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1 ## Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2002, 2004, |
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2 ## 2005, 2006, 2007 John W. Eaton |
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3 ## |
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4 ## This file is part of Octave. |
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5 ## |
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6 ## Octave is free software; you can redistribute it and/or modify it |
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7 ## under the terms of the GNU General Public License as published by |
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8 ## the Free Software Foundation; either version 3 of the License, or (at |
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9 ## your option) any later version. |
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10 ## |
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11 ## Octave is distributed in the hope that it will be useful, but |
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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14 ## General Public License for more details. |
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15 ## |
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16 ## You should have received a copy of the GNU General Public License |
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17 ## along with Octave; see the file COPYING. If not, see |
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18 ## <http://www.gnu.org/licenses/>. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} compan (@var{c}) |
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22 ## Compute the companion matrix corresponding to polynomial coefficient |
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23 ## vector @var{c}. |
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24 ## |
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25 ## The companion matrix is |
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26 ## @iftex |
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27 ## @tex |
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28 ## $$ |
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29 ## A = \left[\matrix{ |
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30 ## -c_2/c_1 & -c_3/c_1 & \cdots & -c_N/c_1 & -c_{N+1}/c_1\cr |
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31 ## 1 & 0 & \cdots & 0 & 0 \cr |
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32 ## 0 & 1 & \cdots & 0 & 0 \cr |
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33 ## \vdots & \vdots & \ddots & \vdots & \vdots \cr |
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34 ## 0 & 0 & \cdots & 1 & 0}\right]. |
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35 ## $$ |
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36 ## @end tex |
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37 ## @end iftex |
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38 ## @ifnottex |
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39 ## |
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40 ## @smallexample |
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41 ## _ _ |
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42 ## | -c(2)/c(1) -c(3)/c(1) ... -c(N)/c(1) -c(N+1)/c(1) | |
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43 ## | 1 0 ... 0 0 | |
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44 ## | 0 1 ... 0 0 | |
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45 ## A = | . . . . . | |
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46 ## | . . . . . | |
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47 ## | . . . . . | |
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48 ## |_ 0 0 ... 1 0 _| |
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49 ## @end smallexample |
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50 ## @end ifnottex |
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51 ## |
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52 ## The eigenvalues of the companion matrix are equal to the roots of the |
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53 ## polynomial. |
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54 ## @seealso{poly, roots, residue, conv, deconv, polyval, polyderiv, |
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55 ## polyinteg} |
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56 ## @end deftypefn |
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57 |
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58 ## Author: Tony Richardson <arichard@stark.cc.oh.us> |
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59 ## Created: June 1994 |
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60 ## Adapted-By: jwe |
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61 |
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62 function A = compan (c) |
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63 |
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64 if (nargin != 1) |
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65 print_usage (); |
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66 endif |
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67 |
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68 if (! isvector (c)) |
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69 error ("compan: expecting a vector argument"); |
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70 endif |
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71 |
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72 n = length (c); |
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73 |
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74 if (n == 1) |
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75 A = []; |
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76 else |
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77 A = diag (ones (n-2, 1), -1); |
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78 A(1,:) = -c(2:n) / c(1); |
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79 endif |
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80 |
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81 endfunction |
