灰色预测MATLAB程序

%灰色模型预测是在数据不呈现一定规律下可以采取的一种建模和预测方法，其预测数据与原始数据存在一定的规律相似性

%下面程序是灰色模型GM(1,1)程序二次拟合和等维新陈代谢改进预测程序,matlab6.5 ,使用本程序请注明，程序存储为gm1.m

%x = [5999,5903,5848,5700,7884];gm1(x);  测试数据 

%二次拟合预测GM(1,1)模型
function  gmcal=gm1(x)
sizexd2 = size(x,2);
%求数组长度

k=0;
for y1=x
    k=k+1;
    if k>1
        x1(k)=x1(k-1)+x(k);
        %累加生成
        z1(k-1)=-0.5*(x1(k)+x1(k-1));   
        %z1维数减1，用于计算B
        yn1(k-1)=x(k);
    else
        x1(k)=x(k);
    end
end
%x1,z1,k,yn1

sizez1=size(z1,2);
%size(yn1);
z2 = z1';
z3 = ones(1,sizez1)';

YN = yn1';   %转置
%YN

B=[z2 z3];
au0=inv(B'*B)*B'*YN;
au = au0';
%B,au0,au

afor = au(1);
ufor = au(2);
ua = au(2)./au(1);
%afor,ufor,ua 
%输出预测的  a u 和 u/a的值

constant1 = x(1)-ua;
afor1 = -afor;
x1t1 = 'x1(t+1)';
estr = 'exp';
tstr = 't';
leftbra = '(';
rightbra = ')';
%constant1,afor1,x1t1,estr,tstr,leftbra,rightbra

strcat(x1t1,'=',num2str(constant1),estr,leftbra,num2str(afor1),tstr,rightbra,'+',leftbra,num2str(ua),rightbra)
%输出时间响应方程

%******************************************************
%二次拟合

k2 = 0;
for y2 = x1
    k2 = k2 + 1;
    if k2 > k  
    else
        ze1(k2) = exp(-(k2-1)*afor);  
    end
end
%ze1

sizeze1 = size(ze1,2);
z4 = ones(1,sizeze1)';
G=[ze1' z4];
X1 = x1';
au20=inv(G'*G)*G'*X1;
au2 = au20';
%z4,X1,G,au20

Aval = au2(1);
Bval = au2(2);
%Aval,Bval
%输出预测的  A,B的值

strcat(x1t1,'=',num2str(Aval),estr,leftbra,num2str(afor1),tstr,rightbra,'+',leftbra,num2str(Bval),rightbra)
%输出时间响应方程

nfinal = sizexd2-1 + 1;
%决定预测的步骤数5  这个步骤可以通过函数传入

%nfinal = sizexd2 - 1 + 1;
%预测的步骤数 1

for  k3=1:nfinal
    x3fcast(k3) = constant1*exp(afor1*k3)+ua;
end
%x3fcast
%一次拟合累加值

for  k31=nfinal:-1:0
    if k31>1
        x31fcast(k31+1) = x3fcast(k31)-x3fcast(k31-1);
    else
        if k31>0
            x31fcast(k31+1) = x3fcast(k31)-x(1);
        else
            x31fcast(k31+1) = x(1);
        end
    end
   
end
x31fcast
%一次拟合预测值

for  k4=1:nfinal
    x4fcast(k4) = Aval*exp(afor1*k4)+Bval;
end
%x4fcast

for  k41=nfinal:-1:0
    if k41>1
        x41fcast(k41+1) = x4fcast(k41)-x4fcast(k41-1);
    else
        if k41>0
            x41fcast(k41+1) = x4fcast(k41)-x(1);
        else
            x41fcast(k41+1) = x(1);
        end
    end
   
end
x41fcast,x
%二次拟合预测值

%***精度检验p C************//
k5 = 0;
for y5 = x
    k5 = k5 + 1;
    if k5 > sizexd2  
    else
        err1(k5) = x(k5) - x41fcast(k5);  
    end
end
%err1
%绝对误差

xavg = mean(x);
%xavg
%x平均值

err1avg = mean(err1);
%err1avg
%err1平均值

k5 = 0;
s1total = 0 ;
for y5 = x
    k5 = k5 + 1;
    if k5 > sizexd2  
    else
        s1total = s1total + (x(k5) - xavg)^2;  
    end
end
s1suqare = s1total ./ sizexd2;
s1sqrt = sqrt(s1suqare);
%s1suqare,s1sqrt
%s1suqare  残差数列x的方差  s1sqrt 为x方差的平方根S1

k5 = 0;
s2total = 0 ;
for y5 = x
    k5 = k5 + 1;
    if k5 > sizexd2  
    else
        s2total = s2total + (err1(k5) - err1avg)^2;  
    end
end
s2suqare = s2total ./ sizexd2;
%s2suqare   残差数列err1的方差S2

Cval = sqrt(s2suqare ./ s1suqare);
Cval
%nnn = 0.6745 * s1sqrt
%Cval  C检验值

k5 = 0;
pnum = 0 ;
for y5 = x
    k5 = k5 + 1;
    if abs( err1(k5) - err1avg ) < 0.6745 * s1sqrt
        pnum = pnum + 1;
        %ppp = abs( err1(k5) - err1avg )     
    else
    end
end
pval = pnum ./ sizexd2;
pval
%p检验值

%arr1 = x41fcast(1:6)

%预测结果为区间范围  预测步长和数据长度可调整程序参数进行改进