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
|
// 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>
//
// 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_DOT_H
#define EIGEN_DOT_H
template<int Index, int Size, typename Derived1, typename Derived2>
struct ei_dot_unroller
{
static void run(const Derived1 &v1, const Derived2& v2, typename Derived1::Scalar &dot)
{
ei_dot_unroller<Index-1, Size, Derived1, Derived2>::run(v1, v2, dot);
dot += v1.coeff(Index) * ei_conj(v2.coeff(Index));
}
};
template<int Size, typename Derived1, typename Derived2>
struct ei_dot_unroller<0, Size, Derived1, Derived2>
{
static void run(const Derived1 &v1, const Derived2& v2, typename Derived1::Scalar &dot)
{
dot = v1.coeff(0) * ei_conj(v2.coeff(0));
}
};
template<int Index, typename Derived1, typename Derived2>
struct ei_dot_unroller<Index, Dynamic, Derived1, Derived2>
{
static void run(const Derived1&, const Derived2&, typename Derived1::Scalar&) {}
};
// prevent buggy user code from causing an infinite recursion
template<int Index, typename Derived1, typename Derived2>
struct ei_dot_unroller<Index, 0, Derived1, Derived2>
{
static void run(const Derived1&, const Derived2&, typename Derived1::Scalar&) {}
};
/** \returns the dot product of *this with other.
*
* \only_for_vectors
*
* \note If the scalar type is complex numbers, then this function returns the hermitian
* (sesquilinear) dot product, linear in the first variable and anti-linear in the
* second variable.
*
* \sa norm2(), norm()
*/
template<typename Derived>
template<typename OtherDerived>
typename ei_traits<Derived>::Scalar
MatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const
{
typedef typename Derived::Nested Nested;
typedef typename OtherDerived::Nested OtherNested;
typedef typename ei_unref<Nested>::type _Nested;
typedef typename ei_unref<OtherNested>::type _OtherNested;
Nested nested(derived());
OtherNested otherNested(other.derived());
ei_assert(_Nested::IsVectorAtCompileTime
&& _OtherNested::IsVectorAtCompileTime
&& nested.size() == otherNested.size());
Scalar res;
const bool unroll = SizeAtCompileTime
* (_Nested::CoeffReadCost + _OtherNested::CoeffReadCost + NumTraits<Scalar>::MulCost)
+ (SizeAtCompileTime - 1) * NumTraits<Scalar>::AddCost
<= EIGEN_UNROLLING_LIMIT;
if(unroll)
ei_dot_unroller<SizeAtCompileTime-1,
unroll ? SizeAtCompileTime : Dynamic,
_Nested, _OtherNested>
::run(nested, otherNested, res);
else
{
res = nested.coeff(0) * ei_conj(otherNested.coeff(0));
for(int i = 1; i < size(); i++)
res += nested.coeff(i)* ei_conj(otherNested.coeff(i));
}
return res;
}
/** \returns the squared norm of *this, i.e. the dot product of *this with itself.
*
* \only_for_vectors
*
* \sa dot(), norm()
*/
template<typename Derived>
typename NumTraits<typename ei_traits<Derived>::Scalar>::Real MatrixBase<Derived>::norm2() const
{
return ei_real(dot(*this));
}
/** \returns the norm of *this, i.e. the square root of the dot product of *this with itself.
*
* \only_for_vectors
*
* \sa dot(), norm2()
*/
template<typename Derived>
typename NumTraits<typename ei_traits<Derived>::Scalar>::Real MatrixBase<Derived>::norm() const
{
return ei_sqrt(norm2());
}
/** \returns an expression of the quotient of *this by its own norm.
*
* \only_for_vectors
*
* \sa norm()
*/
template<typename Derived>
const CwiseUnaryOp<ei_scalar_multiple_op<typename ei_traits<Derived>::Scalar>, Derived>
MatrixBase<Derived>::normalized() const
{
return (*this) * (Scalar(1)/norm());
}
/** \returns true if *this is approximately orthogonal to \a other,
* within the precision given by \a prec.
*
* Example: \include MatrixBase_isOrtho_vector.cpp
* Output: \verbinclude MatrixBase_isOrtho_vector.out
*/
template<typename Derived>
template<typename OtherDerived>
bool MatrixBase<Derived>::isOrtho
(const MatrixBase<OtherDerived>& other, RealScalar prec) const
{
typename ei_nested<Derived,2>::type nested(derived());
typename ei_nested<OtherDerived,2>::type otherNested(other.derived());
return ei_abs2(nested.dot(otherNested)) <= prec * prec * nested.norm2() * otherNested.norm2();
}
/** \returns true if *this is approximately an unitary matrix,
* within the precision given by \a prec. In the case where the \a Scalar
* type is real numbers, a unitary matrix is an orthogonal matrix, whence the name.
*
* \note This can be used to check whether a family of vectors forms an orthonormal basis.
* Indeed, \c m.isOrtho() returns true if and only if the columns of m form an
* orthonormal basis.
*
* Example: \include MatrixBase_isOrtho_matrix.cpp
* Output: \verbinclude MatrixBase_isOrtho_matrix.out
*/
template<typename Derived>
bool MatrixBase<Derived>::isOrtho(RealScalar prec) const
{
typename Derived::Nested nested(derived());
for(int i = 0; i < cols(); i++)
{
if(!ei_isApprox(nested.col(i).norm2(), static_cast<Scalar>(1), prec))
return false;
for(int j = 0; j < i; j++)
if(!ei_isMuchSmallerThan(nested.col(i).dot(nested.col(j)), static_cast<Scalar>(1), prec))
return false;
}
return true;
}
#endif // EIGEN_DOT_H
|
