function thaboundcheck
global m n mrat
m=2; n=4;
mrat = 0;

xdim = m^n;
Aeq = ones(1,xdim);
Beq = ones(1,1);
LB = zeros(xdim,1);
LB = LB+1e-9;
UB = ones(xdim,1);

while 1
  P = pnormdim(rand(m^n,1),1);
  x = P;
  [x,fv] = fmincon(@myopt,x,[],[],Aeq,Beq,LB,UB);
  fprintf('mrat = %1.9f \n',mrat);
end


return

function y = myopt(x)
global m n mrat
P = x;

tha = zeros(1,n-1);
for i=1:n-1
  tha(i) = thai(P,m,n,i);
end

hhat = zeros(n);
for i=1:n-1
  for j=i+1:n
    x = 1;
    for k=i:j-1
      x = x * tha(k);
    end
    hhat(i,j) = x;
  end
end

[hh,Ht,H0] = gethhn(P,m,n);
Hhat = 1+sum(hhat,2)';
Hhat = max(Hhat);

if 0
  tol = 1e-10;
  hh = max(hh,tol);
  hhat = max(hhat,tol);
  
  r = 0;
  for i=1:n-1
    for j=i+1:n
      r = max(r,hh(i,j)/hhat(i,j));
    end
  end
end

r = H0/Hhat;

if r > mrat
  global mP
  mrat = r;
  mP = P;
  fprintf('mrat = %1.9f \n',mrat);
  save THA P mrat
end

y = -r;

return