关联问题 %排序

function output=grayrela(x0)

%参考因子与比较因子共同存储在一个矩阵x0中,参考因子位于第一列

%斜率序列
for i=2:length(x0(:,1))
    x1(i,:)=x0(i,:)-x0(i-1,:);
end

%标准化
m=length(x1(1,:));
for i=1:m
x2(:,i)=x1(:,i)/std(x1(:,i));
end

%排序
[y,pos]=sort(x2(:,1));
x2_sorted=x2(pos,:);

% 判定关联性质
n=length(x1(:,1));
k=[1:n]';
for j=1:m
sig_j(j)=qiuhe(k.*x2_sorted(:,j))-qiuhe(x2_sorted(:,j))*qiuhe(k)/n;
end

%caculation of distantion
for j=2:m
    dist_0i(:,j)=abs(sign(sig_j(:,j)./sig_j(:,1)).*x2_sorted(:,j)-x2_sorted(:,1));
end

%计算关联系数
for i=1:n
    for j=1:m
        coef_rela(i,j)=(min(dist_0i)+0.5*max(dist_0i))/(dist_0i(i,j)+0.5*max(dist_0i));
end
end

for j=1:m
output(j)=qiuhe(coef_rela(:,j))/n;
end

%其中qiuhe=sum

% function output=qiuhe(input)  
 
% output=0; 
% for i=1:length(input) 
% output=output+input(i);
% end