function ephiconv(m0,n0)
global m n
m = m0;
n = n0;

global LB UB saf raf Lipk
saf = 1;
raf = n;
global Ainf Binf mylinopt
mylinopt = optimset('Diagnostics','off');
mylinopt = optimset('Display','off');
[Ainf,Binf] = lipab(m,n);

while 1
  %P1 = unifP(m,n);
  %F1 = rand(m^n,1);
  F1 = randlip';
  ab1 = rand(2,1);
  %P2 = unifP(m,n);
  %F2 = rand(m^n,1);
  F2 = randlip';
  ab2 = rand(2,1);
  lam = rand;

  ab2(2) = ab1(2);  
  
  %P3 = lam*P1 + (1-lam)*P2;
  ab3 = lam*ab1 + (1-lam)*ab2;
  
  F3 = lam*F1 + (1-lam)*F2;

  
  v1 = myfunc2([ab1; F1]);
  v2 = myfunc2([ab2; F1]);  
  v3 = myfunc2([ab3; F1]);
  
  
  %v1 = myfunc([P1; F1]);
  %v2 = myfunc([P2; F2]);  
  %v3 = myfunc([P3; F3]);
  % NOT convex in (P,F)
  
  %v1 = myfunc([P1; F1]);
  %v2 = myfunc([P1; F2]);  
  %v3 = myfunc([P1; F3]);
  % YES convex in F

  %v1 = myfunc([P1; F1]);
  %v2 = myfunc([P2; F1]);  
  %v3 = myfunc([P3; F1]);
  % NOT convex in P
  
  
  good = (v3 < lam*v1 + (1-lam)*v2 +1e-9)
  %good = (v3 < max(v1,v2) + 1e-9)
  if ~good
    keyboard
  end
  
end

return


function y = myfunc1(x)
global m n
P = x(1:m^n);
F = x(m^n+1:end);

U = prodmeas(P,m,n);
[hh,Ht,H] = gethhn(P,m,n);

lhs = P'*F;
rhs = H*U'*F;

y = rhs - lhs;

return

function y = myfunc2(x)
global m n
ab = x(1:2);
F = x(3:end);

a = ab(1); b = ab(2);
A(1,1) = a; A(2,1) = 1-a;
A(1,2) = b; A(2,2) = 1-b;
C = ones(m,1)/m;
P = markfillprob(A,C,n);

U = prodmeas(P,m,n);
%[hh,Ht,H] = gethhn(P,m,n);
tha = abs(a-b);
H = sum(tha.^[0:n-1]);

lhs = P'*F;
rhs = H*U'*F;

y = rhs - lhs;

return



function phi = randlip
global Ainf Binf m n mylinopt
global saf raf
K = genK(m,n);
[x,fval] = linprog(-K,Ainf,Binf,[],[],0*K+saf,0*K+raf,0,mylinopt);
phi = x';
return