%% Hopfield Two Neuron Design
% A Hopfield network consisting of two neurons is designed with two stable
% equilibrium points and simulated using the above functions.
%
% Copyright 1992-2007 The MathWorks, Inc.
% $Revision: 1.17.2.2 $  $Date: 2008/01/10 21:11:00 $

%%
% We would like to obtain a Hopfield network that has the two stable points
% defined by the two target (column) vectors in T.

T = [+1 -1; ...
      -1 +1];

%%
% Here is a plot where the stable points are shown at the corners.  All possible
% states of the 2-neuron Hopfield network are contained within the plots
% boundaries.

plot(T(1,:),T(2,:),'r*')
axis([-1.1 1.1 -1.1 1.1])
title('Hopfield Network State Space')
xlabel('a(1)');
ylabel('a(2)');

%%
% The function NEWHOP creates Hopfield networks given the stable points T.

net = newhop(T);

%%
% First we check that the target vectors are indeed stable.  We check this by
% giving the target vectors to the Hopfield network.  It should return the two
% targets unchanged, and indeed it does.

[Y,Pf,Af] = sim(net,2,[],T);
Y

%%
% Here we define a random starting point and simulate the Hopfield network for
% 20 steps.  It should reach one of its stable points.

a = {rands(2,1)};
[y,Pf,Af] = sim(net,{1 20},{},a);

%%
% We can make a plot of the Hopfield networks activity.
% 
% Sure enough, the network ends up in either the upper-left or lower right
% corners of the plot.

record = [cell2mat(a) cell2mat(y)];
start = cell2mat(a);
hold on
plot(start(1,1),start(2,1),'bx',record(1,:),record(2,:))

%%
% We repeat the simulation for 25 more initial conditions.
% 
% Note that if the Hopfield network starts out closer to the upper-left, it will
% go to the upper-left, and vise versa.  This ability to find the closest memory
% to an initial input is what makes the Hopfield network useful.

color = 'rgbmy';
for i=1:25
   a = {rands(2,1)};
   [y,Pf,Af] = sim(net,{1 20},{},a);
   record=[cell2mat(a) cell2mat(y)];
   start=cell2mat(a);
   plot(start(1,1),start(2,1),'kx',record(1,:),record(2,:),color(rem(i,5)+1))
end


displayEndOfDemoMessage(mfilename)