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1 ## Copyright (C) 1995, 1996, 1999, 2000, 2002, 2005, 2006, 2007 |
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2 ## Kurt Hornik |
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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} {} detrend (@var{x}, @var{p}) |
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22 ## If @var{x} is a vector, @code{detrend (@var{x}, @var{p})} removes the |
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23 ## best fit of a polynomial of order @var{p} from the data @var{x}. |
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24 ## |
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25 ## If @var{x} is a matrix, @code{detrend (@var{x}, @var{p})} does the same |
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26 ## for each column in @var{x}. |
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27 ## |
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28 ## The second argument is optional. If it is not specified, a value of 1 |
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29 ## is assumed. This corresponds to removing a linear trend. |
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30 ## @end deftypefn |
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31 |
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32 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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33 ## Created: 11 October 1994 |
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34 ## Adapted-By: jwe |
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35 |
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36 function y = detrend (x, p) |
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37 |
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38 if (nargin == 1) |
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39 p = 1; |
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40 elseif (nargin == 2) |
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41 if (! (isscalar (p) && p == round (p) && p >= 0)) |
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42 error ("detrend: p must be a nonnegative integer"); |
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43 endif |
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44 else |
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45 print_usage (); |
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46 endif |
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47 |
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48 [m, n] = size (x); |
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49 if (m == 1) |
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50 x = x'; |
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51 endif |
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52 |
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53 r = rows (x); |
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54 b = ((1 : r)' * ones (1, p + 1)) .^ (ones (r, 1) * (0 : p)); |
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55 y = x - b * (b \ x); |
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56 |
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57 if (m == 1) |
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58 y = y'; |
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59 endif |
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60 |
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61 endfunction |
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62 |
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63 %!test |
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64 %! N=32; |
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65 %! x = (0:1:N-1)/N + 2; |
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66 %! y = detrend(x); |
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67 %! assert(all (all (abs (y) < 20*eps))); |
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68 |
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69 %!test |
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70 %! N=32; |
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71 %! t = (0:1:N-1)/N; |
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72 %! x = t .* t + 2; |
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73 %! y = detrend(x,2); |
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74 %! assert(all (all (abs (y) < 30*eps))); |
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75 |
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76 %!test |
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77 %! N=32; |
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78 %! t = (0:1:N-1)/N; |
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79 %! x = [t;4*t-3]'; |
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80 %! y = detrend(x); |
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81 %! assert(all (all (abs (y) < 20*eps))); |
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82 |
