% pooling

function f0=poolf(pred,m,F) 

 fbar=1/m;                          % pre-prior pdf
      
 % matrix F
     for k=1:F
       for l=1:F
         f(k,l)=0;
          for i=1:m
           f(k,l)=f(k,l)+log(pred(i,k))*log(pred(i,l))*fbar;
         end
       end
     end

    % maxium eigenvector v
     v=ones(F,1);     
     epsilon0=0.001;
     epsilon=2*epsilon0;     
     while epsilon>epsilon0
       vbar=f*v/sqrt(v'*f'*f*v);
       epsilon=(vbar-v)'*(vbar-v);
       v=vbar;
     end
     v=v/norm(v);
 
    alpha=rank(f)/(v'*ones(F,1));
    sum=0;  
    for i=1:m
       f0(i)=1;       
        for j=1:F
        f0(i)=f0(i)*pred(i,j)^(alpha*v(j));        
        end
        sum=sum+f0(i);        
    end
    f0=f0/sum;