function [ApEn_value,Cmr,Cmr_1] = fast_ApEn(signal,r_factor)

% Estimate the Aproximate Entropy (ApEn) of a signal, using a fast
% algorithm, for the ApEn parameter "m" equal to 2 

% The pattern length "m" for which this routine was implemented is 2. For
% another values of "m", the instructions marked with a (*) in the end must be changed.

% m=1 or m=2
% r between 0.1*SD and 0.25*SD, where SD is the signal standard deviation
% N (signal length) between 75 and 5000;
% [ApEn_value] = fast_ApEn(signal,r_factor);

% Input variables:
% signal - signal
% r_factor - factor of the criterion of similarity     r_factor*std(signal)

% Output variables:
% ApEn_value - ApEn calculated from the signal

% Optional output variables:
% C_m
% C_m_1

% if length(signal)<75 | length(signal)>5000
% slength=input('Signal length inappropriate. Continue anyway? (y/n)','s');
% if strcmpi(slength,'y')==0
% return
% end
% end
% if r_factor<0.1 | r_factor>0.25
% r_factor_flag=input('Value for r parameter is inappropriate. Continue anyway? (y/n)','s');
% if strcmpi(r_factor_flag,'y')==0
% return
% end
% end


% Initial variables definition.
signal=signal(:);
N=length(signal);
Cmr_ij=[];Cmr_i=[];Cmr=[];
Cmr_ij_1=[];Cmr_i_1=[];Cmr_1=[];

% D and S matrixes computation.
D=abs(signal*ones(1,N)-ones(N,1)*signal');
S=zeros(N,N);
S(find(D<=r_factor*std(signal)))=1;

% C's computation for "m" and "m+1" patterns.
m=2;
S(N+1,(m+1):N)=0; % necessary for the loop to be possible ("artificial" definitions)
for k=1:N-(m-1)
% m pattern.
Cmr_ij=S(k,1:N-1).*S(k+1,2:N); % (*)
Nm_i=sum(Cmr_ij);
Cmr_i=Nm_i/(N-(m-1));
Cmr=[Cmr; Cmr_i];
% m+1 pattern.
Cmr_ij(end)=[];
Cmr_ij_1=Cmr_ij.*S(k+2,3:N);
Nm_i_1=sum(Cmr_ij_1);
Cmr_i_1=Nm_i_1/(N-m);
Cmr_1=[Cmr_1;Cmr_i_1];
end
Cmr_1(end)=[]; % the last C value for the "m+1" pattern is artificial.
% Phi’s computation.
phi_m=mean(log(Cmr));
phi_m_1=mean(log(Cmr_1));
% ApEn final calculation.
ApEn_value=[phi_m-phi_m_1];

% phi_m
% phi_m_1