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1 ## Copyright (C) 1995, 1996, 1997 Friedrich Leisch |
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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 2, or (at your option) |
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6 ## 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, but |
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9 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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11 ## 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 file. If not, write to the Free Software Foundation, |
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15 ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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16 |
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17 ## -*- texinfo -*- |
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18 ## @deftypefn {Function File} {} fractdiff (@var{x}, @var{d}) |
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19 ## Compute the fractional differences @math{(1-L)^d x} where @math{L} |
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20 ## denotes the lag-operator and @math{d} is greater than -1. |
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21 ## @end deftypefn |
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22 |
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23 ## Author: FL <Friedrich.Leisch@ci.tuwien.ac.at> |
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24 ## Description: Compute fractional differences |
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25 |
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26 function retval = fractdiff (x, d) |
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27 |
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28 N = 100; |
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29 |
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30 if (! is_vector (x)) |
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31 error ("fractdiff: x must be a vector") |
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32 endif |
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33 |
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34 if (! is_scalar (d)) |
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35 error ("fractdiff: d must be a scalar") |
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36 endif |
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37 |
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38 |
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39 if (d >= 1) |
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40 for k = 1 : d |
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41 x = x(2 : length (x)) - x(1 : length (x) - 1); |
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42 endfor |
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43 endif |
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44 |
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45 if (d > -1) |
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46 |
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47 d = rem (d, 1); |
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48 |
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49 if (d != 0) |
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50 n = (0 : N)'; |
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51 w = real (gamma (-d+n) ./ gamma (-d) ./ gamma (n+1)); |
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52 retval = fftfilt (w, x); |
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53 retval = retval(1 : length (x)); |
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54 else |
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55 retval = x; |
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56 endif |
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57 |
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58 else |
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59 error ("fractdiff: d must be > -1"); |
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60 |
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61 endif |
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62 |
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63 endfunction |
