X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?a=blobdiff_plain;ds=sidebyside;f=octave_packages%2Fm%2Fstatistics%2Fbase%2Fstd.m;fp=octave_packages%2Fm%2Fstatistics%2Fbase%2Fstd.m;h=cee3a6cf077e73f1db46a212a6f4c49fb9d8f238;hb=1c0469ada9531828709108a4882a751d2816994a;hp=0000000000000000000000000000000000000000;hpb=63de9f36673d49121015e3695f2c336ea92bc278;p=CreaPhase.git diff --git a/octave_packages/m/statistics/base/std.m b/octave_packages/m/statistics/base/std.m new file mode 100644 index 0000000..cee3a6c --- /dev/null +++ b/octave_packages/m/statistics/base/std.m @@ -0,0 +1,127 @@ +## Copyright (C) 1996-2012 John W. Eaton +## +## This file is part of Octave. +## +## Octave is free software; you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation; either version 3 of the License, or (at +## your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +## General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## . + +## -*- texinfo -*- +## @deftypefn {Function File} {} std (@var{x}) +## @deftypefnx {Function File} {} std (@var{x}, @var{opt}) +## @deftypefnx {Function File} {} std (@var{x}, @var{opt}, @var{dim}) +## Compute the standard deviation of the elements of the vector @var{x}. +## @tex +## $$ +## {\rm std} (x) = \sigma = \sqrt{{\sum_{i=1}^N (x_i - \bar{x})^2 \over N - 1}} +## $$ +## where $\bar{x}$ is the mean value of $x$ and $N$ is the number of elements. +## @end tex +## @ifnottex +## +## @example +## @group +## std (x) = sqrt ( 1/(N-1) SUM_i (x(i) - mean(x))^2 ) +## @end group +## @end example +## +## @noindent +## where @math{N} is the number of elements. +## @end ifnottex +## +## If @var{x} is a matrix, compute the standard deviation for +## each column and return them in a row vector. +## +## The argument @var{opt} determines the type of normalization to use. +## Valid values are +## +## @table @asis +## @item 0: +## normalize with @math{N-1}, provides the square root of the best unbiased +## estimator of the variance [default] +## +## @item 1: +## normalize with @math{N}, this provides the square root of the second +## moment around the mean +## @end table +## +## If the optional argument @var{dim} is given, operate along this dimension. +## @seealso{var, range, iqr, mean, median} +## @end deftypefn + +## Author: jwe + +function retval = std (x, opt = 0, dim) + + if (nargin < 1 || nargin > 3) + print_usage (); + endif + + if (! (isnumeric (x) || islogical (x))) + error ("std: X must be a numeric vector or matrix"); + endif + + if (isempty (opt)) + opt = 0; + endif + if (opt != 0 && opt != 1) + error ("std: normalization OPT must be 0 or 1"); + endif + + nd = ndims (x); + sz = size (x); + if (nargin < 3) + ## Find the first non-singleton dimension. + (dim = find (sz > 1, 1)) || (dim = 1); + else + if (!(isscalar (dim) && dim == fix (dim)) + || !(1 <= dim && dim <= nd)) + error ("std: DIM must be an integer and a valid dimension"); + endif + endif + + n = sz(dim); + if (n == 1 || isempty (x)) + if (isa (x, 'single')) + retval = zeros (sz, 'single'); + else + retval = zeros (sz); + endif + else + retval = sqrt (sumsq (center (x, dim), dim) / (n - 1 + opt)); + endif + +endfunction + + +%!test +%! x = ones (10, 2); +%! y = [1, 3]; +%! assert(std (x) == [0, 0]); +%! assert(std (y), sqrt (2), sqrt (eps)); +%! assert(std (x, 0, 2), zeros (10, 1)); + +%!assert(std (ones (3, 1, 2), 0, 2), zeros (3, 1, 2)); +%!assert(std ([1 2], 0), sqrt(2)/2, 5*eps); +%!assert(std ([1 2], 1), 0.5, 5*eps); +%!assert(std(1), 0); +%!assert(std(single(1)), single(0)); +%!assert(std([]), []); +%!assert(std(ones (1,3,0,2)), ones (1,3,0,2)); + +%% Test input validation +%!error std (); +%!error std (1, 2, 3, 4); +%!error std (['A'; 'B']) +%!error std (1, -1); +