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update copyright notices
author John W. Eaton <jwe@octave.org>
date Fri, 14 Jan 2011 05:47:45 -0500
parents e151e23f73bc
children c792872f8942
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John W. Eaton <jwe@octave.org>
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1 ## Copyright (C) 1995-2011 Kurt Hornik
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} var (@var{x})
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21 ## @deftypefnx {Function File} {} var (@var{x}, @var{opt})
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22 ## @deftypefnx {Function File} {} var (@var{x}, @var{opt}, @var{dim})
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23 ## Compute the variance of the elements of the vector @var{x}.
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24 ## @tex
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25 ## $$
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26 ## {\rm std} (x) = \sigma^2 = {\sum_{i=1}^N (x_i - \bar{x})^2 \over N - 1}
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27 ## $$
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28 ## where $\bar{x}$ is the mean value of $x$.
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29 ## @end tex
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30 ## @ifnottex
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31 ##
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32 ## @example
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33 ## @group
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34 ## std (x) = 1/(N-1) SUM_i (x(i) - mean(x))^2
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35 ## @end group
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36 ## @end example
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37 ##
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38 ## @end ifnottex
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39 ## If @var{x} is a matrix, compute the variance for each column
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40 ## and return them in a row vector.
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41 ##
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42 ## The argument @var{opt} determines the type of normalization to use.
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43 ## Valid values are
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44 ##
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45 ## @table @asis
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46 ## @item 0:
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47 ## normalize with @math{N-1}, provides the best unbiased estimator of the
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48 ## variance [default]
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49 ##
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50 ## @item 1:
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51 ## normalizes with @math{N}, this provides the second moment around the mean
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52 ## @end table
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53 ##
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54 ## If the optional argument @var{dim} is given, operate along this dimension.
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55 ## @seealso{cov,std,skewness,kurtosis,moment}
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56 ## @end deftypefn
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57
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58 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
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59 ## Description: Compute variance
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60
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61 function retval = var (x, opt = 0, dim)
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62
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63 if (nargin < 1 || nargin > 3)
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64 print_usage ();
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65 endif
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66
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67 if (!isnumeric (x))
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68 error ("var: X must be a numeric vector or matrix");
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69 endif
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70
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71 if (isempty (opt))
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72 opt = 0;
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73 endif
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74 if (opt != 0 && opt != 1)
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75 error ("var: normalization OPT must be 0 or 1");
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76 endif
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77
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78 if (nargin < 3)
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79 dim = find (size (x) > 1, 1);
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80 if (isempty (dim))
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81 dim = 1;
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82 endif
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83 endif
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84
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85 n = size (x, dim);
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86 if (n == 1)
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87 retval = zeros (size (x), class (x));
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88 elseif (numel (x) > 0)
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89 retval = sumsq (center (x, dim), dim) / (n - 1 + opt);
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90 else
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91 error ("var: X must not be empty");
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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 %!assert (var (13), 0)
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97 %!assert (var ([1,2,3]), 1)
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98 %!assert (var ([1,2,3], 1), 2/3, eps)
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99 %!assert (var ([1,2,3], [], 1), [0,0,0])
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100
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101 %% Test input validation
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102 %!error var ()
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103 %!error var (1,2,3,4)
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104 %!error var (true(1,2))
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105 %!error var (1, -1);
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106 %!error var ([],1)
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107