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maint: Update copyright dates.
author John W. Eaton <jwe@octave.org>
date Wed, 22 Feb 2017 12:39:29 -0500
parents bac0d6f07a3e
children 092078913d54
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1 ## Copyright (C) 2012-2017 Fotios Kasolis
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {} {@var{z} =} polyeig (@var{C0}, @var{C1}, @dots{}, @var{Cl})
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21 ## @deftypefnx {} {[@var{v}, @var{z}] =} polyeig (@var{C0}, @var{C1}, @dots{}, @var{Cl})
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22 ##
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23 ## Solve the polynomial eigenvalue problem of degree @var{l}.
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24 ##
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25 ## Given an @var{n*n} matrix polynomial
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26 ##
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27 ## @code{@var{C}(s) = @var{C0} + @var{C1} s + @dots{} + @var{Cl} s^l}
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28 ##
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29 ## @code{polyeig} solves the eigenvalue problem
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30 ##
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31 ## @code{(@var{C0} + @var{C1} + @dots{} + @var{Cl})v = 0}.
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32 ##
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33 ## Note that the eigenvalues @var{z} are the zeros of the matrix polynomial.
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34 ## @var{z} is a row vector with @var{n*l} elements. @var{v} is a matrix
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35 ## (@var{n} x @var{n}*@var{l}) with columns that correspond to the
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36 ## eigenvectors.
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37 ##
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38 ## @seealso{eig, eigs, compan}
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39 ## @end deftypefn
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40
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41 ## Author: Fotios Kasolis
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42
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43 function [z, v] = polyeig (varargin)
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44
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45 if (nargin < 1 || nargout > 2)
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46 print_usage ();
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47 endif
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48
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49 nin = numel (varargin);
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50 n = rows (varargin{1});
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51
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52 for i = 1 : nin
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53 if (! issquare (varargin{i}))
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54 error ("polyeig: coefficients must be square matrices");
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55 endif
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56 if (rows (varargin{i}) != n)
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57 error ("polyeig: coefficients must have the same dimensions");
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58 endif
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59 endfor
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60
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61 ## matrix polynomial degree
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62 l = nin - 1;
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63
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64 ## form needed matrices
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65 C = [ zeros(n * (l - 1), n), eye(n * (l - 1));
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66 -cell2mat(varargin(1:end-1)) ];
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67
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68 D = [ eye(n * (l - 1)), zeros(n * (l - 1), n);
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69 zeros(n, n * (l - 1)), varargin{end} ];
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70
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71 ## solve generalized eigenvalue problem
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72 if (nargout == 2)
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73 [z, v] = eig (C, D);
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74 v = diag (v);
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75 ## return n-element eigenvectors normalized so that the infinity-norm = 1
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76 z = z(1:n,:);
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77 ## max() takes the abs if complex:
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78 t = max (z);
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79 z /= diag (t);
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80 else
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81 z = eig (C, D);
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82 endif
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83
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84 endfunction
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85
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86
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87 %!shared C0, C1
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88 %! C0 = [8, 0; 0, 4]; C1 = [1, 0; 0, 1];
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89
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90 %!test
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91 %! z = polyeig (C0, C1);
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92 %! assert (z, [-8; -4]);
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93
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94 %!test
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95 %! [v,z] = polyeig (C0, C1);
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96 %! assert (z, [-8; -4]);
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97 %! z = diag (z);
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98 %! d = C0*v + C1*v*z;
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99 %! assert (norm (d), 0.0);
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100
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101 ## Test input validation
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102 %!error polyeig ()
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103 %!error [a,b,c] = polyeig (1)
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104 %!error <coefficients must be square matrices> polyeig (ones (3,2))
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105 %!error <coefficients must have the same dimensions> polyeig (ones (3,3), ones (2,2))