function fitsig(n0,P0,F0)
% P is a distribution on m^n
% F is a collection of functions m*N
randomize
global n P F
n = n0;
P = P0;
F = F0;

P0 = ones(2^n,1); P0 = P0/sum(P0);
zz = P0*0 + 1e-12; oo = P0*0+1;

if 1 % require sym. stationarity
  %Aeq = is_stat(2,n);
  Aeq = is_stat_sym(n);
  Aeq = [Aeq;oo'];
  Beq = zeros(size(Aeq,1),1); Beq(end)=1;
else
  Aeq = oo';
  Beq = 1;
end

global opty
opty = 1e6;
while 1
  %P = rand(2^n,1); P = P/sum(P);
  %P = P/sum(P);
  %%P = ones(2^n,1); P = P + randn(2^n,1)/2^n/10000;
  P = randbinsym(n);
  
  x = [P(:)];
  
  y = fmincon(@myobj,x,[],[],Aeq,Beq,zz,oo);
  
  fprintf('n=%d;  opty = %1.9f \n',n,opty);
end

return



function y = myobj(Psig)
Psig = makepos(Psig);

global n P F opty

E0 = maxdev_sym1(P,F,n);
E1 = maxdev_sym2(P,Psig,F,n);

y = abs(E0-E1);

if y < opty
  global optP
  optP = Psig;
  opty = y;
  fprintf('n=%d;  opty = %1.9f \n',n,opty);
end


return