function T = transferEntropyRank(X,Y,l,k,t,w,Q)
%%%%%
% This function computes the transfer entropy between time series X and Y,
% with the flow of information directed from X to Y, after ranking both X and Y. Probability density
% estimation is based on bin counting with fixed and equally-spaced bins.
%
% For details, please see T Schreiber, "Measuring information transfer", Physical Review Letters, 85(2):461-464, 2000.
%
% Inputs:
% X: first time series in 1-D vector
% Y: second time series in 1-D vector
% l: block length for X
% k: block length for Y
% t: time lag in X from present to where the block of length l ends
% w: time lag in Y from present to where the block of length k ends
% Q: number of quantization levels for both X and Y
%
% Outputs:
% T: transfer entropy (bits)
%
%
% Copyright 2011 Joon Lee
%
% 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/>.
%%%%%
X=X(:)';
Y=Y(:)';
% ordinal sampling (ranking)
Nt=length(X);
[B,IX]=sort(X);
X(IX)=1:Nt;
[B,IX]=sort(Y);
Y(IX)=1:Nt;
% quantize X and Y according to fixed, equally-spaced bins
Xq=quantentr(X,Q);
Yq=quantentr(Y,Q);
% go through the time series X and Y, and populate Xpat, Ypat, and Yt
Xpat=[]; Ypat=[]; Yt=[];
codeX=(Q.^((l-1):-1:0))';
codeY=(Q.^((k-1):-1:0))';
for i=max([l+t k+w]):1:min([length(Xq) length(Yq)])
Xpat=[Xpat; Xq(i-l-t+1:i-t)*codeX];
Ypat=[Ypat; Yq(i-k-w+1:i-w)*codeY];
Yt=[Yt; Yq(i)];
end
% compute transfer entropy
T=0;
idxDone=[];
N=length(Xpat);
for i=1:N
if ~any(i==idxDone)
p1=sum(Xpat==Xpat(i) & Ypat==Ypat(i) & Yt==Yt(i))/N;
p2=sum(Xpat==Xpat(i) & Ypat==Ypat(i) & Yt==Yt(i))/sum(Xpat==Xpat(i) & Ypat==Ypat(i));
p3=sum(Ypat==Ypat(i) & Yt==Yt(i))/sum(Ypat==Ypat(i));
T=T+p1*log2(p2/p3);
idxDone=[idxDone; find(Xpat==Xpat(i) & Ypat==Ypat(i) & Yt==Yt(i))];
idxDone=unique(idxDone);
end
end