function xout=erqa(varargin)
%ERQA Computes and plots the ERQA measures.
% Y=ERQA(X [,Y] [,param1,param2,...])
% Extended recurrence quantification analysis of
% cross-recurrence plots with the first vector
% X and the second Y.
%
% Y=ERQA(X,M,T,E,W,WS) computes the extended
% recurrence quantification analysis of the recurrence
% plot of X by using the dimension M, delay T, the
% size of neighbourhood E, the window size W and
% a window shifting value of WS.
%
% Parameters: dimension M, delay T, the size of
% neighbourhood E, the window size W and the shift
% value WS are the first five numbers after the data
% series; if W is empty, the whole plot will be calculated.
% Further parameters can be used to switch between various
% methods of finding the neighbours of the phasespace
% trajectory, to suppress the normalization of the data
% and to suppress the GUI (useful in order to use this
% programme by other programmes).
%
% Methods of finding the neighbours.
% maxnorm - Maximum norm.
% euclidean - Euclidean norm.
% nrmnorm - Euclidean norm between normalized vectors
% (all vectors have the length one).
% fan - Fixed amount of nearest neighbours.
% inter - Interdependent neighbours.
% distance - Distance coded matrix (global CRP).
%
% Normalization of the data series.
% normalize - Normalization of the data.
% nonormalize - No normalization of the data.
%
% Suppressing the GUI.
% gui - Creates (the GUI and) the output plot.
% nogui - Suppresses the GUI and the output plot.
% silent - Suppresses all output.
%
% Parameters not needed to specify.
%
% Output:
% Y(:,1) = K1
% Y(:,2) = K2
% Y(:,3) = D2
% Y(:,4) = I2
%
% Examples: a = randn(300,1);
% erqa(a,1,1,.2,40,2,'max')
%
% N = 300; w = 40; ws = 2;
% a = 3.4:.6/(N-1):4;
% b = .5; for i = 2:N, b(i) = a(i)*b(i-1)*(1-b(i-1)); end
% y = erqa(b,3,2,.1,w,ws,'nogui');
% subplot(2,1,1), plot(a,b,'.','markersize',.1)
% title('logistic map'), axis([3.4 4 0 1])
% subplot(2,1,2), plot(a(1:ws:N-w), y(1:ws:N-w,1))
% ylabel('recurrence rate'), axis([3.4 4 0 1])
%
%
% See also CRP, CRP2, CRP_BIG, DL, TT.
%
% References:
% Thiel, M., Romano, M. C., Kurths, J.:
% Analytical description of Recurrence Plots of stochastic
% and chaotic processes, to be publ. 2002
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % Please note, that this routine is not yet finished! %
% % Don't use the results of this script! %
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Copyright (c) 2008-2009
% Norbert Marwan, Potsdam Institute for Climate Impact Research, Germany
% http://www.pik-potsdam.de
%
% Copyright (c) 1998-2008
% Norbert Marwan, Potsdam University, Germany
% http://www.agnld.uni-potsdam.de
%
% $Date$
% $Revision$
%
% $Log$
% Revision 1.11 2007/12/20 16:26:05 marwan
% changed gpl splash behaviour
%
% Revision 1.10 2005/04/01 12:19:27 marwan
% *** empty log message ***
%
% Revision 1.9 2004/11/10 07:06:03 marwan
% initial import
%
%
% 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 any later version.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% check and read the input
error(nargchk(1,10,nargin));
if nargout>1, error('Too many output arguments'), end
varargin{11}=[];
i_double=find(cellfun('isclass',varargin,'double'));
i_char=find(cellfun('isclass',varargin,'char'));
% check the text input parameters for gui
check_gui={'gui','nog','sil'}; % gui, nogui, silent
temp_gui=0;
if ~isempty(i_char)
for i=1:length(i_char),
varargin{i_char(i)}(4)='0';
temp_gui=temp_gui+strcmpi(varargin{i_char(i)}(1:3),check_gui');
end
nogui=min(find(temp_gui))-1;
for i=1:length(i_char); temp2(i,:)=varargin{i_char(i)}(1:3); end
i_char(strmatch(check_gui(find(temp_gui)),temp2))=[];
if isempty(nogui), nogui=1; end
if nogui>2, nogui=1; end
else
nogui=1;
end
if nogui==0, warning('Sorry. GUI not yet available.'),end
% get the parameters for creating RP
if max(size(varargin{1}))<=3
error('To less values in data X.')
