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function y = nanmedian(x,dim)
% FORMAT: Y = NANMEDIAN(X,DIM)
%
% Median ignoring NaNs
%
% This function enhances the functionality of NANMEDIAN as distributed
% in the MATLAB Statistics Toolbox and is meant as a replacement (hence
% the identical name).
%
% NANMEDIAN(X,DIM) calculates the mean along any dimension of the N-D
% array X ignoring NaNs. If DIM is omitted NANMEDIAN averages along the
% first non-singleton dimension of X.
%
% Similar replacements exist for NANMEAN, NANSTD, NANMIN, NANMAX, and
% NANSUM which are all part of the NaN-suite.
%
% See also MEDIAN
% -------------------------------------------------------------------------
% author: Jan Gläscher
% affiliation: Neuroimage Nord, University of Hamburg, Germany
% email: glaescher@uke.uni-hamburg.de
%
% $Revision: 1.2 $ $Date: 2007/07/30 17:19:19 $
if isempty(x)
y = [];
return
end
if nargin < 2
dim = min(find(size(x)~=1));
if isempty(dim)
dim = 1;
end
end
siz = size(x);
n = size(x,dim);
% Permute and reshape so that DIM becomes the row dimension of a 2-D array
perm = [dim:max(length(size(x)),dim) 1:dim-1];
x = reshape(permute(x,perm),n,prod(siz)/n);
% force NaNs to bottom of each column
x = sort(x,1);
% identify and replace NaNs
nans = isnan(x);
x(isnan(x)) = 0;
% new dimension of x
[n m] = size(x);
% number of non-NaN element in each column
s = size(x,1) - sum(nans);
y = zeros(size(s));
% now calculate median for every element in y
% (does anybody know a more eefficient way than with a 'for'-loop?)
for i = 1:length(s)
if rem(s(i),2) & s(i) > 0
y(i) = x((s(i)+1)/2,i);
elseif rem(s(i),2)==0 & s(i) > 0
y(i) = (x(s(i)/2,i) + x((s(i)/2)+1,i))/2;
end
end
% Protect against a column of NaNs
i = find(y==0);
y(i) = i + nan;
% permute and reshape back
siz(dim) = 1;
y = ipermute(reshape(y,siz(perm)),perm);
