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
|
// 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_IDENTITY_H
#define EIGEN_IDENTITY_H
/** \class Identity
*
* \brief Expression of the identity matrix of some size.
*
* \sa MatrixBase::identity(), MatrixBase::identity(int,int), MatrixBase::setIdentity()
*/
template<typename MatrixType>
struct ei_traits<Identity<MatrixType> >
{
typedef typename MatrixType::Scalar Scalar;
enum {
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
};
};
template<typename MatrixType> class Identity : NoOperatorEquals,
public MatrixBase<Identity<MatrixType> >
{
public:
EIGEN_BASIC_PUBLIC_INTERFACE(Identity)
Identity(int rows, int cols) : m_rows(rows), m_cols(cols)
{
assert(rows > 0
&& (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows)
&& cols > 0
&& (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols));
}
private:
const Identity& _asArg() const { return *this; }
int _rows() const { return m_rows.value(); }
int _cols() const { return m_cols.value(); }
Scalar _coeff(int row, int col) const
{
return row == col ? static_cast<Scalar>(1) : static_cast<Scalar>(0);
}
protected:
const IntAtRunTimeIfDynamic<RowsAtCompileTime> m_rows;
const IntAtRunTimeIfDynamic<ColsAtCompileTime> m_cols;
};
/** \returns an expression of the identity matrix (not necessarily square).
*
* The parameters \a rows and \a cols are the number of rows and of columns of
* the returned matrix. Must be compatible with this MatrixBase type.
*
* This variant is meant to be used for dynamic-size matrix types. For fixed-size types,
* it is redundant to pass \a rows and \a cols as arguments, so identity() should be used
* instead.
*
* Example: \include MatrixBase_identity_int_int.cpp
* Output: \verbinclude MatrixBase_identity_int_int.out
*
* \sa identity(), setIdentity(), isIdentity()
*/
template<typename Derived>
const Identity<Derived> MatrixBase<Derived>::identity(int rows, int cols)
{
return Identity<Derived>(rows, cols);
}
/** \returns an expression of the identity matrix (not necessarily square).
*
* This variant is only for fixed-size MatrixBase types. For dynamic-size types, you
* need to use the variant taking size arguments.
*
* Example: \include MatrixBase_identity.cpp
* Output: \verbinclude MatrixBase_identity.out
*
* \sa identity(int,int), setIdentity(), isIdentity()
*/
template<typename Derived>
const Identity<Derived> MatrixBase<Derived>::identity()
{
return Identity<Derived>(RowsAtCompileTime, ColsAtCompileTime);
}
/** \returns true if *this is approximately equal to the identity matrix
* (not necessarily square),
* within the precision given by \a prec.
*
* Example: \include MatrixBase_isIdentity.cpp
* Output: \verbinclude MatrixBase_isIdentity.out
*
* \sa class Identity, identity(), identity(int,int), setIdentity()
*/
template<typename Derived>
bool MatrixBase<Derived>::isIdentity
(typename NumTraits<Scalar>::Real prec) const
{
for(int j = 0; j < cols(); j++)
{
for(int i = 0; i < rows(); i++)
{
if(i == j)
{
if(!ei_isApprox(coeff(i, j), static_cast<Scalar>(1), prec))
return false;
}
else
{
if(!ei_isMuchSmallerThan(coeff(i, j), static_cast<RealScalar>(1), prec))
return false;
}
}
}
return true;
}
/** Writes the identity expression (not necessarily square) into *this.
*
* Example: \include MatrixBase_setIdentity.cpp
* Output: \verbinclude MatrixBase_setIdentity.out
*
* \sa class Identity, identity(), identity(int,int), isIdentity()
*/
template<typename Derived>
Derived& MatrixBase<Derived>::setIdentity()
{
return *this = Identity<Derived>(rows(), cols());
}
#endif // EIGEN_IDENTITY_H
|
