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annotate scripts/polynomial/compan.m @ 23083:e9a0469dedd9 stable

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maint: strip extra trailing newlines from files.
author John W. Eaton <jwe@octave.org>
date Fri, 20 Jan 2017 12:19:08 -0500
parents bac0d6f07a3e
children ef4d915df748 3ac9f9ecfae5
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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bac0d6f07a3e maint: Update copyright notices for 2016.
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1 ## Copyright (C) 1994-2016 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 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 {} {} compan (@var{c})
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21 ## Compute the companion matrix corresponding to polynomial coefficient vector
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22 ## @var{c}.
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23 ##
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24 ## The companion matrix is
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25 ## @tex
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26 ## $$
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27 ## A = \left[\matrix{
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28 ## -c_2/c_1 & -c_3/c_1 & \cdots & -c_N/c_1 & -c_{N+1}/c_1\cr
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29 ## 1 & 0 & \cdots & 0 & 0 \cr
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30 ## 0 & 1 & \cdots & 0 & 0 \cr
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31 ## \vdots & \vdots & \ddots & \vdots & \vdots \cr
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32 ## 0 & 0 & \cdots & 1 & 0}\right].
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33 ## $$
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34 ## @end tex
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35 ## @ifnottex
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36 ## @c Set example in small font to prevent overfull line
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37 ##
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38 ## @smallexample
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39 ## @group
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40 ## _ _
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41 ## | -c(2)/c(1) -c(3)/c(1) @dots{} -c(N)/c(1) -c(N+1)/c(1) |
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42 ## | 1 0 @dots{} 0 0 |
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43 ## | 0 1 @dots{} 0 0 |
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44 ## A = | . . . . . |
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45 ## | . . . . . |
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46 ## | . . . . . |
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47 ## |_ 0 0 @dots{} 1 0 _|
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48 ## @end group
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49 ## @end smallexample
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50 ##
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51 ## @end ifnottex
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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{roots, poly, eig}
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55 ## @end deftypefn
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57 ## Author: Tony Richardson <arichard@stark.cc.oh.us>
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58 ## Created: June 1994
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59 ## Adapted-By: jwe
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60
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61 function A = compan (c)
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63 if (nargin != 1)
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64 print_usage ();
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65 endif
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67 if (! isvector (c))
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68 error ("compan: C must be a vector");
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69 endif
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71 n = length (c);
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72
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73 if (n == 1)
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74 A = [];
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75 else
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76 A = diag (ones (n-2, 1), -1);
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77 A(1,:) = -c(2:n) / c(1);
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78 endif
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80 endfunction
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83 %!assert (compan ([1, 2, 3]), [-2, -3; 1, 0])
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84 %!assert (compan ([1; 2; 3]), [-2, -3; 1, 0])
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85 %!assert (isempty (compan (4)))
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86 %!assert (compan ([3, 2, 1]), [-2/3, -1/3; 1, 0])
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88 %!error compan ([1,2;3,4])
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89 %!error compan ([])