function TTENS = treetensor(T,A,ii,jj)
% the probability transition tensor
% from nodes ii to nodes jj

% following my tradition, this will be a 2-d
% column-normalized matrix

global m n

kk = intersect(ii,jj); % handling overlap
ii = setdiff(ii,kk);
jj = setdiff(jj,kk);

TTENS.ii = ii;
TTENS.jj = union(jj,kk);

lii = length(ii);
ljj = length(jj);
lkk = length(kk);

TTENS.A = zeros(m^(lkk+ljj),m^(lkk+lii));

Dii = repmat([m],[1 lii]);
Djj = repmat([m],[1 ljj]);
Dkk = repmat([m],[1 lkk]);

for xi=1:prod(Dii)
  x = ind2coord(xi,Dii);
  for yi=1:prod(Djj)
    y = ind2coord(yi,Djj);
    for zi=1:prod(Dkk)
      z = ind2coord(zi,Dkk);
      xz = zeros([1, n]);
      xz(ii) = x;
      xz(kk) = z;
      xz = xz(TTENS.ii);
      xzi = coord2ind(xz,[Dii Dkk]);
      zy = zeros([1, n]);
      zy(jj) = y;
      zy(kk) = z;
      zy = zy(TTENS.jj);
      zyi = coord2ind(zy,[Djj Dkk]);
      p = 1;
      for vi = 1:length(TTENS.jj)
        v = TTENS.jj(vi);
        [u,ui] = parent(T,v,TTENS.ii);
        p = p * A(u,v,y(vi),x(ui));
      end
      TTENS.A(zyi,xi) = p;
    end
  end
end
return



function [u,ui] = parent(T,v,uu)
u = find(T(:,v));
ui = find(uu==u);
return