end
x=double(varargin{1});
if isempty(varargin{2}) | ~isnumeric(varargin{2}), y=x; else
y=double(varargin{2}); end
if (isnumeric(varargin{2}) & max(size(varargin{2}))==1) | ~isnumeric(varargin{2})
y=x;
if ~isempty(varargin{i_double(2)}), m=varargin{i_double(2)}(1); else m=1; end
if ~isempty(varargin{i_double(3)}), t=varargin{i_double(3)}(1); else t=1; end
if ~isempty(varargin{i_double(4)}), e=varargin{i_double(4)}(1); else e=.1; end
if ~isempty(varargin{i_double(5)}), w=varargin{i_double(5)}(1); else w=varargin{i_double(5)}; end
if ~isempty(varargin{i_double(6)}), wstep=varargin{i_double(6)}(1); else wstep=1; end
else
if ~isempty(varargin{i_double(3)}), m=varargin{i_double(3)}(1); else m=1; end
if ~isempty(varargin{i_double(4)}), t=varargin{i_double(4)}(1); else t=1; end
if ~isempty(varargin{i_double(5)}), e=varargin{i_double(5)}(1); else e=.1; end
if ~isempty(varargin{i_double(6)}), w=varargin{i_double(6)}(1); else w=varargin{i_double(6)}; end
if ~isempty(varargin{i_double(7)}), wstep=varargin{i_double(7)}(1); else wstep=1; end
end
Nx=length(x); Ny=length(y);
if size(x,1)<size(x,2), x=x'; end
if size(y,1)<size(y,2), y=y'; end
if size(x,2)>=2
xscale=x(:,1);
if ~isempty(find(diff(xscale)<0)), error('First column of the first vector must be monotonically non-decreasing.'),end
x=x(:,2);
else
xscale=(1:length(x))';
end
if size(y,2)>=2
yscale=y(:,1);
if ~isempty(find(diff(yscale)<0)), error('First column of the second vector must be monotonically non-decreasing.'),end
y=y(:,2);
else
yscale=(1:length(y))';
end
if max(size(x))~=max(size(y)),error('Data must have the same length.'),end
if e<0, e=1; disp('The threshold size E can not be negative and is now set to 1.'), end
if t<1, t=1; disp('The delay T can not be smaller than one and is now set to 1.'), end
if isempty(w), w=Nx-1; end
if w<2, w=2; disp('The window size W exceeds the valid range.'), end
if w>Nx, w=Nx-1; disp('The window size W exceeds the valid range.'), end
if wstep<2 & wstep>Nx/3, wstep=2; disp('The window shifting value WS exceeds the valid range.'), end
t=round(t); m=round(m); w=round(w); wstep=round(wstep);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% splash the GPL
filename='crp';
which_res=which([filename,'.m']);
gplrc_path=[strrep(which_res,[filename,'.m'],''), 'private'];
gplrc_file=[gplrc_path, filesep, '.gpl.',filename];
if ~exist(gplrc_path)
mkdir(strrep(which_res,[filename,'.m'],''),'private')
end
if ~exist(gplrc_file)
fid=fopen(gplrc_file,'w');
fprintf(fid,'%s\n','If you delete this file, the GNU Public License will');
fprintf(fid,'%s','splash up at the next time the programme starts.');
fclose(fid);
if exist('gpl')
txt=gpl;
else
txt={'The GNU General Public License was not found.'};
end
h=figure('NumberTitle','off',...,
'ButtonDownFcn','close',...
'Name','GNU General Public License');
ha=get(h,'Position');
h=uicontrol('Style','Listbox',...
'ButtonDownFcn','close',...
'CallBack','close',...
'Position',[0 0 ha(3) ha(4)],...
'FontName','Courier',...
'BackgroundColor',[.8 .8 .8],...
