%function cao_m(data,min_m,max_m,tau)
%該程序計(jì)算時(shí)間序列的嵌入維數(shù)
% clc
% clear
% load stock
% data=x; % data為原始數(shù)據(jù)
%   min_m=1;
%    max_m=12;% min_m,max_m分別為最小和最大嵌入維數(shù)
%    tau=4;    % tau為時(shí)間延遲

%------------------------------------------------------

N=length(data);
k=1;

%-------------------------------------------------------
for m=min_m:max_m
    m
    Y=reconstitution(data,N,m,tau);%相重構(gòu)
    [m,M]=size(Y);
    for i=1:N-m*tau
        i;
        %-----計(jì)算第i個(gè)向量與每個(gè)向量的距離存于d(j)中--------
        for j=1:N-m*tau
        d(j)=norm(Y(:,i)-Y(:,j),inf);
        end
        %-----求距離最短向量的下標(biāo)-----------
        temp=sort(d);
        D(i,1)=i;      %D的第一列為向量序號(hào)
        temp1=find(temp>0);
        temp2=find(d==temp(temp1(1)));
        D(i,2)=temp2(1);  %第二列為與之對(duì)應(yīng)的最短距離向量的序號(hào)
        D(i,3)=temp(temp1(1));%第三列為與之對(duì)應(yīng)的最短距離
        %-----------計(jì)算a(i,m)-----------------------
         Y1=[Y(:,i);data(m*tau+i)];
         Y2=[Y(:,D(i,2));data(D(i,2)+m*tau)];
        ad(i)=norm(Y1-Y2,inf)/D(i,3);
        clear d Y1 Y2 temp temp1 temp2
    end
    D;
     %---------------求E(d)-----------------
    E(k,1)=m;
    E(k,2)=sum(ad)/(N-m*tau);
    % k=k+1;
    %---------------求E*(d)-----------------
    En(k,1)=m;
    En1(k,1)=m;
    for kk=1:N-m*tau
         dd(kk)=abs(data(D(kk,1)+m*tau)-data(D(kk,2)+m*tau));
         %dd1(kk)=abs(data(D(kk,1)+1)-data(D(kk,2)+1));
    end
    En(k,2)=sum(dd)/(N-m*tau);
   % En1(k,2)=sum(dd1)/(N-m*tau);
    k=k+1;

    clear D
end

%-----------求E1(d)-------------------
for i=1:(max_m-min_m)
    E1(i,1)=E(i,1);
    E1(i,2)=E(i+1,2)/E(i,2);
end
%-----------求E2(d)-------------------
for i=1:(max_m-min_m)
    E2(i,1)=En(i,1);
    E2(i,2)=En(i+1,2)/En(i,2);
end
%-----------畫(huà)圖------------------------
figure(1)
plot(E1(:,1),E1(:,2),'-bs',E2(:,1),E2(:,2),'-r*');xlabel('維數(shù)');ylabel('E1(d)&E2(d)');
grid on

% disp('-----------求使Ed最小的嵌入維數(shù)-------------------');
% min_E=min(En(:,2));
% for i=1:(max_m-min_m)
%     if En(i,2)==min_E
%         embed_m=En(i,1);
%         break
%     end
% end
% embed_m
% 
% min_E1=min(En1(:,2));
% for i=1:(max_m-min_m)
%     if En1(i,2)==min_E1
%         embed_m1=En1(i,1);
%         break
%     end
% end
% embed_m1

% figure(2)
% plot(En(:,1),En(:,2),En1(:,1),En1(:,2),'r');xlabel('維數(shù)');ylabel('E*(d)');
% grid on
% 
% disp('--------cao法求m---------')
% e=0.1;embed_m=0;
% h=1:length(E1(:,2))-1;
% delt=abs(E1(h,2)-E1(h+1,2));
% num=find(delt<e);
% num1=find(delt==max(delt(num(1):length(delt))));
% e=mean(delt(num1(1):length(E1(:,2))-1));
% for kk=num1(1):length(E1(:,2))
%     if kk+2<=length(E1(:,2))
%         delt1=abs(E1(kk,2)-E1(kk-1,2));
%         delt2=abs(E1(kk+1,2)-E1(kk,2));
%         delt3=abs(E1(kk+2,2)-E1(kk+1,2));
%         
%         if (delt1>delt2)&(delt2>delt3)&(delt2<e)
%             embed_m=kk
%             break
%         end
%     end
% end