polynomial.m

径向基网络对Polynomial函数的逼近和拟合

        %======================================================================
       

        % File name: Polynomial.m 
        % Notes:     应用RBF网络对 Polynomial 进行函数逼近
        %            检验反向传播的逼近效果
        %            最简单的简单的梯度下降算法

      
        %======================================================================        
        
        close all	%关闭所有的窗口
        clear all	%清除所有的变量
        k=input('训练集点数=k,k=[3000]   ');
        if isempty(k),
           k=3000;
        end;
        L=input('最大隐层神经元个数=L,L=[15]   ');
        if isempty(L),
           L=15;
        end;
        S=input('归一化参数=S,S=[1]   ');
        if isempty(S),
           S=1;
        end;

        X=rand(1,k);
        Y=1+2.*X+3.*X.^2+4.*X.^3+5.*X.^4;
        
       
        net=newrb(X,Y,0.01,S,L,1);
        
        X2=linspace(0,1,1000);
        Y2=1+2.*X2+3.*X2.^2+4.*X2.^3+5.*X2.^4;
        
        X1=rand(1,30);
        Y1=1+2.*X1+3.*X1.^2+4.*X1.^3+5.*X1.^4;
        R=sim(net,X1);
        
        G=linspace(min(Y1),max(Y1),1000);
        T=G;
        
        figure(1)
        plot(X2,Y2,'-k',X1,R,'.b',X1,Y1,'+r')
        grid on
        xlabel('x in [0,10]')
        ylabel('y=sin(x).*exp(-x)')
        title('简单bp网络应用于函数逼近')
        
        figure(2)
        plot(G,T,'-k',R,Y1,'+r')