function ephimarkov(m0,n0)
global m n
randomize
m = m0;
n = n0;

global pstr
pstr = 'ephimarkov'
global lstr rstr

global LB UB saf raf
saf = 1;
raf = 1e10;

pdim = m*m;
fdim = m^n;
xdim = pdim + fdim;
LB = zeros(xdim,1);
LB(pdim+1:end) = 0*LB(pdim+1:end) + saf;
UB = LB*0;
UB(1:pdim) = 0*UB(1:pdim) + 1;
UB(pdim+1:end) = 0*UB(pdim+1:end) + n;
%UB(pdim+1:end) = 0*UB(pdim+1:end) + 1e6;

[Aeq0, Beq] = normab(m,m);
Aeq = assembleblock({Aeq0,zeros(0,fdim)});

Ain = [];
Bin = [];

global maxr
maxr = 0;
while 1
  A = pnormdim(rand(m),1);
  %F = saf + rand(m^n,1);
  F = randlip;
  x = [A(:);F(:)];
  y = fmincon(@radrat,x,Ain,Bin,Aeq,Beq,LB,UB);
  fprintf('%s: n=%d m=%d; rat = %s/%s;  maxr = %1.9f \n',pstr,n,m,lstr,rstr,maxr);
end

return


function y = radrat(x)
global m n
global lstr rstr
global LB UB saf raf
global pstr
pdim = m*m;
fdim = m^n;
xdim = pdim + fdim;

A = makepos(reshape(x(1:pdim),[m m]));
F = x(pdim+1:end);
%F = pl(F);
F = max(F,saf);
F = min(F,raf);

C = ones(m,1)/m;
P = markfillprob(A,C,n);
U = prodmeas(P,m,n);

[tha,hh] = stricthh(A);
lam2 = lambda2(A);
Hn = sum( tha.^(0:n-1) );
Hn1 = sqrt(Hn);
Ln = sum( lam2.^(0:n-1) );
%Lam = 1/(1-lam2);

FP = abs(F'*P);
FU = abs(F'*U);

lstr = 'FP';
rstr = 'FU*Hn1';
%rstr = 'FU';
%rstr = 'FU*(1+tha)';

lhs = eval(lstr);
rhs = eval(rstr)+1e-12;
r = lhs/rhs;
y = -r;
global maxr
if r > maxr
  global optP optF
  optP = P;
  optF = F;
  maxr = r;
  fprintf('%s: n=%d m=%d; rat = %s/%s;  maxr = %1.9f \n',pstr,n,m,lstr,rstr,maxr);
end


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


function c=i2c(i,m,n)
dims = repmat(m,[1 n]);
c = ind2coord(i,dims);
return