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
|
// Copyright (C) 2003--2004 Zbigniew Leyk (zbigniew.leyk@anu.edu.au)
// and David E. Stewart (david.stewart@anu.edu.au)
// and Ronan Collobert (collober@idiap.ch)
//
// This file is part of Torch 3.1.
//
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions
// are met:
// 1. Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
// 2. Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
// 3. The name of the author may not be used to endorse or promote products
// derived from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
// IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
// OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
// IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
// INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
// NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
// THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#ifndef MX_SYM_EIG_INC
#define MX_SYM_EIG_INC
#include "Vec.h"
#include "Mat.h"
#include "mx_givens.h"
#include "mx_hessenberg.h"
namespace Torch {
/**
Routines for symmetric eigenvalue problems.
Based on the "Meschach Library", available at the
anonymous ftp site thrain.anu.edu.au in the directory
pub/meschach.
@author David E. Stewart (david.stewart@anu.edu.au)
@author Zbigniew Leyk (zbigniew.leyk@anu.edu.au)
@author Ronan Collobert (collober@idiap.ch)
*/
//@{
/** Finds eigenvalues of symmetric tridiagonal matrices.
The matrix is represented by a pair of vectors #a# (diag entries)
and #b# (sub-diag and super-diag entries).
Eigenvalues in #a# on return, and eigenvectors in #mat_q#, if this one
is not #NULL#.
*/
void mxTriEig(Vec * a, Vec * b, Mat * mat_q);
/** Computes eigenvalues of a dense symmetric matrix.
#mat_a# \emph{must} be symmetric on entry.
Eigenvalues stored in #out#.
#mat_q# contains orthogonal matrix of eigenvectors if not #NULL#.
*/
void mxSymEig(Mat * mat_a, Mat * mat_q, Vec * out);
//@}
}
#endif
|
