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annotate scripts/polynomial/polyaffine.m @ 15063:36cbcc37fdb8

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Refactor configure.ac to make it more understandable. Use common syntax for messages in config.h Correct typos, refer to libraries in all caps, use two spaces after period. Follow Autoconf guidelines and place general tests before specific tests. * configure.ac, m4/acinclude.m4: Use common syntax for messages in config.h Correct typos, refer to libraries in all caps, use two spaces after period. Follow Autoconf guidelines and place general tests before specific tests.
author Rik <rik@octave.org>
date Tue, 31 Jul 2012 10:28:51 -0700
parents 5d3a684236b0
children d63878346099
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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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 function g = polyaffine (f, mu)
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34
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35 if (nargin != 2)
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36 print_usage ();
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37 endif
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38
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39 if (! isvector (f))
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40 error ("polyaffine: F must be a vector");
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41 endif
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42
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43 if (! isvector (mu) || length (mu) != 2)
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44 error ("polyaffine: MU must be a two-element vector");
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45 endif
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46
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47 lf = length (f);
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48
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49 ## Ensure that f is a row vector
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50 if (rows (f) > 1)
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51 f = f.';
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52 endif
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53
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54 g = f;
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55
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56 ## Scale.
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57 if (mu(2) != 1)
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58 g = g ./ (mu(2) .^ (lf-1:-1:0));
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59 endif
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60
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61 ## Translate.
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62 if (mu(1) != 0)
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63 w = (-mu(1)) .^ (0:lf-1);
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64 ii = lf:-1:1;
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65 g = g(ii) * (toeplitz (w) .* pascal (lf, -1));
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66 g = g(ii);
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67 endif
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68
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69 endfunction
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70
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71
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72 %!demo
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73 %! f = [1/5 4/5 -7/5 -2];
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74 %! g = polyaffine (f, [1, 1.2]);
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75 %! x = linspace (-4,4,100);
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76 %! plot (x,polyval (f, x), x,polyval (g, x));
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77 %! legend ("original", "affine");
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78 %! axis ([-4 4 -3 5]);
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79 %! grid on;
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80
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81 %!test
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82 %! f = [1/5 4/5 -7/5 -2];
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83 %! mu = [1, 1.2];
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84 %! g = polyaffine (f, mu);
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85 %! x = linspace (-4,4,100);
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86 %! assert (polyval (f, x, [], mu), polyval (g, x), 1e-10);
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87