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1 ## Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004, 2005, 2006, 2007 |
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2 ## 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} {} median (@var{x}, @var{dim}) |
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22 ## If @var{x} is a vector, compute the median value of the elements of |
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23 ## @var{x}. If the elements of @var{x} are sorted, the median is defined |
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24 ## as |
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25 ## @iftex |
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26 ## @tex |
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27 ## $$ |
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28 ## {\rm median} (x) = |
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29 ## \cases{x(\lceil N/2\rceil), & $N$ odd;\cr |
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30 ## (x(N/2)+x(N/2+1))/2, & $N$ even.} |
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31 ## $$ |
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32 ## @end tex |
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33 ## @end iftex |
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34 ## @ifinfo |
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35 ## |
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36 ## @example |
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37 ## @group |
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38 ## x(ceil(N/2)), N odd |
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39 ## median(x) = |
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40 ## (x(N/2) + x((N/2)+1))/2, N even |
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41 ## @end group |
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42 ## @end example |
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43 ## @end ifinfo |
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44 ## If @var{x} is a matrix, compute the median value for each |
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45 ## column and return them in a row vector. If the optional @var{dim} |
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46 ## argument is given, operate along this dimension. |
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47 ## @seealso{std, mean} |
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48 ## @end deftypefn |
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49 |
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50 ## Author: jwe |
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51 |
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52 function retval = median (a, dim) |
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53 |
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54 if (nargin != 1 && nargin != 2) |
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55 print_usage (); |
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56 endif |
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57 if (nargin < 2) |
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58 dim = find (size (a) > 1, 1); |
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59 if (isempty (dim)) |
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60 dim = 1; |
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61 endif |
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62 endif |
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63 |
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64 sz = size (a); |
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65 s = sort (a, dim); |
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66 if (numel (a) > 0) |
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67 if (numel (a) == sz(dim)) |
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68 if (rem (sz(dim), 2) == 0) |
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69 i = sz(dim) / 2; |
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70 retval = (s(i) + s(i+1)) / 2; |
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71 else |
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72 i = ceil (sz(dim) /2); |
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73 retval = s(i); |
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74 endif |
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75 else |
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76 idx = cell (); |
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77 nd = length (sz); |
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78 for i = 1:nd |
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79 idx{i} = 1:sz(i); |
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80 endfor |
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81 if (rem (sz(dim), 2) == 0) |
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82 i = sz(dim) / 2; |
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83 idx{dim} = i; |
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84 retval = s(idx{:}); |
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85 idx{dim} = i+1; |
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86 retval = (retval + s(idx{:})) / 2; |
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87 else |
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88 idx{dim} = ceil (sz(dim) / 2); |
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89 retval = s(idx{:}); |
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90 endif |
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91 endif |
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92 else |
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93 error ("median: invalid matrix argument"); |
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94 endif |
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95 |
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96 endfunction |
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97 |
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98 %!test |
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99 %! x = [1, 2, 3, 4, 5, 6]; |
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100 %! x2 = x'; |
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101 %! y = [1, 2, 3, 4, 5, 6, 7]; |
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102 %! y2 = y'; |
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103 %! |
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104 %! assert((median (x) == median (x2) && median (x) == 3.5 |
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105 %! && median (y) == median (y2) && median (y) == 4 |
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106 %! && median ([x2, 2*x2]) == [3.5, 7] |
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107 %! && median ([y2, 3*y2]) == [4, 12])); |
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108 |
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109 %!error median (); |
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110 |
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111 %!error median (1, 2, 3); |
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112 |
