function frat(m0,n0,F0)
global m n F
m = m0;
n = n0;
F = F0;

global pstr
pstr = 'frat'
global lstr rstr

xdim = m*F;
%LB = zeros(xdim,1) - 10;
LB = zeros(xdim,1);
UB = LB*0 + pi;

global maxr
maxr = 0;
while 1
  %A = randn(m,F);
  A = rand(m,F);
  
  x = A(:);
  
  y = fmincon(@radrat,x,[],[],[],[],LB,UB);
  
  fprintf('%s: n=%d m=%d F=%d; rat = %s/%s;  maxr = %1.9f \n',pstr,n,m,F,lstr,rstr,maxr);
end

return


function y = radrat(x)
global m n F
global lstr rstr
global pstr
xdim = m*F;
A = reshape(x,[m F]);
FF = A2F(A);

a = min(max(A'));

%lstr = 'a*max(FF)';
%rstr = 'min(FF)';

%lstr = 'a';
%rstr = 'min(FF)';

lstr = '(max(FF)/min(FF))';
rstr = '(n/a)';


lhs = eval(lstr);
rhs = eval(rstr)+1e-12;
r = lhs/rhs;

y = -r;
global maxr
if r > maxr
  global optA
  optA = A;
  maxr = r;
  fprintf('%s: n=%d m=%d F=%d; rat = %s/%s;  maxr = %1.9f \n',pstr,n,m,F,lstr,rstr,maxr);
end


return