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maint: update copyright notices for 2012
author John W. Eaton <jwe@octave.org>
date Mon, 02 Jan 2012 14:25:41 -0500
parents 614505385171
children 11949c9795a0 4d917a6a858b
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1 ## Copyright (C) 2009-2012 Tony Richardson, Jaroslav Hajek
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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} {} polyaffine (@var{f}, @var{mu})
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21 ## Return the coefficients of the polynomial vector @var{f} after an affine
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22 ## transformation. If @var{f} is the vector representing the polynomial f(x),
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23 ## then @code{@var{g} = polyaffine (@var{f}, @var{mu})} is the vector
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24 ## representing:
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25 ##
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26 ## @example
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27 ## g(x) = f((x-@var{mu}(1))/@var{mu}(2)).
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28 ## @end example
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29 ##
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30 ## @seealso{polyval, polyfit}
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31 ## @end deftypefn
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32
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33
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34 function g = polyaffine (f, mu)
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35
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36 if (nargin != 2)
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37 print_usage ();
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38 endif
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39
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40 if (! isvector (f))
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41 error ("polyaffine: F must be a vector");
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42 endif
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43
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44 if (! isvector (mu) || length (mu) != 2)
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45 error ("polyaffine: MU must be a two-element vector");
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46 endif
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47
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48 lf = length (f);
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49
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50 ## Ensure that f is a row vector
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51 if (rows (f) > 1)
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52 f = f.';
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53 endif
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54
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55 g = f;
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56
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57 ## Scale.
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58 if (mu(2) != 1)
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59 g = g ./ (mu(2) .^ (lf-1:-1:0));
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60 endif
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61
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62 ## Translate.
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63 if (mu(1) != 0)
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64 w = (-mu(1)) .^ (0:lf-1);
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65 ii = lf:-1:1;
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66 g = g(ii) * (toeplitz (w) .* pascal (lf, -1));
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67 g = g(ii);
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68 endif
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69
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70 endfunction
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71
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72
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73 %!demo
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74 %! f = [1/5 4/5 -7/5 -2];
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75 %! g = polyaffine (f, [1, 1.2]);
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76 %! x = linspace (-4, 4, 100);
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77 %! plot(x, polyval (f, x), x, polyval (g, x));
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78 %! legend ("original", "affine");
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79 %! axis ([-4 4 -3 5]);
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80 %! grid ("on");
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81
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82 %!test
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83 %! f = [1/5 4/5 -7/5 -2];
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84 %! mu = [1, 1.2];
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85 %! g = polyaffine (f, mu);
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86 %! x = linspace (-4, 4, 100);
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87 %! assert (polyval (f, x, [], mu), polyval (g, x), 1e-10);
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88