function [y,e]=gm1(x,k)
n=length(x);%定義數據的個數.
x0=x;%產生原始數據
budget=k;
n1=n+budget;
%[a b]'=(A'*A)^(-1)*A'*X
  
%----------計算矩陣A,x1----------------------------------
    x1=cumsum(x);
   B=(x1(1:end-1,:)+x1(2:end,:))*(-1/2);
    X=x0(2:end,:);
    A=[B,ones(n-1,1)];
   au=inv((A'*A))*(A'*X);
%------ 預測值計算---------
    
%%% 修要修改
coef1=au(2)/au(1); 
coef2=x(1,:)-coef1; 
coef3=-au(1); 
%comparison of calculated and observed value 
for t=1:n+budget-1 
   mcv(t)=coef1+coef2*exp(coef3*t); 
end 
x1=[x(1) mcv];
x_mcv=diff(x1); 
y=[x(1) x_mcv];
e=y(1:n)-x';
plot(1:n,x','*r'); %'-o',1:n,e,'-or',1:n+budget,x_mcve,,1:n1,y,'-*'
%p=x_mcve(end+1:end); 
xlabel('CURVE OF GREY MODEL ANALYSIS'); 
title('GM(1,1)'); 
grid on