function p = probdev_optphi(A,C)
% the probability that the rv. phi(X), with X ~ Markov(A,C) 
% deviates from its mean by at least 1
% finds "worst" such phi

[m,m,t] = size(A);
if ~exist('C','var')
  C = ones(m,1)/m;
end

n = t+1;
dims = repmat([m],[1 n]);

global P Ainf Binf delta

P = zeros(m^n,1);
F = zeros(m^n,1);
for xind=1:m^n
  x = ind2coord(xind,dims);
  P(xind) = Pr(A,C,x);
  %F(xind) = phi(xind);
end

%[Ainf,Binf] = lipab(m,n);
LB = 0*P;
UB = LB + n;

pp = [];
%while 1
%phi = randlip(m,n);
[v,phi] = probdev_qp(A,C)
[x,fval] = fmincon(@myobj,phi(:),Ainf,Binf,[],[],LB,UB);
p = -fval;
%  pp(end+1) = p;
%  if length(pp)>40
%    break
%  end
%end
%pp
%p = max(pp);

return

function y = myobj(F)
global P delta m n
Ef = P'*F;
del = abs(F-Ef);

ii = find(del>= delta*n);
p = sum(P(ii));

y = -p;
return


function p = Pr(A,C,x)
%p = 1;
p = C(x(1));
for j=2:length(x)
  p = p * A(x(j),x(j-1),j-1);
end
return