%
% Written by:
% -- 
% John L. Weatherwax                2009-04-21
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

W = [ 0, 0, 0; 3, -1, 2; 1, 2, 0 ];
x = [ 1; 1; 3 ];

t = W * x ; 
h = 1./( 1 + exp(-t) )

U = [ -3, 1, -2 ];

t = U * h 
y_1 = 1./( 1 + exp( -t ) )

% the error signals delta y_1, delta h_1, and delta h_2 : 
d_1 = 0.9;
dy_1 = ( y_1 - d_1 ) * y_1 * ( 1 - y_1 ) % delta y_1 

j=1; 
dh_1 = ( y_1 - d_1 ) * y_1 * ( 1 - y_1 ) * U(1,j+1) * h(j+1) * ( 1 - h(j+1) ) 
j=2;
dh_2 = ( y_1 - d_1 ) * y_1 * ( 1 - y_1 ) * U(1,j+1) * h(j+1) * ( 1 - h(j+1) ) 

% compute the weight updates
%
eta = 1.;
Delta_u = - dy_1 * (h')

mu = 1.; 
Delta_w = - mu * [ dh_1; dh_2 ] * (x')