--- /dev/null
+function [o,v]=std(x,opt,DIM,W)
+% STD calculates the standard deviation.
+%
+% [y,v] = std(x [, opt[, DIM [, W]]])
+%
+% opt option
+% 0: normalizes with N-1 [default]
+% provides the square root of best unbiased estimator of the variance
+% 1: normalizes with N,
+% this provides the square root of the second moment around the mean
+% otherwise:
+% best unbiased estimator of the standard deviation (see [1])
+%
+% DIM dimension
+% N STD of N-th dimension
+% default or []: first DIMENSION, with more than 1 element
+% W weights to compute weighted s.d. (default: [])
+% if W=[], all weights are 1.
+% number of elements in W must match size(x,DIM)
+%
+% y estimated standard deviation
+%
+% features:
+% - provides an unbiased estimation of the S.D.
+% - can deal with NaN's (missing values)
+% - weighting of data
+% - dimension argument also in Octave
+% - compatible to Matlab and Octave
+%
+% see also: RMS, SUMSKIPNAN, MEAN, VAR, MEANSQ,
+%
+%
+% References(s):
+% [1] http://mathworld.wolfram.com/StandardDeviationDistribution.html
+
+
+% This program 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.
+%
+% This program 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 this program; If not, see <http://www.gnu.org/licenses/>.
+
+% $Id: std.m 8223 2011-04-20 09:16:06Z schloegl $
+% Copyright (C) 2000-2003,2006,2009,2010 by Alois Schloegl <alois.schloegl@gmail.com>
+% This is part of the NaN-toolbox for Octave and Matlab
+% http://pub.ist.ac.at/~schloegl/matlab/NaN/
+
+if nargin<4,
+ W = [];
+end;
+if nargin<3,
+ DIM = [];
+end;
+if isempty(DIM),
+ DIM = find(size(x)>1,1);
+ if isempty(DIM), DIM=1; end;
+end;
+
+
+[y,n,ssq] = sumskipnan(x,DIM,W);
+if all(ssq(:).*n(:) > 2*(y(:).^2))
+ %% rounding error is neglectable
+ y = ssq - y.*y./n;
+else
+ %% rounding error is not neglectable
+ szx = size(x);
+ szy = size(y);
+ if length(szy)<length(szx);
+ szy(length(szy)+1:length(szx)) = 1;
+ end;
+ [y,n] = sumskipnan((x-repmat(y./n,szx./szy)).^2,DIM,W);
+end;
+
+
+if nargin<2,
+ opt = 0;
+end;
+if isempty(opt),
+ opt = 0;
+end;
+
+
+if opt==0,
+ % square root if the best unbiased estimator of the variance
+ ib = inf;
+ o = sqrt(y./max(n-1,0)); % normalize
+
+elseif opt==1,
+ ib = NaN;
+ o = sqrt(y./n);
+
+else
+ % best unbiased estimator of the mean
+ if exist('unique','file'),
+ % usually only a few n's differ
+ [N,tmp,tix] = unique(n(:)); % compress n and calculate ib(n)
+ ib = sqrt(N/2).*gamma((N-1)./2)./gamma(N./2); %inverse b(n) [1]
+ ib = ib(reshape(tix,size(y))); % expand ib to correct size
+
+ elseif exist('histo3','file'),
+ % usually only a few n's differ
+ [N,tix] = histo3(n(:)); N = N.X;
+ ib = sqrt(N/2).*gamma((N-1)./2)./gamma(N./2); %inverse b(n) [1]
+ ib = ib(reshape(tix,size(y))); % expand ib to correct size
+
+ else % gamma is called prod(size(n)) times
+ ib = sqrt(n/2).*gamma((n-1)./2)./gamma(n./2); %inverse b(n) [1]
+ end;
+ ib = reshape(ib,size(y));
+ o = sqrt(y./n).*ib;
+end;
+
+if nargout>1,
+ v = y.*((max(n-1,0)./(n.*n))-1./(n.*ib.*ib)); % variance of the estimated S.D. ??? needs further checks
+end;
+
+