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1 ## Copyright (C) 1995, 1996, 1997, 1998, 1999, 2000, 2002, 2004, 2005, |
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2 ## 2006, 2007, 2008 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} {} cov (@var{x}, @var{y}) |
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22 ## Compute covariance. |
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23 ## |
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24 ## If each row of @var{x} and @var{y} is an observation and each column is |
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25 ## a variable, the (@var{i}, @var{j})-th entry of |
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26 ## @code{cov (@var{x}, @var{y})} is the covariance between the @var{i}-th |
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27 ## variable in @var{x} and the @var{j}-th variable in @var{y}. |
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28 ## @iftex |
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29 ## @tex |
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30 ## $$ |
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31 ## \sigma_{ij} = {1 \over N-1} \sum_{i=1}^N (x_i - \bar{x})(y_i - \bar{y}) |
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32 ## $$ |
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33 ## where $\bar{x}$ and $\bar{y}$ are the mean values of $x$ and $y$. |
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34 ## @end tex |
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35 ## @end iftex |
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36 ## If called with one argument, compute @code{cov (@var{x}, @var{x})}. |
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37 ## @end deftypefn |
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38 |
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39 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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40 ## Description: Compute covariances |
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41 |
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42 function c = cov (x, y) |
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43 |
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44 if (nargin < 1 || nargin > 2) |
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45 print_usage (); |
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46 endif |
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47 |
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48 if (rows (x) == 1) |
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49 x = x'; |
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50 endif |
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51 n = rows (x); |
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52 |
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53 if (nargin == 2) |
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54 if (rows (y) == 1) |
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55 y = y'; |
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56 endif |
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57 if (rows (y) != n) |
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58 error ("cov: x and y must have the same number of observations"); |
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59 endif |
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60 x = x - ones (n, 1) * sum (x) / n; |
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61 y = y - ones (n, 1) * sum (y) / n; |
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62 c = conj (x' * y / (n - 1)); |
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63 elseif (nargin == 1) |
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64 x = x - ones (n, 1) * sum (x) / n; |
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65 c = conj (x' * x / (n - 1)); |
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66 endif |
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67 |
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68 endfunction |
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69 |
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70 %!test |
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71 %! x = rand (10); |
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72 %! cx1 = cov (x); |
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73 %! cx2 = cov (x, x); |
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74 %! assert(size (cx1) == [10, 10] && size (cx2) == [10, 10] && norm(cx1-cx2) < 1e1*eps); |
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75 |
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76 %!error cov (); |
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77 |
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78 %!error cov (1, 2, 3); |
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79 |
