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1 ## Copyright (C) 1994, 1995, 1996, 1997, 1999, 2000, 2005, 2006, 2007, 2008 |
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2 ## 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} {} poly (@var{a}) |
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22 ## If @var{a} is a square @math{N}-by-@math{N} matrix, @code{poly (@var{a})} |
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23 ## is the row vector of the coefficients of @code{det (z * eye (N) - a)}, |
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24 ## the characteristic polynomial of @var{a}. As an example we can use |
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25 ## this to find the eigenvalues of @var{a} as the roots of @code{poly (@var{a})}. |
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26 ## @example |
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27 ## roots(poly(eye(3))) |
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28 ## @result{} 1.00000 + 0.00000i |
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29 ## @result{} 1.00000 - 0.00000i |
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30 ## @result{} 1.00000 + 0.00000i |
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31 ## @end example |
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32 ## In real-life examples you should, however, use the @code{eig} function |
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33 ## for computing eigenvalues. |
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34 ## |
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35 ## If @var{x} is a vector, @code{poly (@var{x})} is a vector of coefficients |
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36 ## of the polynomial whose roots are the elements of @var{x}. That is, |
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37 ## of @var{c} is a polynomial, then the elements of |
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38 ## @code{@var{d} = roots (poly (@var{c}))} are contained in @var{c}. |
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39 ## The vectors @var{c} and @var{d} are, however, not equal due to sorting |
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40 ## and numerical errors. |
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41 ## @seealso{eig, roots} |
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42 ## @end deftypefn |
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43 |
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44 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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45 ## Created: 24 December 1993 |
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46 ## Adapted-By: jwe |
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47 |
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48 function y = poly (x) |
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49 |
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50 if (nargin != 1) |
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51 print_usage (); |
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52 endif |
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53 |
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54 m = min (size (x)); |
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55 n = max (size (x)); |
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56 if (m == 0) |
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57 y = 1; |
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58 return; |
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59 elseif (m == 1) |
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60 v = x; |
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61 elseif (m == n) |
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62 v = eig (x); |
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63 else |
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64 print_usage (); |
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65 endif |
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66 |
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67 y = zeros (1, n+1); |
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68 y(1) = 1; |
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69 for j = 1:n; |
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70 y(2:(j+1)) = y(2:(j+1)) - v(j) .* y(1:j); |
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71 endfor |
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72 |
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73 if (all (all (imag (x) == 0))) |
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74 y = real (y); |
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75 endif |
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76 |
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77 endfunction |
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78 |
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79 %!assert(all (all (poly ([1, 2, 3]) == [1, -6, 11, -6]))); |
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80 |
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81 %!assert(all (all (abs (poly ([1, 2; 3, 4]) - [1, -5, -2]) < sqrt (eps)))); |
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82 |
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83 %!error poly ([1, 2, 3; 4, 5, 6]); |
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84 |
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85 %!assert(poly ([]),1); |
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86 |
