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update Octave Project Developers copyright for the new year In files that have the "Octave Project Developers" copyright notice, update for 2020.
author John W. Eaton <jwe@octave.org>
date Mon, 06 Jan 2020 22:29:51 -0500
parents b442ec6dda5c
children bd51beb6205e
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27919
1891570abac8 update Octave Project Developers copyright for the new year
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1 ## Copyright (C) 2012-2020 The Octave Project Developers
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2 ##
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3 ## See the file COPYRIGHT.md in the top-level directory of this distribution
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4 ## or <https://octave.org/COPYRIGHT.html/>.
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5 ##
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6 ##
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7 ## This file is part of Octave.
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8 ##
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9 ## Octave is free software: you can redistribute it and/or modify it
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10 ## under the terms of the GNU General Public License as published by
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11 ## the Free Software Foundation, either version 3 of the License, or
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12 ## (at your option) any later version.
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13 ##
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14 ## Octave is distributed in the hope that it will be useful, but
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15 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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16 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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17 ## GNU General Public License for more details.
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18 ##
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19 ## You should have received a copy of the GNU General Public License
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20 ## along with Octave; see the file COPYING. If not, see
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21 ## <https://www.gnu.org/licenses/>.
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22
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23 ## -*- texinfo -*-
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24 ## @deftypefn {} {@var{z} =} polyeig (@var{C0}, @var{C1}, @dots{}, @var{Cl})
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25 ## @deftypefnx {} {[@var{v}, @var{z}] =} polyeig (@var{C0}, @var{C1}, @dots{}, @var{Cl})
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26 ##
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27 ## Solve the polynomial eigenvalue problem of degree @var{l}.
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28 ##
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29 ## Given an @var{n}x@var{n} matrix polynomial
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30 ##
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31 ## @code{@var{C}(@var{s}) = @var{C0} + @var{C1} @var{s} + @dots{} + @var{Cl}
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32 ## @var{s}^@var{l}}
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33 ##
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34 ## @code{polyeig} solves the eigenvalue problem
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35 ##
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36 ## @code{(@var{C0} + @var{C1} @var{z} + @dots{} + @var{Cl} @var{z}^@var{l})
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37 ## @var{v} = 0}.
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38 ##
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39 ## Note that the eigenvalues @var{z} are the zeros of the matrix polynomial.
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40 ## @var{z} is a row vector with @code{@var{n}*@var{l}} elements. @var{v} is a
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41 ## matrix (@var{n} x @var{n}*@var{l}) with columns that correspond to the
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42 ## eigenvectors.
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43 ##
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44 ## @seealso{eig, eigs, compan}
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45 ## @end deftypefn
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46
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47 function [z, v] = polyeig (varargin)
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48
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49 if (nargin < 1 || nargout > 2)
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50 print_usage ();
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51 endif
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52
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53 n = rows (varargin{1});
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54
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55 for i = 1 : nargin
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56 if (! issquare (varargin{i}))
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57 error ("polyeig: coefficients must be square matrices");
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58 endif
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59 if (rows (varargin{i}) != n)
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60 error ("polyeig: coefficients must have the same dimensions");
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61 endif
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62 endfor
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63
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64 ## matrix polynomial degree
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65 l = nargin - 1;
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66
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67 ## form needed matrices
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68 C = [ zeros(n * (l - 1), n), eye(n * (l - 1));
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69 -cell2mat(varargin(1:end-1)) ];
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70
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71 D = [ eye(n * (l - 1)), zeros(n * (l - 1), n);
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72 zeros(n, n * (l - 1)), varargin{end} ];
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73
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74 ## solve generalized eigenvalue problem
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75 if (nargout < 2)
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76 z = eig (C, D);
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77 else
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78 [z, v] = eig (C, D);
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79 v = diag (v);
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80 ## return n-element eigenvectors normalized so that the infinity-norm = 1
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81 z = z(1:n,:);
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82 t = max (z); # max() takes the abs if complex.
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83 z ./= t;
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84 endif
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85
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86 endfunction
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87
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88
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89 %!shared C0, C1
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90 %! C0 = [8, 0; 0, 4];
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91 %! C1 = [1, 0; 0, 1];
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92
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93 %!test
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94 %! z = polyeig (C0, C1);
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95 %! assert (z, [-8; -4]);
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96
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97 %!test
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98 %! [v,z] = polyeig (C0, C1);
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99 %! assert (z, [-8; -4]);
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100 %! z = diag (z);
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101 %! d = C0*v + C1*v*z;
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102 %! assert (norm (d), 0.0);
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103
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104 ## Test input validation
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105 %!error polyeig ()
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106 %!error [a,b,c] = polyeig (1)
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107 %!error <coefficients must be square matrices> polyeig (ones (3,2))
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108 %!error <coefficients must have the same dimensions>
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109 %! polyeig (ones (3,3), ones (2,2))