% Approximating a SISO function by a two-layer BP NN

% p:input data; t:desired output data
p=-1:0.1:1;
t=[-0.96 -0.577 -0.0729 0.377 0.641 0.66 0.461 0.1336 -0.201 -0.434 -0.5 -0.393 -0.1647 0.0988 0.3072 0.396 0.3449 0.1816 -0.0312 -0.2183 -0.3201]; 
% Initializing the BP NN
[R,Q]=size(p);
[S2,Q]=size(t);
S1=5;
% RANDS is a weight/bias initialization function.
[w1,b1]=rands(S1,R);
[w2,b2]=rands(S2,S1);
A2=purelin(w2*tansig(w1*p,b1),b2);
plot(p,t,'-k',p,A2,':k')
title('Function Approximation')
xlabel('Input')
ylabel('Output')
pause

% Set the parameters for BP NN training
disp_fqre=10;max_epoch=18000;err_goal=0.01;lr=0.01;
TP=[disp_fqre max_epoch err_goal lr];
[w1,b1,w2,b2,epochs,errors]=trainbp(w1,b1,'tansig',w2,b2,'purelin',p,t,TP);
pause

% Plot the sum square error vs training epochs
ploterr(errors)