%APPELM1 Demonstrates Elman recurrent network.

% Mark Beale, 12-15-93
% Copyright 1992-2007 The MathWorks, Inc.
% $Revision: 1.18.2.2 $  $Date: 2007/11/09 20:47:57 $


echo on

%    NEWELM  - Inititializes an Elman recurrent network.
%    SIM   - Simulates an Elman recurrent network.
%    TRAIN - Trains an Elman recurrent network.

%    AMPLITUDE DETECTION:

%    Using the above functions an Elman network is trained
%    to output the amplitude of a sine wave being presented
%    in time.

pause % Strike any key to continue...

%    DEFINING THE PROBLEM
%    ====================

%    The first wave form has an amplitude of 1.

p1 = sin(1:20);     % If input is wave with amplitude of 1
t1 = ones(1,20);    % then output should be 1

%    The second wave form has an amplitude of 2.

p2 = sin(1:20)*2;   % If input is wave with amplitude of 2
t2 = ones(1,20)*2;  % then output should be 2

%    The network will be trained on the sequence formed by
%    repeating each wave form twice.

p = [p1 p2 p1 p2];
t = [t1 t2 t1 t2];
Pseq = con2seq(p);
Tseq = con2seq(t);

pause % Strike any key to define the Elman network...

% DEFINE THE EHLMAN NETWORK
% =========================

%    The function NEWELM creates an Elman network whose input
%    varies from -2 to 2, and has 10 hidden neurons and 1 output.

net = newelm([-2 2],[10 1],{'tansig','purelin'},'traingdx');
net.trainParam.epochs = 500;
net.trainParam.show = 5;
net.trainParam.goal = 0.01;

pause % Strike any key to train the Elman network...

%    TRAINING THE ELMAN NETWORK
%    ===========================

%    TRAIN trains Elman networks.  Here it is trained
%    without training parameters. (The default will be used.)

%    Training begins...please wait, this takes a while...

tic
[net,tr] = train(net,Pseq,Tseq);
toc

%    ...training done.

semilogy(tr.epoch,tr.perf)
title('Mean Squared Error of Elman Network')
xlabel('Epoch')
ylabel('Mean Squared Error')

pause % Strike any key to test the Elman network...

% TESTING THE ELMAN NETWORK
% =========================

%    SIM simulates an Elman network for as many timesteps
%    as input vectors in P.

a = sim(net,Pseq);

%    The network outputs and targets can then be plotted.

time = 1:length(p);
plot(time,t,'--',time,cat(2,a{:}))
title('Testing Amplitute Detection')
xlabel('Time Step')
ylabel('Target - -  Output ---')

%    The network does a fairly good job, if not perfect.

pause % Strike any key to test the network's generalization...

%    CHECKING GENERALIZATION
%    =======================

%    We will try waveforms with amplitudes of 1.6 and 1.2.

p3 = sin(1:20)*1.6;     % Input wave with amplitude of 1.6
t3 = ones(1,20)*1.6;    % We would like the output to be 1.6.

p4 = sin(1:20)*1.2;     % Try input wave with amplitude of 1.2
t4 = ones(1,20)*1.2;    % We would like the output to be 1.2.

%    Repeating each twice results in the series of test inputs.

pg = [p3 p4 p3 p4];
tg = [t3 t4 t3 t4];
pgseq = con2seq(pg);

pause % Strike any key to see generalization results...

%    GENERALIZATION RESULTS
%    ======================

%    SIM is used to simulate the network to these inputs.

a = sim(net,pgseq);

%    The network outputs and targets are plotted.

time = 1:length(pg);
plot(time,tg,'--',time,cat(2,a{:}))
title('Testing Generalization')
xlabel('Time Step')
ylabel('Target - -  Output ---')

%    The network does not do as well for amplitudes for
%    which it was not trained.

pause % Strike any key for conclusions...

%    CONCLUSIONS
%    ===========

%    The Elman recurrent network can learn to recognize time-
%    varying patterns.

%    In this case the network did a fairly good job with only
%    10 neurons in the recurrent layer, and 500 training epochs.

%    More recurrent neurons and longer training times could be
%    used to increase the network's accuracy on the training data.

%    Training the network on more amplitudes will result in
%    a network that generalizes better.

%    Type HELP ELMAN for a list of all Elman functions.

echo off
disp('End of APPELM1')


