1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
|
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob@math.jussieu.fr>
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifndef EIGEN_PRODUCT_H
#define EIGEN_PRODUCT_H
template<int Index, int Size, typename Lhs, typename Rhs>
struct ei_product_unroller
{
static void run(int row, int col, const Lhs& lhs, const Rhs& rhs,
typename Lhs::Scalar &res)
{
ei_product_unroller<Index-1, Size, Lhs, Rhs>::run(row, col, lhs, rhs, res);
res += lhs.coeff(row, Index) * rhs.coeff(Index, col);
}
};
template<int Size, typename Lhs, typename Rhs>
struct ei_product_unroller<0, Size, Lhs, Rhs>
{
static void run(int row, int col, const Lhs& lhs, const Rhs& rhs,
typename Lhs::Scalar &res)
{
res = lhs.coeff(row, 0) * rhs.coeff(0, col);
}
};
template<int Index, typename Lhs, typename Rhs>
struct ei_product_unroller<Index, Dynamic, Lhs, Rhs>
{
static void run(int, int, const Lhs&, const Rhs&, typename Lhs::Scalar&) {}
};
// prevent buggy user code from causing an infinite recursion
template<int Index, typename Lhs, typename Rhs>
struct ei_product_unroller<Index, 0, Lhs, Rhs>
{
static void run(int, int, const Lhs&, const Rhs&, typename Lhs::Scalar&) {}
};
/** \class Product
*
* \brief Expression of the product of two matrices
*
* \param Lhs the type of the left-hand side
* \param Rhs the type of the right-hand side
* \param EvalMode internal use only
*
* This class represents an expression of the product of two matrices.
* It is the return type of the operator* between matrices, and most of the time
* this is the only way it is used.
*
* \sa class Sum, class Difference
*/
template<typename Lhs, typename Rhs, int EvalMode>
struct ei_traits<Product<Lhs, Rhs, EvalMode> >
{
typedef typename Lhs::Scalar Scalar;
typedef typename ei_meta_if<
(int)NumTraits<Scalar>::ReadCost < (int)Lhs::CoeffReadCost,
typename Lhs::Eval,
Lhs>::ret ActualLhs;
typedef typename ei_meta_if<
(int)NumTraits<Scalar>::ReadCost < (int)Lhs::CoeffReadCost,
typename Lhs::Eval,
typename Lhs::XprCopy>::ret ActualLhsXprCopy;
typedef typename ei_meta_if<
(int)NumTraits<Scalar>::ReadCost < (int)Rhs::CoeffReadCost,
typename Rhs::Eval,
Rhs>::ret ActualRhs;
typedef typename ei_meta_if<
(int)NumTraits<Scalar>::ReadCost < (int)Rhs::CoeffReadCost,
typename Rhs::Eval,
typename Rhs::XprCopy>::ret ActualRhsXprCopy;
enum {
RowsAtCompileTime = Lhs::RowsAtCompileTime,
ColsAtCompileTime = Rhs::ColsAtCompileTime,
MaxRowsAtCompileTime = Lhs::MaxRowsAtCompileTime,
MaxColsAtCompileTime = Rhs::MaxColsAtCompileTime,
Flags = (RowsAtCompileTime == Dynamic || ColsAtCompileTime == Dynamic)
? (unsigned int)(Lhs::Flags | Rhs::Flags)
: (unsigned int)(Lhs::Flags | Rhs::Flags) & ~LargeBit,
CoeffReadCost
= Lhs::ColsAtCompileTime == Dynamic
? Dynamic
: Lhs::ColsAtCompileTime
* (NumTraits<Scalar>::MulCost + ActualLhs::CoeffReadCost + ActualRhs::CoeffReadCost)
+ (Lhs::ColsAtCompileTime - 1) * NumTraits<Scalar>::AddCost
};
};
template<typename Lhs, typename Rhs> struct ei_product_eval_mode
{
enum{ value = Lhs::MaxRowsAtCompileTime == Dynamic || Rhs::MaxColsAtCompileTime == Dynamic
? CacheOptimal : UnrolledDotProduct };
};
