%% EXAMPLE:  Adaptive training
%
%  In this example, we look at how online learning can be very beneficial.
%  Here, we construct a toy signal that changes in time.  Our goal:  Using
%  the past 5 values, predict the 6th value.  That is, build a linear
%  mapping so that: f(x_1, ..., x_5)=x_6 and f(x_2, ..., x_6)=x_7, etc.
%
%
%  First, build the time vectors:

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

%%  The data
T = [sin(time1*4*pi) sin(time2*8*pi)];
lr = 0.2;

% The domain will be vectors in R^5 found by lagging the vector T:
X=lag(T,4,1);  %X is 5 x 159.  That is, T(1:5) is the first column of X,
               % and is used to predict T(6).
X(:,159)=[];   %Last column not used.

% Construct the desired targets:
Targets=T(6:158+5);

%Online training.  In this case, track the error point-by-point:
[W,B,err]=wid_hoff1(X',Targets',0.01,120);

%The error is an array, 80 x 158 (80=number of epochs, 158=number of
%  points)
plot(mean(err))
               
%Plot the predicted values and the actual values:
Yout=W*X+B;
tt=time(6:158+5);
figure
plot(tt,Targets-Yout)