灰色关联分析

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：

function output=qiuhe(input)

output=0;

for i=1:length(input)

output=output+input(i);

end

计算方法参考文献：王宁练：冰川平衡线变化的主导气候因子灰色关联分析 冰川冻土