% Code for a 2 x 2 x 1 network- Training by gradient descent by hand.

s=inline('1./(1+exp(-x))');
STEP=0.1;


% Set up the parameters

x=[0.35; 0.9]; t=0.5;

w11=[0.1; 0.8];
w12=[0.4;0.6];
w2=[0.3;0.9];

for j=1:100

% FORWARD PASS:

P01=x(1);
S01=x(1);
dS01=1;

P02=x(2);
S02=x(2);
dS02=1;

P11=w11'*[S01;S02];
S11=s(P11);
dS11=S11*(1-S11);

P12=w12'*[S01;S02];
S12=s(P11);
dS12=S12*(1-S12);

P2=w2'*[S11;S12];
S2=P2;
dS2=1;

Out(j)=S2;
Err(j)=t-S2;

% BACKWARDS Compute Deltas

% Last layer:
Delta2=(t-S2)*dS2

Delta11=dS11*w2(1)*Delta2;
Delta12=dS12*w2(2)*Delta2;

Delta01=dS01*(w11(1)*Delta11+w12(1)*Delta12);
Delta02=dS02*(w11(2)*Delta11+w12(2)*Delta12);

% Update the weights using the deltas
w11(1)=w11(1)+STEP*Delta11*S01;
w11(2)=w11(2)+STEP*Delta11*S02;
w12(1)=w12(1)+STEP*Delta12*S01;
w12(2)=w12(2)+STEP*Delta12*S02;

w2(1)=w2(1)+STEP*Delta2*S11;
w2(2)=w2(2)+STEP*Delta2*S12;
end