function [s,delt_s,s_cor]=C_CMethod(data)
%this function calculate time delay and embedding demension with C-C
%Method,which proved by H.S.Kim
%skyhawk&flyinghawk
% %****************调试程序段****************************
clear all;
data=load('c:/a11.txt');
% %************************************************

N=length(data);
max_d=9;%the maximum value of the time delay

sigma=std(data);%calcute standard deviation s_d

for t=1:max_d
    t
    s_t=0;
    delt_s_s=0;
    for m=2:5
        s_t1=0;
        for j=1:4
            r=sigma*j/2;
            data_d=disjoint(data,N,t);%将时间序列分解成t个不相交的时间序列
            [ll,N_d]=size(data_d);
            s_t3=0;
            for i=1:t
                i
                Y=data_d(i,:);
                C_1(i)=correlation_integral(Y,N_d,r,i);%计算C(1,N_d,r,t)
                X=reconstitution(Y,N_d,m,t);%相空间重构
                N_r=N_d-(m-1)*t;
                C_I(i)=correlation_integral(X,N_r,r,i);%计算C(m,N_r,r,t)
                s_t3=s_t3+(C_I(i)-C_1(i)^m);%对t个不相关的时间序列求和
            end
            s_t2(j)=s_t3/t;
            s_t1=s_t1+s_t2(j);%对rj求和
        end
        delt_s_m(m)=max(s_t2)-min(s_t2);%求delt S(m,t)
        delt_s_s=delt_s_s+delt_s_m(m);%delt S(m,t)对m求和
        s_t0(m)=s_t1;
        s_t=s_t+s_t0(m);%S对m求和
    end
    s(t)=s_t/16;
    delt_s(t)=delt_s_s/4;
    s_cor(t)=delt_s(t)+abs(s(t));
   
end
fid=fopen('result.txt','w');
fprintf(fid,'%f %f %f %f/n',t,s(t),delt_s(t),s_cor(t));
fclose(fid);
t=1:max_d;
plot(t,s,t,delt_s,'.',t,s_cor,'*')
title('铁路货运量增长率时间序列C-C方法求嵌入时延及嵌入窗')

function C_I=correlation_integral(X,M,r,qs)
%the function is used to calculate correlation integral
%C_I:the value of the correlation integral
%X:the reconstituted state space, is a m*M matrix
%m:the embedding demention
%M:M is the number of embedded points in m-dimensional space
%r:the radius of the Heaviside function,sigma/2<r<2sigma
%calculate the sum of all the values of Heaviside
%skyhawk
sum_H=zeros(1,M);
for i=1:M
    for j=1:M
        if j==i
            continue;
        end
        d=norm((X(:,i)-X(:,j)),inf);%calculat the distances of each two points in matris M with sup-norm
        sita=heaviside(r-d);%calculate the value of the heaviside function
        sum_H(i)=sum_H(i)+sita;
    end
    sum_H(i)=sum_H(i)^qs;
end
C_I=sum(sum_H);%the value of correlation integral


function data_d=disjoint(data,N,t)
%the function is used to subdivid the time series into t disjoint time
%series.
%data:the time series
%N:the length of the time series
%t:the index lag
%skyhawk
for i=1:t
    for j=1:(N/t)
        data_d(i,j)=data(i+(j-1)*t);
    end
end

function sita=heaviside(r)
%the function is used to calculate the value of the Heaviside function
%sita:the value of the Heaviside function
%r:the radius in the Heaviside function,sigma/2<r<2sigma
%d:the distance of two points
%skyhawk
if (r)<0
    sita=0;
else sita=1;
end