数学建模中常用的模型,及程序

1、数学建模中常用的模型及程序:1灰色预测:程序一:先建立M文件:function GM1=fungry1(x0T=input('T='x1=zeros(1,length(x0;B=zeros(length(x0-1,2;yn=zeros(length(x0-1,1;Hatx0=zeros(1,length(x0+T;Hatx00=zeros(1,length(x0;Hatx1=zeros(1,length(x0+T;epsilon=zeros(length(x0,1;omega=zeros(length(x0,1;for i=1:length(x0for j=1:ix1(i=x1

2、(i+x0(j;endendfor i=1:length(x0-1B(i,1=(-1/2*(x1(i+x1(i+1;B(i,2=1;yn(i=x0(i+1;endHatA=(inv(B'*B*B'*ynfor k=1:length(x0+THatx1(k=(x0(1-HatA(2/HatA(1*exp(-HatA(1*(k-1+HatA(2/HatA(1; endHatx0(1=Hatx1(1;for k=2:length(x0+THatx0(k=Hatx1(k-Hatx1(k-1;endfor i=1:length(x0epsilon(i=x0(i-Hatx0(i;omega

3、(i=(epsilon(i/x0(i*100;end%x0,Hatx1,Hatx0,epsilon,omega,c=std(epsilon/std(x0;p=0;for i=1:length(x0if abs(epsilon(i-mean(epsilon<0.6745*std(x0p=p+1;endendp=p/length(x0if p>0.95 & c<0.35disp('The model is good and the forecast is :',disp (Hatx0(length(x0+Telseif p>0.85 & c&

4、lt;0.5disp('The model is eligibility and the forecast is :',disp (Hatx0(length(x0+Telseif p>0.70 & c<0.65disp('The model is not good and the forecast is :',disp (Hatx0(length(x0+Telse p<=0.70 & c>0.65disp('The model is bad and try again 'endfor i=1:length(

5、x0Hatx00(i= Hatx0(i;endz=1:length(x0;plot(z,x0,'-',z,Hatx00,':'text(2,x0(2,'History data :real line'text(length(x0/2,Hatx00(length(x0/2,'Simulation data :broken line'end在matlab命令窗口中输入:>> x0=。; %原始数据矩阵>> fungry1(x0;Matlab命令窗口中将提示:T=这时输入1将表示所得结果为从原始数据最后一个算起的

6、第一个预测值,输入2表示。程序二:y=input('请输入数据 'n=length(y;yy=ones(n,1;yy(1=y(1;for i=2:nyy(i=yy(i-1+y(i;endB=ones(n-1,2;for i=1:(n-1B(i,1=-(yy(i+yy(i+1/2;B(i,2=1;endBT=B'for i=1:(n-1YN(i=y(i+1;endYM=YN'A=inv(BT*B*BT*YM;a=A(1;u=A(2;t=u/a;for i=1:n-1yyy(i+1=(y(1-t*exp(-a*i+t; endfor i=1:n-1y_y(i+1=y

7、yy(i+1-yyy(i;endfor i=1:nm(i=abs(y_y(i-y(i;endp=1:n;subplot(1,2,1,plot(p,y_y,p,y,'r*',title('申请量模拟曲线'subplot(1,2,2,plot(m,title('误差曲线't_n=input('请输入需要预测个数:'for i=0:t_n-1q(i+1=(y(1-t*exp(-a*i+t;endff(1=q(1;for i=1:t_n-1ff(i+1=q(i+1-q(i;enddisp(vpa(ff,6神经模型:>> P=1

8、601 5421 1890 4439 1703 3232 376 1167 1897 3737 1807 1628 1723 2584 1551 2479 1199 4148 2449 2026 1690 3374 2015 2480 850 2249 1674 3666 2029;>> T=5421 1890 4439 1703 3232 376 1167 1897 3737 1807 1628 1723 2584 1551 2479 1199 4148 2449 2026 1690 3374 2015 2480 850 2249 1674 3666 2029 1238;%这样建

9、立的是根据第一个月,预测第二个月的神经系统模型,P中每一个对应于T中每一个,而T中每一个是P中相对应的下一个月的数据>> net = newff(minmax(P,5 1,'tansig' 'purelin'>> Y = sim(net,P;>> plot(P,T,P,Y,'o'>> net = train(net,P,T;Y = sim(net,P;>> plot(P,T,P,Y,'o'>> x0=1601 5421 1890 4439 1703 3232 376 1167 1897 3737 1807 1628 1723 2584 1551 2479 1199 4148 2449 2026 1690 3374 2015 2480 850 2249 1674 3666 2029 1238;Y = sim(net,x0 %记下最后一个数据,作为7月1号的x1=1601 5421 1890 4439 1703 3232 376