'String',txt);
waitfor(h)
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% compute
%try
de=.1;
if nogui~=2, h=waitbar(0,'1');h1=get(h,'chil');h1=get(h1,'title'); end
for i=1:wstep:Nx-w;
if nogui~=2, waitbar(i/(Nx-w));
txt=['CRP1 - ',num2str(i),'/',num2str(Nx-w)];
set(h1,'str',txt); drawnow, end
try
X1=crp(x(i:i+w-1,:),y(i:i+w-1,:),m,t,e,varargin{i_char},'silent');
if nogui~=2, txt=['CRP1a - ',num2str(i),'/',num2str(Nx-w)]; set(h1,'str',txt); drawnow, end
X1a=crp(x(i:i+w-1,:),y(i:i+w-1,:),m,t,e,varargin{i_char},'silent');
X2 = X1 .* X1a; X1 = X2;
if nogui~=2, txt=['CRP2 - ',num2str(i),'/',num2str(Nx-w)]; set(h1,'str',txt); drawnow, end
X2=crp(x(i:i+w-1,:),y(i:i+w-1,:),m,t,e+de,varargin{i_char},'silent');
X1a=crp(x(i:i+w-1,:),y(i:i+w-1,:),m,t,e+de,varargin{i_char},'silent');
X2a = X2 .* X1a; X2 = X2a;
if nogui~=2, txt=['CRP3 - ',num2str(i),'/',num2str(Nx-w)]; set(h1,'str',txt); drawnow, end
X3=crp(x(i:i+w-1,:),y(i:i+w-1,:),m+2,t,e,varargin{i_char},'silent');
X1a=crp(x(i:i+w-1,:),y(i:i+w-1,:),m+2,t,e,varargin{i_char},'silent');
X2a = X3 .* X1a; X3 = X2a;
catch
if nogui~=2, close(h), end
error(lasterr)
end
txt=['ERQA - ',num2str(i),'/',num2str(Nx-w)];
if nogui~=2, set(h1,'str',txt); drawnow, end
warning off
N=length(X1);
[ml NL]=dl(X1);
pl=hist(NL,[0:N]);
for j=1:N;
plc(j)=sum(pl([1:N-j]+j).*([1:N-j]+1));
end
Np=min(find(plc==0));
% 1st measure
i1=[round(.04*Np):round(.12*Np)]+1;
i2=[round(.3*Np):round(.85*Np)]+1;
%i1=2:round(.12*Np);
if length(i1)==1, i1=[]; end
if length(i2)==1, i2=[]; end
if ~isempty(i1),K1=-regress(log(plc(i1))',[i1',ones(length(i1),1)]);else K1=NaN; end
if ~isempty(i2),K2=-regress(log(plc(i2))',[i2',ones(length(i2),1)]);else K2=NaN; end
%K2=regress(log(plc(i2))',[i2',ones(length(i1),1)]);
%K2=log(plc(i2));
% 2nd measure
txt=['2RQA - ',num2str(i),'/',num2str(Nx-w)];
if nogui~=2, set(h1,'str',txt); drawnow, end
[ml NL]=dl(X2); N2=length(X2);
pl=hist(NL,[0:N2]);
for j=1:N2; plc2(j)=sum(pl([1:N2-j]+j).*([1:N2-j]+1)); end
l=round(ml);
D2=log(plc(l)/plc2(l))/log(e/(e+de));
% 3rd measure
H2=-log(sum(X1(:))/(N^2));
X1=double(X1);
for t=1:3;
j=1:N-t;k=1:N-t;
H2t(t)=-log(sum(sum(X1(k,j).*X1(k+t,j+t)))/(N^2));
end
I2=2*H2-H2t;
% ApEn
B=(sum(X1,1)-1)/(length(X1)+1); A=(sum(X3,1)-1)/(length(X3)+1);
ApEn = sum(log(B(find(B))))/(length(X1)+1) - sum(log(A(find(A))))/(length(X3)+1);
%SampEn
B=(sum(X1,1)-1)/(length(X1)-1); A=(sum(X3,1)-1)/(length(X1)-1);
SampEn = -log(mean(A)/mean(B));
warning on
Y(i,1)=K1(1);
Y(i,2)=K2(1);
Y(i,3)=D2;
Y(i,4)=I2(1);
Y(i,5)=I2(2);
Y(i,6)=I2(3);
Y(i,7)=ApEn;
Y(i,8)=SampEn;
end
if nogui~=2
close(h)
tx={'K1';'K2';'D2';'I2';'I2';'I2'};
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% plot
for i=1:4,subplot(2,2,i),plot(Y(1:wstep:end,i)),ylabel(tx(i));end
hold on
plot(Y(1:wstep:end,i+1),'r')
plot(Y(1:wstep:end,i+2),'g')
end
if nargout, xout=Y; end
if 0
%catch
if ishandle(h),close(h),end
error(lasterr)
end