Mercurial > octave-nkf

annotate scripts/polynomial/polyeig.m @ 15190:ee9b1270c25a

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
polyeig.m: Style fixes
author Jordi Gutiérrez Hermoso <jordigh@octave.org>
date Thu, 16 Aug 2012 12:18:52 -0400
parents 2ad5e6212cd7
children 0c0f4eef30f4
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
15189
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
1 ## Copyright (C) 2012 Fotios Kasolis
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
2 ##
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
3 ## This file is part of Octave.
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
4 ##
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
5 ## Octave is free software; you can redistribute it and/or modify it
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
6 ## under the terms of the GNU General Public License as published by
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
7 ## the Free Software Foundation; either version 3 of the License, or (at
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
8 ## your option) any later version.
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
9 ##
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
10 ## Octave is distributed in the hope that it will be useful, but
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
13 ## General Public License for more details.
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
14 ##
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
15 ## You should have received a copy of the GNU General Public License
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
16 ## along with Octave; see the file COPYING. If not, see
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
17 ## <http://www.gnu.org/licenses/>.
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
18
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
19 ## -*- texinfo -*-
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
20 ## @deftypefn {Function File} {@var{z} =} polyeig (@var{C0}, @var{C1}, @dots{}, @var{Cl})
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
21 ## @deftypefnx {Function File} {[ @var{v}, @var{z} ] =} polyeig (@var{C0}, @var{C1}, @dots{}, @var{Cl})
15190
ee9b1270c25a polyeig.m: Style fixes
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15189
diff changeset
22 ##
15189
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
23 ## Solve the polynomial eigenvalue problem of degree @var{l}.
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
24 ##
15190
ee9b1270c25a polyeig.m: Style fixes
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15189
diff changeset
25 ## Given a @var{n*n} matrix polynomial @var{C(s)} = @var{C0 + C1 s +
ee9b1270c25a polyeig.m: Style fixes
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15189
diff changeset
26 ## @dots{} + Cl s^l} polyeig solves the eigenvalue problem (@var{C0} +
ee9b1270c25a polyeig.m: Style fixes
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15189
diff changeset
27 ## @var{C1} + @dots{} + @var{Cl})v = 0. Note that the eigenvalues
ee9b1270c25a polyeig.m: Style fixes
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15189
diff changeset
28 ## @var{z} are the zeros of the matrix polynomial. @var{z} is a
ee9b1270c25a polyeig.m: Style fixes
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15189
diff changeset
29 ## @var{lxn} vector and @var{v} is a @var{(n x n)l} matrix with columns
ee9b1270c25a polyeig.m: Style fixes
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15189
diff changeset
30 ## that correspond to the eigenvectors.
ee9b1270c25a polyeig.m: Style fixes
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15189
diff changeset
31 ##
15189
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
32 ## @seealso{eig, eigs, compan}
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
33 ## @end deftypefn
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
34
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
35 ## Author: Fotios Kasolis
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
36
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
37 function [ z, varargout ] = polyeig (varargin)
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
38
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
39 if ( nargout > 2 )
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
40 print_usage ();
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
41 endif
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
42
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
43 nin = numel (varargin);
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
44
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
45 n = zeros (1, nin);
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
46
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
47 for cnt = 1 : nin
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
48 if ! ( issquare (varargin{cnt}) )
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
49 error ("polyeig: coefficients must be square matrices");
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
50 endif
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
51 n(cnt) = size (varargin{cnt}, 1);
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
52 endfor
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
53
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
54 if numel (unique (n)) > 1
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
55 error ("polyeig: coefficients must have the same dimensions");
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
56 endif
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
57 n = unique (n);
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
58
15190
ee9b1270c25a polyeig.m: Style fixes
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15189
diff changeset
59 ## matrix polynomial degree
15189
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
60 l = nin - 1;
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
61
15190
ee9b1270c25a polyeig.m: Style fixes
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15189
diff changeset
62 ## form needed matrices
ee9b1270c25a polyeig.m: Style fixes
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15189
diff changeset
63 C = [ zeros(n * (l - 1), n), eye(n * (l - 1));
ee9b1270c25a polyeig.m: Style fixes
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15189
diff changeset
64 -cell2mat(varargin(1 : end - 1)) ];
15189
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
65
15190
ee9b1270c25a polyeig.m: Style fixes
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15189
diff changeset
66 D = [ eye(n * (l - 1)), zeros(n * (l - 1), n);
ee9b1270c25a polyeig.m: Style fixes
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15189
diff changeset
67 zeros(n, n * (l - 1)), varargin{end} ];
ee9b1270c25a polyeig.m: Style fixes
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15189
diff changeset
68
ee9b1270c25a polyeig.m: Style fixes
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15189
diff changeset
69 ## solve generalized eigenvalue problem
15189
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
70 if ( isequal (nargout, 1) )
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
71 z = eig (C, D);
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
72 else
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
73 [ z, v ] = eig (C, D);
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
74 varargout{1} = v;
15190
ee9b1270c25a polyeig.m: Style fixes
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15189
diff changeset
75 ## return n-element eigenvectors normalized so
ee9b1270c25a polyeig.m: Style fixes
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15189
diff changeset
76 ## that the infinity-norm = 1
15189
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
77 z = z(1:n,:);
15190
ee9b1270c25a polyeig.m: Style fixes
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15189
diff changeset
78 ## max() takes the abs if complex:
ee9b1270c25a polyeig.m: Style fixes
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15189
diff changeset
79 t = max (z);
ee9b1270c25a polyeig.m: Style fixes
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15189
diff changeset
80 z /= diag (t);
15189
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
81 endif
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
82
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
83 endfunction
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
84
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
85 %!test
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
86 %! C0 = [8, 0; 0, 4]; C1 = [1, 0; 0, 1];
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
87 %! [v,z] = polyeig (C0, C1);
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
88 %! assert (isequal (z(1), -8), true);
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
89 %! d = C0*v + C1*v*z
2ad5e6212cd7 polyeig: remove DOS newlines
Jordi Gutiérrez Hermoso <jordigh@octave.org>
parents: 15187
diff changeset
90 %! assert (isequal (norm(d), 0.0), true);