Mercurial > octave
annotate scripts/statistics/base/std.m @ 20852:516bb87ea72e
2015 Code Sprint: remove class of function from docstring for all m-files.
author | Rik <rik@octave.org> |
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date | Sat, 12 Dec 2015 07:31:00 -0800 |
parents | d9341b422488 |
children | 7fbecef105ca |
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1 ## Copyright (C) 1996-2015 John W. Eaton |
3200 | 2 ## |
3 ## This file is part of Octave. | |
4 ## | |
5 ## Octave is free software; you can redistribute it and/or modify it | |
6 ## under the terms of the GNU General Public License as published by | |
7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
8 ## your option) any later version. | |
3200 | 9 ## |
10 ## Octave is distributed in the hope that it will be useful, but | |
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
13 ## General Public License for more details. | |
14 ## | |
15 ## You should have received a copy of the GNU General Public License | |
7016 | 16 ## along with Octave; see the file COPYING. If not, see |
17 ## <http://www.gnu.org/licenses/>. | |
3200 | 18 |
3367 | 19 ## -*- texinfo -*- |
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20 ## @deftypefn {} {} std (@var{x}) |
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21 ## @deftypefnx {} {} std (@var{x}, @var{opt}) |
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22 ## @deftypefnx {} {} std (@var{x}, @var{opt}, @var{dim}) |
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23 ## Compute the standard deviation of the elements of the vector @var{x}. |
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24 ## |
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25 ## The standard deviation is defined as |
3367 | 26 ## @tex |
27 ## $$ | |
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28 ## {\rm std} (x) = \sigma = \sqrt{{\sum_{i=1}^N (x_i - \bar{x})^2 \over N - 1}} |
3367 | 29 ## $$ |
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30 ## where $\bar{x}$ is the mean value of $x$ and $N$ is the number of elements. |
3367 | 31 ## @end tex |
6754 | 32 ## @ifnottex |
3426 | 33 ## |
3367 | 34 ## @example |
35 ## @group | |
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36 ## std (x) = sqrt ( 1/(N-1) SUM_i (x(i) - mean(x))^2 ) |
3367 | 37 ## @end group |
38 ## @end example | |
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39 ## |
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40 ## @noindent |
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41 ## where @math{N} is the number of elements. |
6754 | 42 ## @end ifnottex |
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43 ## |
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44 ## If @var{x} is a matrix, compute the standard deviation for each column and |
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45 ## return them in a row vector. |
4844 | 46 ## |
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47 ## The argument @var{opt} determines the type of normalization to use. |
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48 ## Valid values are |
4844 | 49 ## |
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50 ## @table @asis |
4844 | 51 ## @item 0: |
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52 ## normalize with @math{N-1}, provides the square root of the best unbiased |
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53 ## estimator of the variance [default] |
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54 ## |
4844 | 55 ## @item 1: |
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56 ## normalize with @math{N}, this provides the square root of the second |
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57 ## moment around the mean |
4844 | 58 ## @end table |
59 ## | |
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60 ## If the optional argument @var{dim} is given, operate along this dimension. |
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61 ## @seealso{var, range, iqr, mean, median} |
3367 | 62 ## @end deftypefn |
3200 | 63 |
64 ## Author: jwe | |
65 | |
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66 function retval = std (x, opt = 0, dim) |
3200 | 67 |
4844 | 68 if (nargin < 1 || nargin > 3) |
6046 | 69 print_usage (); |
4844 | 70 endif |
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71 |
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72 if (! (isnumeric (x) || islogical (x))) |
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73 error ("std: X must be a numeric vector or matrix"); |
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74 endif |
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75 |
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76 if (isempty (opt)) |
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77 opt = 0; |
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78 endif |
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79 if (opt != 0 && opt != 1) |
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80 error ("std: normalization OPT must be 0 or 1"); |
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81 endif |
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82 |
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83 nd = ndims (x); |
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84 sz = size (x); |
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85 if (nargin < 3) |
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86 ## Find the first non-singleton dimension. |
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87 (dim = find (sz > 1, 1)) || (dim = 1); |
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88 else |
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89 if (!(isscalar (dim) && dim == fix (dim)) |
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90 || !(1 <= dim && dim <= nd)) |
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91 error ("std: DIM must be an integer and a valid dimension"); |
8507 | 92 endif |
4844 | 93 endif |
3200 | 94 |
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95 n = sz(dim); |
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96 if (n == 1 || isempty (x)) |
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97 if (isa (x, "single")) |
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98 retval = zeros (sz, "single"); |
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99 else |
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100 retval = zeros (sz); |
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101 endif |
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102 else |
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103 retval = sqrt (sumsq (center (x, dim), dim) / (n - 1 + opt)); |
3200 | 104 endif |
105 | |
106 endfunction | |
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108 |
7411 | 109 %!test |
110 %! x = ones (10, 2); | |
111 %! y = [1, 3]; | |
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112 %! assert (std (x), [0, 0]); |
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113 %! assert (std (y), sqrt (2), sqrt (eps)); |
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114 %! assert (std (x, 0, 2), zeros (10, 1)); |
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115 |
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116 %!assert (std (ones (3, 1, 2), 0, 2), zeros (3, 1, 2)); |
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117 %!assert (std ([1 2], 0), sqrt (2)/2, 5*eps); |
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118 %!assert (std ([1 2], 1), 0.5, 5*eps); |
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119 %!assert (std (1), 0); |
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120 %!assert (std (single (1)), single (0)); |
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121 %!assert (std ([]), []); |
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122 %!assert (std (ones (1,3,0,2)), ones (1,3,0,2)); |
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124 ## Test input validation |
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125 %!error std () |
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126 %!error std (1, 2, 3, 4) |
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127 %!error std (['A'; 'B']) |
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128 %!error std (1, -1) |
7411 | 129 |