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
|
/*!
* \file
* \brief Definitions of QR factorisation functions
* \author Tony Ottosson
*
* -------------------------------------------------------------------------
*
* IT++ - C++ library of mathematical, signal processing, speech processing,
* and communications classes and functions
*
* Copyright (C) 1995-2008 (see AUTHORS file for a list of contributors)
*
* This program is free software; 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.
*
* This program 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 General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
*
* -------------------------------------------------------------------------
*/
#ifndef QR_H
#define QR_H
#include <itpp/base/mat.h>
namespace itpp {
/*! \addtogroup matrixdecomp
*/
//!@{
/*!
\brief QR factorisation of real matrix
The QR factorization of the real matrix \f$\mathbf{A}\f$ of size \f$m \times n\f$ is given
by
\f[
\mathbf{A} = \mathbf{Q} \mathbf{R} ,
\f]
where \f$\mathbf{Q}\f$ is an \f$m \times m\f$ orthogonal matrix and \f$\mathbf{R}\f$ is an \f$m \times n\f$ upper triangular matrix.
Returns true is calculation succeeds. False otherwise.
Uses the LAPACK routine DGEQRF and DORGQR.
*/
bool qr(const mat &A, mat &Q, mat &R);
/*!
\brief QR factorisation of real matrix with pivoting
The QR factorization of the real matrix \f$\mathbf{A}\f$ of size \f$m \times n\f$ is given
by
\f[
\mathbf{A} \mathbf{P} = \mathbf{Q} \mathbf{R} ,
\f]
where \f$\mathbf{Q}\f$ is an \f$m \times m\f$ orthogonal matrix, \f$\mathbf{R}\f$ is an \f$m \times n\f$ upper triangular matrix
and \f$\mathbf{P}\f$ is an \f$n \times n\f$ permutation matrix.
Returns true is calculation succeeds. False otherwise.
Uses the LAPACK routines DGEQP3 and DORGQR.
*/
bool qr(const mat &A, mat &Q, mat &R, bmat &P);
/*!
\brief QR factorisation of a complex matrix
The QR factorization of the complex matrix \f$\mathbf{A}\f$ of size \f$m \times n\f$ is given
by
\f[
\mathbf{A} = \mathbf{Q} \mathbf{R} ,
\f]
where \f$\mathbf{Q}\f$ is an \f$m \times m\f$ unitary matrix and \f$\mathbf{R}\f$ is an \f$m \times n\f$ upper triangular matrix.
Returns true is calculation succeeds. False otherwise.
Uses the LAPACK routines ZGEQRF and ZUNGQR.
*/
bool qr(const cmat &A, cmat &Q, cmat &R);
/*!
\brief QR factorisation of a complex matrix with pivoting
The QR factorization of the complex matrix \f$\mathbf{A}\f$ of size \f$m \times n\f$ is given
by
\f[
\mathbf{A} \mathbf{P} = \mathbf{Q} \mathbf{R} ,
\f]
where \f$\mathbf{Q}\f$ is an \f$m \times m\f$ unitary matrix, \f$\mathbf{R}\f$ is an \f$m \times n\f$ upper triangular matrix
and \f$\mathbf{P}\f$ is an \f$n \times n\f$ permutation matrix.
Returns true is calculation succeeds. False otherwise.
Uses the LAPACK routines ZGEQP3 and ZUNGQR.
*/
bool qr(const cmat &A, cmat &Q, cmat &R, bmat &P);
//!@}
} // namespace itpp
#endif // #ifndef QR_H
|
