function [PARCOR,sig,cil,ciu]= pacf(Z,KMAX);
% Partial Autocorrelation function
% [parcor,sig,cil,ciu] = pacf(Z,N);
%
% Input:
%	Z    Signal, each row is analysed
%	N    # of coefficients

% Output:	
%	parcor autocorrelation function
%	sig	p-value for significance test
%	cil	lower confidence interval 
%	ciu	upper confidence interval 
% 
% see also: DURLEV, LATTICE, AC2RC, AR2RC,
% 	FLAG_IMPLICIT_SIGNIFICANCE

%	$Id$
%	Copyright (C) 1997-2002,2008 by Alois Schloegl <alois.schloegl@gmail.com>	
%
%    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/>.

[nr,nc] = size(Z);
if nc<KMAX,
        warning('too less elements.\nmake sure the data is row order\n')
end;
[s,n] = sumskipnan(Z,2);
Z = Z - repmat(s./n,1,nc); 	% remove mean

if (nargin == 1), KMAX = N-1; end;

AutoCov = acovf(Z,KMAX);
[AR,PARCOR,PE] = durlev(AutoCov); % PARCOR are the reflection coefficients
%[AR,PARCOR,PE] = lattice(Z,KMAX); % PARCOR are the reflection coefficients
PARCOR = -PARCOR;			% the partial correlation coefficients are the negative reflection coefficient.

if nargout<2, return, end;


% significance test
s = 1./sqrt(repmat(n,1,KMAX)-1-ones(nr,1)*(1:KMAX));
sig = normcdf(PARCOR,0,s);
sig = min(sig,1-sig);


if nargout<3, return, end;
% calculate confidence interval
if exist('flag_implicit_significance')==2;
        alpha = flag_implicit_significance;
else	
        alpha = 0.05;
end;        

fprintf(1,'PACF: confidence interval for alpha=%f\n', alpha);
ciu = norminv(alpha/2).*s;
cil = -ciu;