function dirsketch(n)
keyboard

while 1
    a = rand;
    P = fillprob(n,a);
    [hh,Ht,H] = gethhn(P,n,n);
    H = hh+eye(n);
    G=sqrt(H)'*sqrt(H);
    g = sqrt(max(eig(G)));
    hold on
    plot(a,g,'.');
    drawnow
end

return

function p = getprob(x,alf)
p = 1;
for t=1:length(x)
  P = conddistr(x(1:t-1),alf);
  if x(t)>length(P)
    p = 0;
    return
  end
  p = p * P(x(t));
end
return

function P = fillprob(n,alf)
MN = repmat([n],[1 n]);
mn = n^(n);
P = zeros(mn,1);
for xi = 1:mn
  x = ind2coord(xi,MN);
  P(xi) = getprob(x,alf);
end
return

function P = conddistr(x,alf)
% conditional distribution on next table
% given the previous tables
if isempty(x)
  P = 1; % always pick table 1 first
else
  Uniq = unique(x(:));
  N = length(Uniq);
  P = zeros(N+1,1);
  Ucnt = getucnt(x,Uniq);
  P(1:N) = alf * Ucnt/sum(Ucnt);
  P(N+1) = 1-alf;
  P = P/sum(P);
end
return



function p = condprob0(x,alf)
T = length(x);
if T==1
  p = (x==1); % always pick table 1 first
else
  Uniq = unique(x(1:T-1));
  if x(T) > max(Uniq)+1
    p = 0;
  else
    Ucnt = getucnt(U,Uniq);
    
  end
end
return

function Ucnt = getucnt(U,Uniq)
Ucnt = zeros(size(Uniq));
for j=1:length(Uniq)
  Ucnt(j) = length(find(U==Uniq(j)));
end
return