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

global pstr
pstr = 'ephimarkovy'
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) + raf;

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

global Ainf Binf mylinopt
mylinopt = optimset('Diagnostics','off');
mylinopt = optimset('Display','off');
[Ainf,Binf] = lipab(m,n);

Ain = assembleblock({zeros(0,pdim), Ainf});
Bin = Binf;

global maxr
maxr = 0;
while 1
  A = pnormdim(rand(m),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 pstr
pdim = m*m;
fdim = m^n;
xdim = pdim + fdim;

A = makepos(reshape(x(1:pdim),[m m]));
[tha,hh] = stricthh(A);
Hn = sum( tha.^(0:n-1) );
Hn1 = sum( tha.^(0:n-2) );

F = x(pdim+1:end);
C = ones(m,1)/m;
P = markfillprob(A,C,n);
[U,margs] = prodmeas(P,m,n);

PF1 = P'*F;
P0 = markfillprob(A,C,n-1);
F0 = getky(F,1,m,n,n);
PF0 = P0'*F0;


[th,tth] = stricthh(A);
thn = th^(n-1);

UF = U'*F

lstr = 'pl(PF1-PF0';
rstr = 'thn*UF';

lhs = eval(lstr);
rhs = eval(rstr)+1e-12;
r = lhs/rhs;
y = -r;
global maxr
if r > maxr
  global optP optF optA
  optP = P;
  optF = F;
  optA = A;
  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 saf raf
K = genK(m,n);
[x,fval] = linprog(-K,Ainf,Binf,[],[],0*K+saf,0*K+raf,0,mylinopt);
phi = x';
return


function Ky = getky(K,y,m,n,i)
MN = repmat([m],[1 n]);
Ky = [];
mn = m^n;
for ind = 1:mn
  z = ind2coord(ind,MN);
  if z(i)==y
    Ky(end+1) = K(ind);
  end
end
Ky = reshape(Ky,size(K(1:length(Ky))));
return