%% An Example Write Up in Matlab
% 
%
%  In this problem, we want to build a linear neural network that will
%  learn how to distinguish T's from G's and F's.  First we will define the
%  data and visualize it.
%

%% Section Title
%
%  Descriptive Text
%  We can even include LaTeX code (we'll be exporting to Latex):  
%
% <latex>
% \begin{tabular}{|c|c|} 
% \hline
% Letter & Output\\
% \hline
% T & $-60$\\
% G & $0$\\
% F & $60$\\
% \end{tabular}
% </latex>


T1=[1 1 1 -1
    -1 1 -1 -1
    -1 1 -1 -1
    -1 1 -1 -1];
T2=[-1 1 1 1
    -1 -1 1 -1
    -1 -1 1 -1
    -1 -1 1 -1];
G1=[1 1 1 -1
    1 -1 -1 -1
    1 1 1 -1
    1 1 1 -1];
G2=[-1 1 1 1
    -1 1 -1 -1
    -1 1 1 1
    -1 1 1 1];
F1=[1 1 1 -1
    1 1 -1 -1
    1 -1 -1 -1
    1 -1 -1 -1];
F2=[-1 1 1 1
    -1 1 1 -1
    -1 1 -1 -1
    -1 1 -1 -1];

gg=colormap(gray);
gg=gg(end:-1:1,:);

subplot(2,3,1)
imagesc(T1)
colormap(gg)
subplot(2,3,2)
imagesc(G1)
subplot(2,3,3)
imagesc(F1)

subplot(2,3,4)
imagesc(T2)
subplot(2,3,5)
imagesc(G2)
subplot(2,3,6)
imagesc(F2)

%% Initialize Parameters
%

X=[T1(:) T2(:) G1(:) G2(:) F1(:) F2(:)];  %Domain
T=[60 60 0 0 -60 -60];                    %Range
alpha=0.03;                     %Learning Rate
W=randn(1,16);                  %Weights
b=0;                            %biases
TotalErr=0;                     %Keep a running track of the error
NumPoints=6;                    %Number of training points

%% Main Code
%
%  In Hebb's rule, we update W and b by running through the data multiple
%  times.  In this case, we will run through all 6 points a total of 60
%  times - (each of the 60 trials is called an epoch). 
%

for k=1:60               % 60 times through the data
    idx=randperm(6);     % 6 points presented at random

    for j=1:NumPoints              % Hebbian rule loop
        ThisOut=W*X(:,idx(j))+b;   % Compute y
        ThisErr=T(idx(j))-ThisOut; % Compute t-y
 
        W=W+alpha*ThisErr*X(:,idx(j))';  %Hebb's Rule for W  
        b=b+alpha*ThisErr;               %Hebb's Rule for b
 
    end
    EpochErr(k)=norm((W*X+b*ones(1,6))-T);  %This is the error between the
                                            % y's and the t's
end
%% Look at the output:
%
%  Since we have one dimensional output and only 6 points, we can actually
%  look at our network output and compare it to the desired values:
%
T
W*X+b*ones(1,6)

%% Visualize the error.
%
%  The plot below has the epoch along the horizontal axis, and error along
%  the vertical axis (as defined in the vector EpochErr).
figure(2)
plot(EpochErr);