function [embedm fnn1 fnn2]=fnn(y,maxm)
% Usage: This function calculates corrected false nearest neighbour.
% Inputs:
% y is a vertical vector of time series.
% maxm: maximum value of embedding dimension.
% Output:
% embedm: proper value for embedding dimension.
% fnn1: First criteria of false nearest neighbors.
% fnn2: second criteria of false nearest neighbors.
% Copyright(c) Shapour Mohammadi, University of Tehran, 2009
% shmohammadi@gmail.com
% Keywords: Embedding Dimension, Chaos Theory, Lyapunov Exponent,
% False Nearest Neighbors.
% Ref:
% -Sprott, J. C. (2003). Chaos and Time Series Analysis. Oxford University
% Press.
%__________________________________________________________________________
y=y(:);
RT=15;
AT=2;
sigmay=std(y);
[nyr,nyc]=size(y);
%Embedding matrix
m=maxm;
EM=lagmatrix(y,0:m-1);
%EM after nan elimination.
EEM=EM(1+(m-1):end,:);
[rEEM cEEM]=size(EEM);
embedm=[];
for k=1:cEEM
fnn1=[];
fnn2=[];
D=dist(EEM(:,1:k)');
for i=1:rEEM-m-k
d11 = min(D(i,1:i-1));
d12=min(D(i,i+1:end));
Rm=min([d11;d12]);
l=find(D(i,1:end)== Rm);
if Rm>0
if l+m+k-1<nyr
fnn1=[fnn1;abs(y(i+m+k-1,1)-y(l+m+k-1,1))/Rm];
fnn2=[fnn2;abs(y(i+m+k-1,1)-y(l+m+k-1,1))/sigmay];
end
end
end
Ind1=find(fnn1>RT);
Ind2=find(fnn2>AT);
if length(Ind1)/length(fnn1)<.1 && length(Ind2)/length(fnn1)<.1;
embedm=k; break
end
end
