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
|
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 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_EXTRACT_H
#define EIGEN_EXTRACT_H
/** \class Extract
*
* \brief Expression of a triangular matrix extracted from a given matrix
*
* \param MatrixType the type of the object in which we are taking the triangular part
* \param Mode the kind of triangular matrix expression to construct. Can be Upper, StrictlyUpper,
* UnitUpper, Lower, StrictlyLower, UnitLower. This is in fact a bit field; it must have either
* UpperTriangularBit or LowerTriangularBit, and additionnaly it may have either ZeroDiagBit or
* UnitDiagBit.
*
* This class represents an expression of the upper or lower triangular part of
* a square matrix, possibly with a further assumption on the diagonal. It is the return type
* of MatrixBase::extract() and most of the time this is the only way it is used.
*
* \sa MatrixBase::extract()
*/
template<typename MatrixType, unsigned int Mode>
struct ei_traits<Extract<MatrixType, Mode> >
{
typedef typename MatrixType::Scalar Scalar;
typedef typename ei_nested<MatrixType>::type MatrixTypeNested;
typedef typename ei_unref<MatrixTypeNested>::type _MatrixTypeNested;
enum {
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
Flags = (_MatrixTypeNested::Flags & ~(PacketAccessBit | LinearAccessBit | DirectAccessBit)) | Mode,
CoeffReadCost = _MatrixTypeNested::CoeffReadCost
};
};
template<typename MatrixType, unsigned int Mode> class Extract
: public MatrixBase<Extract<MatrixType, Mode> >
{
public:
EIGEN_GENERIC_PUBLIC_INTERFACE(Extract)
inline Extract(const MatrixType& matrix) : m_matrix(matrix) {}
EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Extract)
inline int rows() const { return m_matrix.rows(); }
inline int cols() const { return m_matrix.cols(); }
inline Scalar coeff(int row, int col) const
{
if(Flags & LowerTriangularBit ? col>row : row>col)
return (Flags & SelfAdjointBit) ? ei_conj(m_matrix.coeff(col, row)) : (Scalar)0;
if(Flags & UnitDiagBit)
return col==row ? (Scalar)1 : m_matrix.coeff(row, col);
else if(Flags & ZeroDiagBit)
return col==row ? (Scalar)0 : m_matrix.coeff(row, col);
else
return m_matrix.coeff(row, col);
}
protected:
const typename MatrixType::Nested m_matrix;
};
/** \returns an expression of a triangular matrix extracted from the current matrix
*
* The parameter \a Mode can have the following values: \c Upper, \c StrictlyUpper, \c UnitUpper,
* \c Lower, \c StrictlyLower, \c UnitLower.
*
* Example: \include MatrixBase_extract.cpp
* Output: \verbinclude MatrixBase_extract.out
*
* \sa class Extract, part(), marked()
*/
template<typename Derived>
template<unsigned int Mode>
const Extract<Derived, Mode> MatrixBase<Derived>::extract() const
{
return derived();
}
/** \returns true if *this is approximately equal to an upper triangular matrix,
* within the precision given by \a prec.
*
* \sa isLower(), extract(), part(), marked()
*/
template<typename Derived>
bool MatrixBase<Derived>::isUpper(RealScalar prec) const
{
if(cols() != rows()) return false;
RealScalar maxAbsOnUpperPart = static_cast<RealScalar>(-1);
for(int j = 0; j < cols(); j++)
for(int i = 0; i <= j; i++)
{
RealScalar absValue = ei_abs(coeff(i,j));
if(absValue > maxAbsOnUpperPart) maxAbsOnUpperPart = absValue;
}
for(int j = 0; j < cols()-1; j++)
for(int i = j+1; i < rows(); i++)
if(!ei_isMuchSmallerThan(coeff(i, j), maxAbsOnUpperPart, prec)) return false;
return true;
}
/** \returns true if *this is approximately equal to a lower triangular matrix,
* within the precision given by \a prec.
*
* \sa isUpper(), extract(), part(), marked()
*/
template<typename Derived>
bool MatrixBase<Derived>::isLower(RealScalar prec) const
{
if(cols() != rows()) return false;
RealScalar maxAbsOnLowerPart = static_cast<RealScalar>(-1);
for(int j = 0; j < cols(); j++)
for(int i = j; i < rows(); i++)
{
RealScalar absValue = ei_abs(coeff(i,j));
if(absValue > maxAbsOnLowerPart) maxAbsOnLowerPart = absValue;
}
for(int j = 1; j < cols(); j++)
for(int i = 0; i < j; i++)
if(!ei_isMuchSmallerThan(coeff(i, j), maxAbsOnLowerPart, prec)) return false;
return true;
}
#endif // EIGEN_EXTRACT_H
|
