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1 ## Copyright (C) 1995, 1996, 1997, 1998, 2000, 2002, 2005, 2007 |
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2 ## Friedrich Leisch |
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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} {} fractdiff (@var{x}, @var{d}) |
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22 ## Compute the fractional differences @math{(1-L)^d x} where @math{L} |
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23 ## denotes the lag-operator and @math{d} is greater than -1. |
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24 ## @end deftypefn |
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25 |
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26 ## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at> |
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27 ## Description: Compute fractional differences |
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28 |
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29 function retval = fractdiff (x, d) |
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30 |
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31 if (nargin != 2) |
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32 print_usage (); |
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33 endif |
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34 |
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35 N = 100; |
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36 |
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37 if (! isvector (x)) |
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38 error ("fractdiff: x must be a vector") |
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39 endif |
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40 |
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41 if (! isscalar (d)) |
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42 error ("fractdiff: d must be a scalar") |
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43 endif |
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44 |
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45 |
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46 if (d >= 1) |
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47 for k = 1 : d |
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48 x = x(2 : length (x)) - x(1 : length (x) - 1); |
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49 endfor |
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50 endif |
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51 |
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52 if (d > -1) |
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53 |
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54 d = rem (d, 1); |
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55 |
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56 if (d != 0) |
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57 n = (0 : N)'; |
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58 w = real (gamma (-d+n) ./ gamma (-d) ./ gamma (n+1)); |
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59 retval = fftfilt (w, x); |
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60 retval = retval(1 : length (x)); |
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61 else |
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62 retval = x; |
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63 endif |
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64 |
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65 else |
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66 error ("fractdiff: d must be > -1"); |
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67 |
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68 endif |
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69 |
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70 endfunction |
