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function y = nanstd(x,dim,flag)
% FORMAT: Y = NANSTD(X,DIM,FLAG)
%
% Standard deviation ignoring NaNs
%
% This function enhances the functionality of NANSTD as distributed in
% the MATLAB Statistics Toolbox and is meant as a replacement (hence the
% identical name).
%
% NANSTD(X,DIM) calculates the standard deviation along any dimension of
% the N-D array X ignoring NaNs.
%
% NANSTD(X,DIM,0) normalizes by (N-1) where N is SIZE(X,DIM). This make
% NANSTD(X,DIM).^2 the best unbiased estimate of the variance if X is
% a sample of a normal distribution. If omitted FLAG is set to zero.
%
% NANSTD(X,DIM,1) normalizes by N and produces the square root of the
% second moment of the sample about the mean.
%
% If DIM is omitted NANSTD calculates the standard deviation along first
% non-singleton dimension of X.
%
% Similar replacements exist for NANMEAN, NANMEDIAN, NANMIN, NANMAX, and
% NANSUM which are all part of the NaN-suite.
%
% See also STD
% -------------------------------------------------------------------------
% author: Jan Gläscher
% affiliation: Neuroimage Nord, University of Hamburg, Germany
% email: glaescher@uke.uni-hamburg.de
%
% $Revision: 1.1 $ $Date: 2004/07/15 22:42:15 $
if isempty(x)
y = NaN;
return
end
if nargin < 3
flag = 0;
end
if nargin < 2
dim = min(find(size(x)~=1));
if isempty(dim)
dim = 1;
end
end
% Find NaNs in x and nanmean(x)
nans = isnan(x);
avg = nanmean(x,dim);
% create array indicating number of element
% of x in dimension DIM (needed for subtraction of mean)
tile = ones(1,max(ndims(x),dim));
tile(dim) = size(x,dim);
% remove mean
x = x - repmat(avg,tile);
count = size(x,dim) - sum(nans,dim);
% Replace NaNs with zeros.
x(isnan(x)) = 0;
% Protect against a all NaNs in one dimension
i = find(count==0);
if flag == 0
y = sqrt(sum(x.*x,dim)./max(count-1,1));
else
y = sqrt(sum(x.*x,dim)./max(count,1));
end
y(i) = i + NaN;
% $Id: nanstd.m,v 1.1 2004/07/15 22:42:15 glaescher Exp glaescher $