wolffd@0: function bel = tree_protocol(engine, evidence, pot_type, local_kernel, msg)
wolffd@0: 
wolffd@0: bnet = bnet_from_engine(engine);
wolffd@0: ns = bnet.node_sizes;
wolffd@0: onodes = find(~isemptycell(evidence));
wolffd@0: 
wolffd@0: ndoms = length(engine.gdl.doms);
wolffd@0: prod_of_msg = cell(1, ndoms);
wolffd@0: bel = cell(1, ndoms);
wolffd@0:   
wolffd@0: % collect to root (node to parents)
wolffd@0: for n=engine.postorder
wolffd@0:   % absorb msgs from children
wolffd@0:   prod_of_msg{n} = mk_initial_pot(pot_type, engine.gdl.doms{n}, ns, bnet.cnodes, onodes);
wolffd@0:   for c=children(engine.tree, n)
wolffd@0:     prod_of_msg{n} = multiply_by_pot(prod_of_msg{n}, msg{c,n});
wolffd@0:   end
wolffd@0:   % send msg to parents
wolffd@0:   for p=parents(engine.tree, n)
wolffd@0:     if iter==1
wolffd@0:       temp = prod_of_msg{n};
wolffd@0:     else
wolffd@0:       temp = divide_by_pot(prod_of_msg{n}, old_msg{p,n});
wolffd@0:     end
wolffd@0:     temp = multiply_by_pot(temp, local_kernel{n});
wolffd@0:     temp2 = marginalize_pot(temp, engine.gdl.sepset{n,p}, engine.maximize);
wolffd@0:     %fprintf('%d sends %d\n', n, p);
wolffd@0:     msg{n,p} = normalize_pot(temp2);
wolffd@0:   end
wolffd@0: end
wolffd@0: 
wolffd@0: % distribute from root (node to children)
wolffd@0: for n=engine.preorder
wolffd@0:   % absorb from parents
wolffd@0:   %prod_of_msg{n} = mk_initial_pot(pot_type, doms{n}, ns, cnodes, onodes);
wolffd@0:   for p=parents(engine.tree, n)
wolffd@0:     prod_of_msg{n} = multiply_by_pot(prod_of_msg{n}, msg{p,n});
wolffd@0:   end
wolffd@0:   bel{n} = normalize_pot(multiply_pots(prod_of_msg{n}, local_kernel{n}));
wolffd@0:   % send msg to children
wolffd@0:   for c=children(engine.tree, n)
wolffd@0:     temp = divide_by_pot(prod_of_msg{n}, msg{c,n});
wolffd@0:     temp = multiply_by_pot(temp, local_kernel{n});
wolffd@0:     temp2 = marginalize_pot(temp, engine.gdl.sepset{n,c}, engine.maximize);
wolffd@0:     %fprintf('%d sends %d\n', n, c);
wolffd@0:     msg{n,c} = normalize_pot(temp2);
wolffd@0:   end
wolffd@0: end