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interpft.m: Fix interpolation to preserve spectral symmetry (bug #39566) * interpft.m: Fix interpolation to preserve spectral symmetry, be compatible with Matlab. Add test cases.
author Mike Miller <mtmiller@ieee.org>
date Sun, 04 Aug 2013 17:27:40 -0400
parents e39f00a32dc7
children 1c89599167a6
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1 ## Copyright (C) 2012 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 {Function File} {@var{z} =} polyeig (@var{C0}, @var{C1}, @dots{}, @var{Cl})
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21 ## @deftypefnx {Function File} {[@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 ## @code{@var{C}(s) = @var{C0} + @var{C1} s + @dots{} + @var{Cl} s^l}
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27 ## polyeig solves the eigenvalue problem
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28 ## @code{(@var{C0} + @var{C1} + @dots{} + @var{Cl})v = 0}.
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29 ## Note that the eigenvalues @var{z} are the zeros of the matrix polynomial.
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30 ## @var{z} is an @var{lxn} vector and @var{v} is an (@var{n} x @var{n})l matrix
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31 ## with columns that correspond to the eigenvectors.
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32 ##
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33 ## @seealso{eig, eigs, compan}
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34 ## @end deftypefn
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35
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36 ## Author: Fotios Kasolis
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37
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38 function [ z, varargout ] = polyeig (varargin)
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39
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40 if ( nargout > 2 )
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41 print_usage ();
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42 endif
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43
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44 nin = numel (varargin);
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45
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46 n = zeros (1, nin);
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47
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48 for cnt = 1 : nin
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49 if (! issquare (varargin{cnt}))
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50 error ("polyeig: coefficients must be square matrices");
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51 endif
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52 n(cnt) = size (varargin{cnt}, 1);
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53 endfor
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54
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55 if (numel (unique (n)) > 1)
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56 error ("polyeig: coefficients must have the same dimensions");
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57 endif
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58 n = unique (n);
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59
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60 ## matrix polynomial degree
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61 l = nin - 1;
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62
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63 ## form needed matrices
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64 C = [ zeros(n * (l - 1), n), eye(n * (l - 1));
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65 -cell2mat(varargin(1 : end - 1)) ];
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66
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67 D = [ eye(n * (l - 1)), zeros(n * (l - 1), n);
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68 zeros(n, n * (l - 1)), varargin{end} ];
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69
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70 ## solve generalized eigenvalue problem
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71 if ( isequal (nargout, 1) )
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72 z = eig (C, D);
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73 else
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74 [ z, v ] = eig (C, D);
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75 varargout{1} = v;
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76 ## return n-element eigenvectors normalized so
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77 ## that the infinity-norm = 1
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78 z = z(1:n,:);
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79 ## max() takes the abs if complex:
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80 t = max (z);
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81 z /= diag (t);
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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 %!test
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87 %! C0 = [8, 0; 0, 4]; C1 = [1, 0; 0, 1];
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88 %! [v,z] = polyeig (C0, C1);
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89 %! assert (isequal (z(1), -8), true);
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90 %! d = C0*v + C1*v*z;
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91 %! assert (isequal (norm(d), 0.0), true);