%written by Ryan Jessup, 20090218
%This script demonstrates a comparison between a filtering method and a
%loop method for generating expectations from a reinformcent learning
%model.  Functions fastrl.m and fastrln.m should be used fitting and
%predicting purposes when there is one and n actions, respectively.  


%Generate some sample data (observed outcomes)
nTrials = 1000;
mu=13; sig=4;
v0=5; %initial expectation
x=((randn(1,nTrials)*sig) + mu);
lambda= .05; %learning rate

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%                      Filter Method                 %%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('The following elapsed time is for the filter method')
tic %start time
a=[1 lambda-1]; 
%modify the v0; this must be done because otherwise the filter does not 
%correctly apply the initial expectation
modv0=v0/lambda; 
x=[modv0 x]; %append the intial expectation onto the dataset
v = filter(lambda,a,x);
%trim the initial v, which has been trasformed back into the orig v0
yFilt = v(2:end); 
toc %end time


%cf.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%                      Loop Method                   %%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('The following elapsed time is for the loop method')
tic %start time
yLoop=v0; 
for i=2:length(x)
    yLoop(i) = (1-lambda)*yLoop(i-1) + lambda*x(i);
end
%remove the initial y
yLoop=yLoop(2:end);
toc %end time

%Now, test to see whether any cell differs; if min yields 1 then they're
%all equivalent
disp('If the following yields 1 then all cells from the two methods are equivalent')
min(yFilt==yLoop)