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1 ## Copyright (C) 1996, 1997 John W. Eaton |
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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 2, or (at your option) |
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8 ## 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, write to the Free |
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17 ## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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18 ## 02110-1301, USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} roots (@var{v}) |
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22 ## |
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23 ## For a vector @var{v} with @math{N} components, return |
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24 ## the roots of the polynomial |
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25 ## @iftex |
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26 ## @tex |
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27 ## $$ |
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28 ## v_1 z^{N-1} + \cdots + v_{N-1} z + v_N. |
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29 ## $$ |
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30 ## @end tex |
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31 ## @end iftex |
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32 ## @ifinfo |
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33 ## |
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34 ## @example |
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35 ## v(1) * z^(N-1) + ... + v(N-1) * z + v(N) |
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36 ## @end example |
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37 ## @end ifinfo |
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38 ## @end deftypefn |
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39 |
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40 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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41 ## Created: 24 December 1993 |
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42 ## Adapted-By: jwe |
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43 |
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44 function r = roots (v) |
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45 |
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46 if (min (size (v)) > 1 || nargin != 1) |
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47 usage ("roots (v), where v is a vector"); |
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48 endif |
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49 |
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50 n = length (v); |
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51 v = reshape (v, 1, n); |
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52 |
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53 ## If v = [ 0 ... 0 v(k+1) ... v(k+l) 0 ... 0 ], we can remove the |
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54 ## leading k zeros and n - k - l roots of the polynomial are zero. |
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55 |
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56 f = find (v); |
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57 m = max (size (f)); |
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58 |
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59 if (m > 0 && n > 1) |
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60 v = v(f(1):f(m)); |
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61 l = max (size (v)); |
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62 if (l > 1) |
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63 A = diag (ones (1, l-2), -1); |
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64 A(1,:) = -v(2:l) ./ v(1); |
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65 r = eig (A); |
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66 if (f(m) < n) |
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67 tmp = zeros (n - f(m), 1); |
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68 r = [r; tmp]; |
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69 endif |
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70 else |
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71 r = zeros (n - f(m), 1); |
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72 endif |
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73 else |
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74 r = []; |
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75 endif |
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76 |
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77 endfunction |
