && this->cols() == 1);
173       return derived().coeffRef(i);
174     }
175 
176   protected:
177 
178     LhsNested m_lhs;
179     RhsNested m_rhs;
180 
181     mutable PlainObject m_result;
182 };
183 
184 // here we need to overload the nested rule for products
185 // such that the nested type is a const reference to a plain matrix
186 namespace internal {
187 template<typename Lhs, typename Rhs, int Mode, int N, typename PlainObject>
188 struct nested<GeneralProduct<Lhs,Rhs,Mode>, N, PlainObject>
189 {
190   typedef typename GeneralProduct<Lhs,Rhs,Mode>::PlainObject const& type;
191 };
192 template<typename Lhs, typename Rhs, int Mode, int N, typename PlainObject>
193 struct nested<const GeneralProduct<Lhs,Rhs,Mode>, N, PlainObject>
194 {
195   typedef typename GeneralProduct<Lhs,Rhs,Mode>::PlainObject const& type;
196 };
197 }
198 
199 template<typename NestedProduct>
200 class ScaledProduct;
201 
202 // Note that these two operator* functions are not defined as member
203 // functions of ProductBase, because, otherwise we would have to
204 // define all overloads defined in MatrixBase. Furthermore, Using
205 // "using Base::operator*" would not work with MSVC.
206 //
207 // Also note that here we accept any compatible scalar types
208 template<typename Derived,typename Lhs,typename Rhs>
209 const ScaledProduct<Derived>
210 operator*(const ProductBase<Derived,Lhs,Rhs>& prod, const typename Derived::Scalar& x)
211 { return ScaledProduct<Derived>(prod.derived(), x); }
212 
213 template<typename Derived,typename Lhs,typename Rhs>
214 typename internal::enable_if<!internal::is_same<typename Derived::Scalar,typename Derived::RealScalar>::value,
215                       const ScaledProduct<Derived> >::type
216 operator*(const ProductBase<Derived,Lhs,Rhs>& prod, const typename Derived::RealScalar& x)
217 { return ScaledProduct<Derived>(prod.derived(), x); }
218 
219 
220 template<typename Derived,typename Lhs,typename Rhs>
221 const ScaledProduct<Derived>
222 operator*(const typename Derived::Scalar& x,const ProductBase<Derived,Lhs,Rhs>& prod)
223 { return ScaledProduct<Derived>(prod.derived(), x); }
224 
225 template<typename Derived,typename Lhs,typename Rhs>
226 typename internal::enable_if<!internal::is_same<typename Derived::Scalar,typename Derived::RealScalar>::value,
227                       const ScaledProduct<Derived> >::type
228 operator*(const typename Derived::RealScalar& x,const ProductBase<Derived,Lhs,Rhs>& prod)
229 { return ScaledProduct<Derived>(prod.derived(), x); }
230 
231 namespace internal {
232 template<typename NestedProduct>
233 struct traits<ScaledProduct<NestedProduct> >
234  : traits<ProductBase<ScaledProduct<NestedProduct>,
235                          typename NestedProduct::_LhsNested,
236                          typename NestedProduct::_RhsNested> >
237 {
238   typedef typename traits<NestedProduct>::StorageKind StorageKind;
239 };
240 }
241 
242 template<typename NestedProduct>
243 class ScaledProduct
244   : public ProductBase<ScaledProduct<NestedProduct>,
245                        typename NestedProduct::_LhsNested,
246                        typename NestedProduct::_RhsNested>
247 {
248   public:
249     typedef ProductBase<ScaledProduct<NestedProduct>,
250                        typename NestedProduct::_LhsNested,
251                        typename NestedProduct::_RhsNested> Base;
252     typedef typename Base::Scalar Scalar;
253     typedef typename Base::PlainObject PlainObject;
254 //     EIGEN_PRODUCT_PUBLIC_INTERFACE(ScaledProduct)
255 
256     ScaledProduct(const NestedProduct& prod, const Scalar& x)
257     : Base(prod.lhs(),prod.rhs()), m_prod(prod), m_alpha(x) {}
258 
259     template<typename Dest>
260     inline void evalTo(Dest& dst) const { dst.setZero(); scaleAndAddTo(dst, Scalar(1)); }
261 
262     template<typename Dest>
263     inline void addTo(Dest& dst) const { scaleAndAddTo(dst, Scalar(1)); }
264 
265     template<typename Dest>
266     inline void subTo(Dest& dst) const { scaleAndAddTo(dst, Scalar(-1)); }
267 
268     template<typename Dest>
269     inline void scaleAndAddTo(Dest& dst, const Scalar& a_alpha) const { m_prod.derived().scaleAndAddTo(dst,a_alpha * m_alpha); }
270 
271     const Scalar& alpha() const { return m_alpha; }
272 
273   protected:
274     const NestedProduct& m_prod;
275     Scalar m_alpha;
276 };
277 
278 /** \internal
279   * Overloaded to perform an efficient C = (A*B).lazy() */
280 template<typename Derived>
281 template<typename ProductDerived, typename Lhs, typename Rhs>
282 Derived& MatrixBase<Derived>::lazyAssign(const ProductBase<ProductDerived, Lhs,Rhs>& other)
283 {
284   other.derived().evalTo(derived());
285   return derived();
286 }
287 
288 } // end namespace Eigen
289 
290 #endif // EIGEN_PRODUCTBASE_H
291