template<typename Lhs, typename Rhs, int EvalMode> class Product : ei_no_assignment_operator,
public MatrixBase<Product<Lhs, Rhs, EvalMode> >
{
public:
EIGEN_GENERIC_PUBLIC_INTERFACE(Product)
typedef typename ei_traits<Product>::ActualLhs ActualLhs;
typedef typename ei_traits<Product>::ActualRhs ActualRhs;
typedef typename ei_traits<Product>::ActualLhsXprCopy ActualLhsXprCopy;
typedef typename ei_traits<Product>::ActualRhsXprCopy ActualRhsXprCopy;
Product(const Lhs& lhs, const Rhs& rhs)
: m_lhs(lhs), m_rhs(rhs)
{
ei_assert(lhs.cols() == rhs.rows());
}
/** \internal */
template<typename DestDerived>
void _cacheOptimalEval(DestDerived& res) const;
private:
int _rows() const { return m_lhs.rows(); }
int _cols() const { return m_rhs.cols(); }
const Scalar _coeff(int row, int col) const
{
Scalar res;
if(EIGEN_UNROLLED_LOOPS
&& Lhs::ColsAtCompileTime != Dynamic
&& Lhs::ColsAtCompileTime <= EIGEN_UNROLLING_LIMIT)
ei_product_unroller<Lhs::ColsAtCompileTime-1,
Lhs::ColsAtCompileTime <= EIGEN_UNROLLING_LIMIT
? Lhs::ColsAtCompileTime : Dynamic,
ActualLhs, ActualRhs>
::run(row, col, m_lhs, m_rhs, res);
else
{
res = m_lhs.coeff(row, 0) * m_rhs.coeff(0, col);
for(int i = 1; i < m_lhs.cols(); i++)
res += m_lhs.coeff(row, i) * m_rhs.coeff(i, col);
}
return res;
}
protected:
const ActualLhsXprCopy m_lhs;
const ActualRhsXprCopy m_rhs;
};
/** \returns the matrix product of \c *this and \a other.
*
* \note This function causes an immediate evaluation. If you want to perform a matrix product
* without immediate evaluation, call .lazy() on one of the matrices before taking the product.
*
* \sa lazy(), operator*=(const MatrixBase&)
*/
template<typename Derived>
template<typename OtherDerived>
const typename ei_eval_unless_lazy<Product<Derived, OtherDerived> >::type
MatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const
{
return Product<Derived, OtherDerived>(derived(), other.derived()).eval();
}
/** replaces \c *this by \c *this * \a other.
*
* \returns a reference to \c *this
*/
template<typename Derived>
template<typename OtherDerived>
Derived &
MatrixBase<Derived>::operator*=(const MatrixBase<OtherDerived> &other)
{
return *this = *this * other;
}
template<typename Derived>
template<typename Derived1, typename Derived2>
Derived& MatrixBase<Derived>::operator=(const Product<Derived1,Derived2,CacheOptimal>& product)
{
product._cacheOptimalEval(*this);
return derived();
}
template<typename Lhs, typename Rhs, int EvalMode>
template<typename DestDerived>
void Product<Lhs,Rhs,EvalMode>::_cacheOptimalEval(DestDerived& res) const
{
res.setZero();
const int cols4 = m_lhs.cols()&0xfffffffC;
for (int k=0; k<m_rhs.cols(); ++k)
{
int j=0;
for (; j<cols4; j+=4)
{
const Scalar tmp0 = m_rhs.coeff(j ,k);
const Scalar tmp1 = m_rhs.coeff(j+1,k);
const Scalar tmp2 = m_rhs.coeff(j+2,k);
const Scalar tmp3 = m_rhs.coeff(j+3,k);
for (int i=0; i<m_lhs.rows(); ++i)
res.coeffRef(i,k) += tmp0 * m_lhs.coeff(i,j) + tmp1 * m_lhs.coeff(i,j+1)
+ tmp2 * m_lhs.coeff(i,j+2) + tmp3 * m_lhs.coeff(i,j+3);
}
for (; j<m_lhs.cols(); ++j)
{
const Scalar tmp = m_rhs.coeff(j,k);
for (int i=0; i<m_lhs.rows(); ++i)
res.coeffRef(i,k) += tmp * m_lhs.coeff(i,j);
}
}
}
#endif // EIGEN_PRODUCT_H
|
