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annotate scripts/polynomial/polyaffine.m @ 14872:c2dbdeaa25df

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maint: use rows() and columns() to clarify m-files. * gradient.m, interp1q.m, rat.m, tsearchn.m, image.m, imwrite.m, area.m, contourc.m, hist.m, isocolors.m, isonormals.m, meshz.m, print.m, __bar__.m, __go_draw_axes__.m, __interp_cube__.m, __marching_cube__.m, __patch__.m, __print_parse_opts__.m, __quiver__.m, rose.m, shrinkfaces.m, stairs.m, surfnorm.m, tetramesh.m, text.m, deconv.m, spline.m, intersect.m, setdiff.m, setxor.m, union.m, periodogram.m, pcg.m, perms.m: Replace size (x,1) with rows (x) and size(x,2) with columns(x).
author Rik <octave@nomad.inbox5.com>
date Tue, 17 Jul 2012 13:34:19 -0700
parents 5d3a684236b0
children
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