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1 ## Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004, 2005, 2006, 2007, 2008, |
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2 ## 2009 John W. Eaton |
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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} {} std (@var{x}) |
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22 ## @deftypefnx {Function File} {} std (@var{x}, @var{opt}) |
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23 ## @deftypefnx {Function File} {} std (@var{x}, @var{opt}, @var{dim}) |
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24 ## If @var{x} is a vector, compute the standard deviation of the elements |
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25 ## of @var{x}. |
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26 ## @iftex |
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27 ## @tex |
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28 ## $$ |
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29 ## {\rm std} (x) = \sigma (x) = \sqrt{{\sum_{i=1}^N (x_i - \bar{x})^2 \over N - 1}} |
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30 ## $$ |
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31 ## where $\bar{x}$ is the mean value of $x$. |
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32 ## @end tex |
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33 ## @end iftex |
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34 ## @ifnottex |
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35 ## |
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36 ## @example |
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37 ## @group |
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38 ## std (x) = sqrt (sumsq (x - mean (x)) / (n - 1)) |
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39 ## @end group |
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40 ## @end example |
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41 ## @end ifnottex |
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42 ## If @var{x} is a matrix, compute the standard deviation for |
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43 ## each column and return them in a row vector. |
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44 ## |
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45 ## The argument @var{opt} determines the type of normalization to use. Valid values |
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46 ## are |
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47 ## |
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48 ## @table @asis |
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49 ## @item 0: |
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50 ## normalizes with @math{N-1}, provides the square root of best unbiased estimator of |
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51 ## the variance [default] |
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52 ## @item 1: |
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53 ## normalizes with @math{N}, this provides the square root of the second moment around |
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54 ## the mean |
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55 ## @end table |
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56 ## |
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57 ## The third argument @var{dim} determines the dimension along which the standard |
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58 ## deviation is calculated. |
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59 ## @seealso{mean, median} |
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60 ## @end deftypefn |
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61 |
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62 ## Author: jwe |
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63 |
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64 function retval = std (a, opt, dim) |
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65 |
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66 if (nargin < 1 || nargin > 3) |
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67 print_usage (); |
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68 endif |
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69 if nargin < 3 |
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70 dim = find (size (a) > 1, 1); |
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71 if (isempty (dim)) |
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72 dim = 1; |
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73 endif |
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74 endif |
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75 if (nargin < 2 || isempty (opt)) |
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76 opt = 0; |
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77 endif |
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78 |
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79 sz = size(a); |
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80 if (sz (dim) == 1) |
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81 retval = zeros(sz); |
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82 elseif (numel (a) > 0) |
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83 rng = ones (1, length (sz)); |
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84 rng (dim) = sz (dim); |
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85 if (opt == 0) |
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86 retval = sqrt (sumsq (a - repmat(mean (a, dim), rng), dim) / (sz(dim) - 1)); |
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87 else |
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88 retval = sqrt (sumsq (a - repmat(mean (a, dim), rng), dim) / sz(dim)); |
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89 endif |
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90 else |
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91 error ("std: invalid matrix argument"); |
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92 endif |
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93 |
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94 endfunction |
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95 |
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96 %!test |
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97 %! x = ones (10, 2); |
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98 %! y = [1, 3]; |
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99 %! assert(std (x) == [0, 0] && abs (std (y) - sqrt (2)) < sqrt (eps)); |
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100 |
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101 %!error std (); |
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102 |
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103 %!error std (1, 2, 3, 4); |
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104 |
