function [As,Q,R,p]=banditS(N,Aq,tau)
%FUNCTION [As,Q,R,p]=banditS(N,Aq,tau)
%  Performs the N-armed bandit example using softmax strategy, fixed tau
%  Inputs:
%        N=number of trials total
%        Aq=Actual rewards for each bandit (these are the mean rewards)
%        tau=temperature for softmax update
%  Ouputs:
%        As=Action selected on trial j, j=1:N
%        Q= Current reward estimates
%        R= Reward on action j, j=1:N
%        p= probability estimates  (Use P for cumulative)

numbandits=length(Aq);   %Number of Bandits
ActNum=zeros(numbandits,1);  %Keep a running sum of the number of times
                             %each action is selected.
ActVal=zeros(numbandits,1);  %Keep a running sum of the total reward 
                             %obtained for each action.
Q=zeros(1,numbandits);  %Current reward estimates
As=zeros(N,1);  %Storage for action
R=zeros(N,1);  %Storage for averaging reward (for Figure 2.1, p 28)
p=(1/numbandits)*ones(1, numbandits);  %Set initial probabilities
                                       %to all equal

%********************************************************************
%
%  Now we're ready for the main loop
%********************************************************************

for j=1:N
   %STEP ONE:  SELECT AN ACTION (cQ) using the probabilities 
   P=cumsum([0 p]);
   t=rand;  %Random number between 0 and 1
   n1=histc(t,P);
   cQ=find(n1==1);  %This is the action we select.
   cR=randn+Aq(cQ); %This is our reward.
   
   %STEP TWO:  STORAGE AND UPDATES:
   R(j)=cR;
   As(j)=cQ;
   ActNum(cQ)=ActNum(cQ)+1;
   ActVal(cQ)=ActVal(cQ)+cR;
   Q(cQ)=ActVal(cQ)/ActNum(cQ);
   p=exp(Q./tau);  %This is the softmax update
   p=p./sum(p);   
end