function x = babyaux(x)
global saf raf Ainf Binf
x = fmincon(@radrat,x,Ainf,Binf,[],[],0*x+saf,0*x+raf);
return


function y = radrat(x)
global m n P U a b

lhs = P'*x;
rhs = U'*x;
tha = abs(a-b);
Hn = sum(tha.^[0:n-1]);
%rhs = rhs*(1+abs(a-b));
rhs = rhs*Hn;

  %hold on
  %plot(lhs,rhs,'.b');
  %drawnow


%[L1 R1] = babycheck(x)
%if abs(L1-lhs)+abs(R1-rhs) > 1e-9
%    keyboard
%end

r = lhs/rhs;
y = -r;

global maxr
if r > maxr
  maxr = r;
end


return


function [lhs, rhs] = babycheck(x)
global m n a b
lhs = 1/2 * ( a*x(c2i([0 0])) + (1-a)*x(c2i([0 1])) + b*x(c2i([1 0])) + (1-b)*x(c2i([1 1])) );
rhs = 1/4 * (1+abs(a-b)) * ((a+b)*(x(c2i([0 0]))+x(c2i([1 0]))) + (2-a-b)*(x(c2i([0 1]))+x(c2i([1 1]))));
return


function i=c2i(c)
global m n
dims = repmat(m,[1 n]);
i = coord2ind(c+1,dims);
return