自创建神经网络

自创建神经网络， 使用传递函数（激活函数）为logsig（S型对数函数）。具体实现如下：

%自创建神经网络
P=[-3,2];
T=[0.4,0.8]; 
Wrange=-4:0.4:4;
Brange=-4:0.4:4;            %W值的行向量、B值的行向量 
ES=errsurf(P,T,Wrange,Brange,'logsig');       %求单神经元的误差平面（只用在单神经元中）
%Error surface of single input neuron
% errsurf(P,T,WV,BV,F) takes these arguments, 
% P -- 1 x Q matrix of input vectors 
% T -- 1 x Q matrix of target vectors 
% WV -- Row vector of values of W 
% BV -- Row vector of values of B 
% F -- Transfer function (string) 
% and returns a matrix of error values over WV and BV.
mesh(ES,[60,30]);                         %作三维网状面，视角【60，30】  
title('Error Surface Graph')                  %标题 
xlabel('W') 
ylabel('B') 
zlabel('Sum Squared Error') 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%华丽分割线
max_epoch=1500;                         %赋最大训练次数  
err=[];
xx=[];
yy=[];                         %定义矩阵                      
lr=0.5; 
W1=-4*rand(1);                           %赋权值和偏差的初值 
b1=-4*rand(1); 
x1=W1;
y1=b1; 
for i=1:max_epoch 
    A1 = logsig(W1*P+b1*ones(1,2));        %计算输出 
    %     Log sigmoid transfer function
    %     
    % logsig is a transfer function. Transfer functions calculate a layer's output from its net input. 
    % logsig(N) takes one input, 
    % N -- S x Q matrix of net input (column) vectors 
    % and returns each element of N squashed between 0 and 1. 
    % logsig(code) returns useful information for each code string: 
    % 'deriv' -- Name of derivative function 
    % 'name' -- Full name 
    % 'output' -- Output range 
    % 'active' -- Active input range
    E = T-A1;                            %求误差 
    D1 = A1.*(1-A1).*E;                   %矩阵对应元素相乘 
    dW1 = D1*P'*lr;                      %求权值增量 
    db1 = D1*ones(2,1)*lr;                 %求偏差增量 
    newx = W1(1,1) + dW1(1,1);            %新的权值 
    W1(1,1) = newx;
    xx =[xx newx]; 
    newy = b1(1)   + db1(1);              %新的偏差   
    b1(1) = newy; 
    yy =[yy newy];                  
    SSE = sumsqr(E);                  %求误差平方和 
    err=[err SSE]; 
    if (SSE<1e-8) 
        break; 
    end 
end 
 
figure(2) 
[C,h] =contour(Wrange,Brange,ES);       %作等高线图，ES为高 
%返回等高线矩阵C，列向量h是线或对象的句柄，一条线一个句柄，这些被用作CLABEL的输入，  
%每个对象包含每个等高线的高度  
%A contour graph displays isolines of matrix Z. Label the contour lines using clabel
% contour(X,Y,Z,n), and contour(X,Y,Z,v) draw contour plots of Z.
% X and Y specify the x- and y-axis limits. When X and Y are matrices,
%they must be the same size as Z, in which case they specify a surface, 
%as defined by the surf function. 
% If X or Y is irregularly spaced, 
% contour calculates contours using a regularly spaced contour grid, 
% then transforms the data to X or Y.
clabel(C,h)                           %标上高度值 
colormap cool                         %背景的颜色cool 
axis('equal') 
hold on 
plot(x1,y1,'r+') 
plot(xx,yy,'b*')                            %作矩阵变化曲线 
hold off 
 
figure(3) 
plot(err)                              %作误差曲线 
err