gm_1_1.m

一个GM(1,1)模型的程序,添加到matlab目录中即可直接调用.附有一个关于灰色模型的简述文档,可对GM(1,1)原理有一个初始的了解.

function [y,p,e]=gm_1_1(X,k) 
%Build the calculating dieplate for the typical gray model. 
%Example [y,p]=gm_1_1([200 250 300 350],2) 

%Designed by NIXIUHUI,Dalian Fisher University. 
%20 April,2004. Last modified by NXH at 25 September,2004    

if nargout>3,error('Too many output argument.');end 
if nargin==1,k=1;x_orig=X; 
elseif nargin==0|nargin>2 
   error('Wrong number of input arguments.'); 
end 
x_orig=X; 
predict=k; 

%AGO process 
x=cumsum(x_orig); 


%compute the coefficient(a and u)------------------------ 
n=length(x_orig); 
%first generate the matrix B 
for i=1:(n-1); 
B(i)=-(x(i)+x(i+1))/2; 
end 
B=[B' ones(n-1,1)]; 
%then generate the matrix Y 
for i=1:(n-1); 
y(i)=x_orig(i+1); 
end 
Y=y'; 
%get the coefficient. a=au(1) u=au(2) 
au=(inv(B'*B))*(B'*Y); 
%-------------------------------------------------------- 
%change the grey model to symbolic expression 
coef1=au(2)/au(1); 
coef2=x_orig(1)-coef1; 
coef3=0-au(1); 
costr1=num2str(coef1); 
costr2=num2str(abs(coef2)); 
costr3=num2str(coef3); 
eq=strcat(costr1,'+',costr2,'.*exp(',costr3,'*(t-1))'); 

 

%comparison of calculated and observed value 
for t=1:n+predict 
   mcv(t)=coef1+coef2*exp(coef3*(t-1)); 
end 
x_mcv0=diff(mcv); 
x_mcve=[x_orig(1) x_mcv0]; 
x_mcv=diff(mcv(1:end-predict)); 
x_orig_n=x_orig(2:end); 
x_c_error=x_orig_n-x_mcv; 
x_error=mean(abs(x_c_error./x_orig_n)); 

if x_error>0.2 
   disp('model disqualification!'); 
elseif x_error>0.1 
   disp('model check out'); 
else 
   disp('model is perfect!'); 
end 
%predicting model and plot gragh 
plot(1:n,x_orig,'diamond',1:n+predict,x_mcve); 
p=x_mcve(end-predict+1:end); 
xlabel('CURVE OF GREY MODEL ANALYSIS'); 
title('GM(1,1)'); 
grid on 
y=eq; 
e=x_error; 
p=x_mcve(end-predict+1:end);