The algorithm of entropy realization

近似熵的一种快速实用算法

Pincus提出的近似熵算法中有很多冗余的计算，效率低，速度慢，不利于实际应用，洪波等人在定义的基础上引入二值距离矩阵的概率，提出了一种实用快速的算法。

function ApEn=EntropyCompute(sig,m,r0)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%       计算一维信号的近似熵,采用快速算法
%       sig: 待求近似熵的源信号
%       m:  一般取 2
%       r0:  一般取0.1 ~ 0.25
%       Ref:   近似熵：一种应用于短数据的的复杂性度量，杨福生
%              近似熵及其在机械设备故障诊断中的应用，胥永刚
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
N = size(sig,1);
r=r0*std(sig);
d=zeros(N,N);

%%% 计算距离矩阵 %%%
for i=1:N
   d(i,:)=abs(sig(i)-sig) < r;
end

%%% 计算C2 %%%
c2=zeros(1,N-m+1);
for i=1:N-m+1    
       for j=1:N-1;
          buf = d(i,j) & d(i+1,j+1);
          c2(i)=c2(i)+buf;
      end
end

Fi(1)=sum(log(c2))/(N-m+1);    
m=m+1;


%%% 计算C3  %%%
c3=zeros(1,N-m+1);
for i=1:N-m+1
       for j=1:N-2;
           c3(i)=c3(i)+(d(i,j) & d(i+1,j+1) & d(i+2,j+2));
      end
end

Fi(2)=sum(log(c3))/(N-m+1);
ApEn=Fi(1)-Fi(2);

return;