function main()
clc;clear all;close all;
%用Mexihat函数作为样本输入和输出
x=0:0.03:3; %样本输入值
c=2/(sqrt(3).*pi.^(1/4));
d=1/sqrt(2);
u=x/2-1;
targ=d.*c.*exp(-u.^2/2).*(1-u.^2); % 目标函数的样本输出值
eta=0.02;aerfa=0.735; %赋予网络学习速率和动量因子初始值
%初始化输出层和隐层的连接权wjh和隐层和输出层的连接权.
%假设小波函数节点数为H,样本数为P,输出节点数为J,输入节点数为I.
H=15;P=2;I=length(x);J=length(targ);
b=rand(H,1);a=rand(H,1); %初始化小波参数
whi=rand(I,H);wjh=rand(H,J); %初始化权系数；
b1=rand(H,1);b2=rand(J,1);%阈值初始化;
p=0;
Err_NetOut=[];%保存的误差；
flag=1;count=0;
while flag>0
flag=0;
count=count+1;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
xhp1=0;
for h=1:H
for i=1:I
xhp1=xhp1+whi(i,h)*x(i);
end
ixhp(h)=xhp1+b1(h);
xhp1=0;
end
for h=1:H
oxhp(h)=fai((ixhp(h)-b(h))/a(h));
end
ixjp1=0;
for j=1:J
for h=1:H
ixjp1=ixjp1+wjh(h,j)*oxhp(h);
end
ixjp(j)=ixjp1+b2(j);
ixjp1=0;
end
for i=1:J
oxjp(i)=fnn(ixjp(i));
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
wuchayy=1/2*sumsqr(oxjp-targ);
Err_NetOut=[Err_NetOut wuchayy];%保存每次的误差;
%求解小波网络运用BP算法，各参数每次学习的调整量
for j=1:J
detaj(j)=-(oxjp(j)-targ(j))*oxjp(j)*(1-oxjp(j));
end
for j=1:J
for h=1:H
detawjh(h,j)=eta*detaj(j)*oxhp(h);
end
end
detab2=eta*detaj;
sum=0;
for h=1:H
for j=1:J
sum=detaj(j)*wjh(h,j)*diffai((ixhp(h)-b(h))/a(h))/a(h)+sum;
end
detah(h)=sum;
sum=0;
end
for h=1:H
for i=1:I
detawhi(i,h)=eta*detah(h)*x(i);
end
end
detab1=eta*detah;
detab=-eta*detah;
for h=1:H
detaa(h)=-eta*detah(h)*((ixhp(h)-b(h))/a(h));
end
%引入动量因子aerfa，加快收敛速度和阻碍陷入局部极小值.
wjh=wjh+(1+aerfa)*detawjh;
whi=whi+(1+aerfa)*detawhi;
a=a+(1+aerfa)*detaa';
b=b+(1+aerfa)*detab';
b1=b1+(1+aerfa)*detab1';
b2=b2+(1+aerfa)*detab2';
%本算法采用的是样本逐个处理而不是数据批处理
p=p+1;
if p~=P
flag=flag+1;
else
if Err_NetOut(end)>0.008
flag=flag+1;
else
figure;
plot(Err_NetOut);
xlabel('网络学习的次数');ylabel('网络输出的误差');
title('网络学习误差曲线','fontsize',20,'color',[0 1 1],'fontname','隶书');
end
end
if count>6000
figure(1);
subplot(1,2,1)
plot(Err_NetOut,'color','b','linestyle','-','linewidth',2.2,...
'marker','^','markersize',3.5);
xlabel('网络学习的次数');ylabel('网络输出的误差');
title('误差曲线','fontsize',20,'color',[1 1 1],'fontname','隶书');
subplot(1,2,2)
handle1=plot(x,targ,'color','r','linestyle','--','linewidth',2.2,...
'marker','p','markersize',3.5);
hold on
handle1=plot(x,oxjp,'color','g','linestyle','-.','linewidth',2.2,...
'marker','d','markersize',3.5);
xlabel('样本输入值');ylabel('样本目标值与网络输出值');
title('目标值与网络输出值比较','fontsize',20,'color',[1 1 1],'fontname','隶书');
legend('样本目标值','网络仿真值');
break;
end
end
function y3=diffai(x) %子程序
y3=-1.75*sin(1.75*x).*exp(-x.^2/2)-cos(1.75*x).*exp(-x.^2/2).*x;
function yl=fai(x) %子程序
yl=cos(1.75.*x).*exp(-x.^2/2);
function y2=fnn(x) %子程序
y2=1/(1+exp(-x));
