%% Quiz 8 Problem 4:  Adaptively training a linear neural network

%Define the dataset:

time1 = 0:0.05:4;      % from 0 to 4 seconds
time2 = 4.05:0.024:6;  % from 4 to 6 seconds
time = [time1 time2];  % from 0 to 6 seconds

T = [sin(time1*4*pi) sin(time2*8*pi)];  %Original time series

lags=5;  %The matrix will be embedded into lags+1 dim space
X = lag(T,lags,1);
Patterns=X(1:lags,:);
Targets=X(lags+1,:);

figure(1)
plot(time,T)
xlabel('Time');
ylabel('Target Signal');
title('Signal to be Predicted');


lr = 0.1;  %The learning rate takes the place of 2 alpha in the class notes
[dimIn,numPts]=size(Patterns);
[dimOut,numPts]=size(Targets);

%
%Initialize the weights W using random points in [0,1].
% Initalize the bias vector b using zeros.  
% Notice that we have parameters dimOut and dimIn to use.
%


%
% Main loop 
%

for k=1:numPts  %Use the kth data point:
   y(k)=
   err(k)=norm(    );
   W = W + lr*(  );
   b = b + lr*(  );
end


timeindex=lags+1:numPts+lags;
figure(2)
plot(time(timeindex),err)
title('Error as time progresses');
figure(3)
plot(time(timeindex),y,time(timeindex),Targets);
legend('Predicted','Actual');
title('Predicted v. Actual Signal');