%% Training a Linear Neuron
% A linear neuron is trained to respond to specific inputs with target outputs.
%
% Copyright 1992-2005 The MathWorks, Inc.
% $Revision: 1.14.2.1 $  $Date: 2005/11/15 01:15:08 $

%%
% P defines two 1-element input patterns (column vectors).  T defines associated
% 1-element targets (column vectors).  A single input linear neuron with a bias
% can be used to solve this problem.

P = [1.0 -1.2];
T = [0.5 1.0];

%%
% ERRSURF calculates errors for a neuron with a range of possible weight and
% bias values.  PLOTES plots this error surface with a contour plot underneath.
% The best weight and bias values are those that result in the lowest point on
% the error surface.

w_range = -1:0.2:1;  b_range = -1:0.2:1;
ES = errsurf(P,T,w_range,b_range,'purelin');
plotes(w_range,b_range,ES);

%%
% MAXLINLR finds the fastest stable learning rate for training a linear network.
% For this demo, this rate will only be 40% of this maximum.  NEWLIN creates a
% linear neuron.  NEWLIN takes these arguments: 1) Rx2 matrix of min and max
% values for R input elements, 2) Number of elements in the output vector, 3)
% Input delay vector, and 4) Learning rate.

maxlr = 0.40*maxlinlr(P,'bias');
net = newlin([-2 2],1,[0],maxlr);

%%
% Override the default training parameters by setting the performance goal.

net.trainParam.goal = .001;

%%
% To show the path of the training we will train only one epoch at a time and
% call PLOTEP every epoch.  The plot shows a history of the training.  Each dot
% represents an epoch and the blue lines show each change made by the learning
% rule (Widrow-Hoff by default).

% [net,tr] = train(net,P,T);
net.trainParam.epochs = 1;
net.trainParam.show = NaN;
h=plotep(net.IW{1},net.b{1},mse(T-sim(net,P)));     
[net,tr] = train(net,P,T);                                                    
r = tr;
epoch = 1;
while true
   epoch = epoch+1;
   [net,tr] = train(net,P,T);
   if length(tr.epoch) > 1
      h = plotep(net.IW{1,1},net.b{1},tr.perf(2),h);
      r.epoch=[r.epoch epoch]; 
      r.perf=[r.perf tr.perf(2)];
      r.vperf=[r.vperf NaN];
      r.tperf=[r.tperf NaN];
   else
      break
   end
end
tr=r;

%%
% The train function outputs the trained network and a history of the training
% performance (tr).  Here the errors are plotted with respect to training
% epochs: The error dropped until it fell beneath the error goal (the black
% line).  At that point training stopped.

plotperf(tr,net.trainParam.goal);

%%
% Now use SIM to test the associator with one of the original inputs, -1.2, and
% see if it returns the target, 1.0.  The result is very close to 1, the target.
% This could be made even closer by lowering the performance goal.

p = -1.2;
a = sim(net, p)


displayEndOfDemoMessage(mfilename)