wolffd@0: function msg = tree_protocol(engine, evidence, msg)
wolffd@0: 
wolffd@0: bnet = bnet_from_engine(engine);
wolffd@0: N = length(bnet.dag);
wolffd@0: 
wolffd@0: % Send messages from leaves to root
wolffd@0: for i=1:N-1
wolffd@0:   n = engine.postorder(i);
wolffd@0:   above = parents(engine.adj_mat, n);
wolffd@0:   msg = send_msgs_to_some_neighbors(n, msg, above, bnet, engine.child_index, engine.parent_index, ...
wolffd@0: 				    engine.msg_type, evidence);
wolffd@0: end
wolffd@0: 
wolffd@0: % Process root
wolffd@0: n = engine.root;
wolffd@0: cs = children(bnet.dag, n);
wolffd@0: %msg{n}.lambda = compute_lambda(n, cs, msg, engine.msg_type);
wolffd@0: msg{n}.lambda = prod_lambda_msgs(n, cs, msg, engine.msg_type);
wolffd@0: ps = parents(bnet.dag, n);
wolffd@0: msg{n}.pi = CPD_to_pi(bnet.CPD{bnet.equiv_class(n)}, engine.msg_type, n, ps, msg, evidence);
wolffd@0: 
wolffd@0: % Send messages from root to leaves
wolffd@0: for i=1:N
wolffd@0:   n = engine.preorder(i);
wolffd@0:   below = children(engine.adj_mat, n);
wolffd@0:   msg = send_msgs_to_some_neighbors(n, msg, below, bnet, engine.child_index, engine.parent_index, ...
wolffd@0: 				    engine.msg_type, evidence);
wolffd@0: end
wolffd@0: 
wolffd@0:   
wolffd@0: %%%%%%%%%%
wolffd@0: 
wolffd@0: function msg = send_msgs_to_some_neighbors(n, msg, valid_nbrs, bnet, child_index, parent_index, ...
wolffd@0: 					   msg_type, evidence)
wolffd@0: 
wolffd@0: verbose = 0;
wolffd@0: 
wolffd@0: ns = bnet.node_sizes;
wolffd@0: dag = bnet.dag;
wolffd@0: e = bnet.equiv_class(n);
wolffd@0: CPD = bnet.CPD{e};
wolffd@0: 
wolffd@0: 
wolffd@0: cs = children(dag, n);
wolffd@0: %msg{n}.lambda = compute_lambda(n, cs, msg);
wolffd@0: msg{n}.lambda = prod_lambda_msgs(n, cs, msg, msg_type);
wolffd@0: if verbose, fprintf('%d computes lambda\n', n); display(msg{n}.lambda); end
wolffd@0: 
wolffd@0: ps = parents(dag, n);
wolffd@0: msg{n}.pi = CPD_to_pi(CPD, msg_type, n, ps, msg, evidence);
wolffd@0: if verbose, fprintf('%d computes pi\n', n); display(msg{n}.pi); end
wolffd@0: 
wolffd@0: ps2 = myintersect(parents(dag, n), valid_nbrs);
wolffd@0: for p=ps2(:)'
wolffd@0:   lam_msg = CPD_to_lambda_msg(CPD, msg_type, n, ps, msg, p, evidence);
wolffd@0:   j = child_index{p}(n); % n is p's j'th child
wolffd@0:   msg{p}.lambda_from_child{j} = lam_msg;
wolffd@0:   if verbose, fprintf('%d sends lambda to %d\n', n, p); display(lam_msg); end
wolffd@0: end
wolffd@0: 
wolffd@0: cs2 = myintersect(cs, valid_nbrs);
wolffd@0: for c=cs2(:)'
wolffd@0:   %pi_msg = compute_pi_msg(n, cs, msg, c);
wolffd@0:   pi_msg = compute_bel(msg_type, msg{n}.pi, prod_lambda_msgs(n, cs, msg, msg_type, c));
wolffd@0:   j = parent_index{c}(n); % n is c's j'th parent
wolffd@0:   msg{c}.pi_from_parent{j} = pi_msg;
wolffd@0:   if verbose, fprintf('%d sends pi to %d\n', n, c); display(pi_msg); end
wolffd@0: end
wolffd@0: 
wolffd@0: 
wolffd@0: