% pooling

function finpre=poolt(ypred) 

global my m sn T ymin ymax yl1 yl2
 
 fbar=1/my;                          % pre-prior pdf
   for mod=2:m
     for t=m+1:T
       for s=1:sn-2
        for p=1:mod
         for dis=1:s
          pred(dis,(p-1)*(sn-2)+s)=ypred(1+(s-1)*my+(p-1)*my*(sn-2),t)/s;
         end
          pred(s+1,(p-1)*(sn-2)+s)=ypred(2+(s-1)*my+(p-1)*my*(sn-2),t);
         for dis=s+2:sn
          pred(dis,(p-1)*(sn-2)+s)=ypred(3+(s-1)*my+(p-1)*my*(sn-2),t)/(sn-s-1);
         end
        end
       end
      
     % matrix F
     for k=1:mod*(sn-2)
       for l=1:mod*(sn-2)
         f(k,l)=0;
          for i=1:sn
           f(k,l)=f(k,l)+log(pred(i,k))*log(pred(i,l))*fbar;
         end
       end
     end

    % maxium eigenvector v
     v=ones(mod*(sn-2),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(mod*(sn-2),1));
    sum=0;  
    for i=1:sn
       f0(i)=1;       
        for j=1:mod*(sn-2)
        f0(i)=f0(i)*pred(i,j)^(alpha*v(j));        
        end
        sum=sum+f0(i);        
    end
    f0=f0/sum;
       finpre(mod,t)=0;
       for lev=2:sn-1
        finpre(mod,t)=finpre(mod,t)+(ymin+(ymax-ymin)/(2*sn)+(ymax-ymin)*(lev-1)/(sn))*f0(lev);
       end
        finpre(mod,t)=finpre(mod,t)+ymin*f0(1)+ymax*f0(sn);
     end 
   end