function [o,count,SSQ,S4M] = sumskipnan(i,DIM)
% SUMSKIPNAN adds all non-NaN values. 
%
% All NaN's are skipped; NaN's are considered as missing values. 
% SUMSKIPNAN of NaN's only  gives O; and the number of valid elements is return. 
% SUMSKIPNAN is also the elementary function for calculating 
% various statistics (e.g. MEAN, STD, VAR, RMS, MEANSQ, SKEWNESS, 
% KURTOSIS, MOMENT, STATISTIC etc.) from data with missing values.  
% SUMSKIPNAN implements the DIMENSION-argument for data with missing values.
% Also the second output argument return the number of valid elements (not NaNs) 
% 
% Y = sumskipnan(x [,DIM])
% [Y,N,SSQ] = sumskipnan(x [,DIM])
% 
% DIM	dimension
%	1 sum of columns
%	2 sum of rows
%	default or []: first DIMENSION with more than 1 element
%
% Y	resulting sum
% N	number of valid (not missing) elements
% SSQ	sum of squares
%
% The mean & standard error of the mean and 
%	Y./N & sqrt((SSQ-Y.*Y./N)./(N.*max(N-1,0))); 
% the mean square & the standard error of the mean square and
% 	SSQ./N & sqrt((S4M-SSQ.^2./N)./(N.*max(N-1,0)))
%
% features:
% - can deal with NaN's (missing values)
% - implements dimension argument. 
% - compatible with Matlab and Octave
%
% see also: SUM, NANSUM, MEAN, STD, VAR, RMS, MEANSQ, 
%      SSQ, MOMENT, SKEWNESS, KURTOSIS, SEM


%    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 2 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, write to the Free Software
%    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

%	$Revision: 1.23 $
%	$Id: sumskipnan.m,v 1.23 2003/10/31 18:15:38 schloegl Exp $
%    Copyright (C) 2000-2004 by Alois Schloegl <a.schloegl@ieee.org>	
%    This is part of the NaN-toolbox. For more details see
%    http://www.dpmi.tu-graz.ac.at/~schloegl/matlab/NaN/


if nargin<2,
        DIM = [];
end;

% an efficient implementation in C of the following lines 
% could significantly increase performance 
% only one loop and only one check for isnan is needed.
% A MEX-Implementation is available in sumskipnan.cpp.
%
% Outline of the algorithm: 
% for { k=1,o=0,count=0; k++; k<N} 
% 	if ~isnan(i(k)) 
% 	{ 	o     += i(k);
%               count += 1;
%		tmp    = i(k)*i(k)
%		o2    += tmp;
%		o3    += tmp.*tmp;
%       }; 


if isempty(DIM),
        DIM=min(find(size(i)>1));
        if isempty(DIM), DIM = 1; end;
end;
if nargout>1,
        count = sum(~isnan(i),DIM); 
end;

%if flag_implicit_skip_nan, %%% skip always NaN's
i(isnan(i)) = 0;
%end;
o = sum(i,DIM);
if nargout>2,
        i = real(i).^2 + imag(i).^2;
        SSQ = sum(i,DIM);
        if nargout>3,
                S4M = sum(i.^2,DIM);
        end;
end;