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

global pstr
pstr = 'spectralmarkov'
global lstr rstr

global C
%C=ones(m,1)/m;

LL = [];
HH = [];

while 1
  A = pnormdim(rand(m),1);
  C=rand(m,1); C=C/sum(C);

  P = markfillprob(A,C,n);


ae = sort(abs(eig(A)));
lam2 = ae(end-1);
tha = stricthh(A);


Ln = sum(lam2.^(0:n-1));
%Ln = sum(sqrt(lam2).^(0:n-1));
[hh,Ht,Hn] = gethhn(P,m,n);
hh = hh+eye(n);
H2 = (max(eig(hh'*hh)));

LL(end+1) = 1/(1-lam2);
HH(end+1) = Hn;
plot(HH,LL,'.');
drawnow
  
end

return


function y = radrat(x)
global m n
global lstr rstr
global pstr
global C
pdim = m*m;
%fdim = m;
%xdim = pdim + fdim;
xdim = pdim;

A = makepos(reshape(x(1:pdim),[m m]));
%f = x(pdim+1:end);

P = markfillprob(A,C,n);


ae = sort(abs(eig(A)));
lam2 = ae(end-1);
tha = stricthh(A);

%rstr = 'tha';
%lstr = 'lam2';


Ln = sum(lam2.^(0:n-1));
%Ln = sum(sqrt(lam2).^(0:n-1));
[hh,Ht,Hn] = gethhn(P,m,n);
hh = hh+eye(n);
H2 = (max(eig(hh'*hh)));


%lstr = 'TV(A*f)';
%rstr = 'lam2*TV(f)';

lstr = 'Hn';
%lstr = 'H2';
rstr = 'Ln';




lhs = eval(lstr);
rhs = eval(rstr)+1e-12;
r = lhs/rhs;
y = -r;
global maxr
if r > maxr
  global optA optC optf
  optA = A;
  optC = C;
  %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