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annotate scripts/polynomial/polyaffine.m @ 12118:973f585cfdf2 release-3-2-x

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include PTHREAD_CFLAGS in LINK_DEPS for liboctave
author Jaroslav Hajek <highegg@gmail.com>
date Fri, 22 Jan 2010 10:21:33 +0100
parents a8be2f7c81ee
children 09da0bd91412
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1 ## Copyright (C) 2009 Tony Richardson, Jaroslav Hajek
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2 ##
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3 ## This program is free software; you can redistribute it and/or modify
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4 ## it under the terms of the GNU General Public License as published by
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5 ## the Free Software Foundation; either version 3 of the License, or
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6 ## (at your option) any later version.
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7 ##
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8 ## This program is distributed in the hope that it will be useful,
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9 ## but WITHOUT ANY WARRANTY; without even the implied warranty of
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10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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11 ## GNU General Public License for more details.
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12 ##
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13 ## You should have received a copy of the GNU General Public License
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14 ## along with this program; If not, see <http://www.gnu.org/licenses/>.
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15
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16 ## -*- texinfo -*-
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17 ## @deftypefn {Function File} {} polyaffine (@var{f}, @var{mu})
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18 ## Return the coefficients of the polynomial whose coefficients are given by
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19 ## vector @var{f} after an affine tranformation. If @var{f} is the vector
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20 ## representing the polynomial f(x), then @var{g} = polytrans (@var{f},
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21 ## @var{mu}) is the vector representing
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22 ## @example
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23 ## g(x) = f((x-@var{mu}(1))/@var{mu}(2)).
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24 ## @end example
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25 ##
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26 ## @seealso{polyval}
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27 ## @end deftypefn
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28
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29
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30 function g = polyaffine (f, mu)
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31
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32 if (nargin != 2)
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33 print_usage ();
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34 endif
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35
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36 if (! isvector (f))
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37 error ("polyaffine: first argument must be a vector.");
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38 endif
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39
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40 if (! isvector (mu) || length (mu) != 2)
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41 error ("polyaffine: second argument must be a two-element vector.");
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42 endif
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43
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44 lf = length (f);
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45
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46 ## Ensure that f is a row vector
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47 if (rows (f) > 1)
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48 f = f.';
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49 endif
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50
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51 g = f;
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52
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53 ## Scale.
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54 if (mu(2) != 1)
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55 g = g ./ (mu(2) .^ (lf-1:-1:0));
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56 endif
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57
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58 ## Translate.
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59 if (mu(1) != 0)
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60 w = (-mu(1)) .^ (0:lf-1);
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61 ii = lf:-1:1;
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62 g = g(ii) * (toeplitz (w) .* pascal (lf, -1));
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63 g = g(ii);
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64 endif
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65
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66 endfunction
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67
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68 %!test
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69 %! f = [1/5 4/5 -7/5 -2];
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70 %!
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71 %! mu = [1, 1.2];
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72 %!
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73 %! g = polyaffine (f, mu);
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74 %!
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75 %! x = linspace (-4, 4, 100);
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76 %!
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77 %! assert (polyval(f, x, [], mu), polyval (g, x), 1e-10);
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78 %!
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79 %!demo
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80 %! f = [1/5 4/5 -7/5 -2];
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81 %!
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82 %! g = polyaffine (f, [1, 1.2]);
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83 %!
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84 %! x = linspace (-4, 4, 100);
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85 %!
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86 %! plot(x, polyval (f, x), x, polyval (g, x));
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87 %!
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88 %! axis ([-4 4 -3 5]);
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89 %! grid ("on");