function v = fastrl(v0, x, lambda)
%FASTRL Generates reinforcement learning expectations without using loops
%written by Ryan Jessup, 20090206
%v = FASTRL(v0,x,lambda) generates reinforcement learning trial by trial 
%expectations v using the initialized value v0, the vector of observed 
%outcomes in x, and the learning rate lambda.
%v0 scalar initial expectation for v
%x vector of observed outcomes
%lambda scalar learning parameter

%set the weights on preceding information in a form the filter uses
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);
v = v(1:end-1);