function marginal = marginal_nodes(engine, nodes, t, add_ev, fam)% MARGINAL_NODES Compute the marginal on the specified query nodes (bk)%%   marginal = marginal_nodes(engine, i, t)% returns Pr(X(i,t) | Y(1:T)), where X(i,t) is the i'th node in the t'th slice.%%   marginal = marginal_nodes(engine, query, t)% returns Pr(X(query(1),t), ... X(query(end),t) | Y(1:T)),% where 't' specifies the time slice of the earliest node in the query.% 'query' cannot span more than 2 time slices.%% Example:% Consider a DBN with 2 nodes per slice.% Then t=2, nodes=[1 3] refers to node 1 in slice 2 and node 1 in slice 3.%% marginal = marginal_nodes(engine, nodes, t, add_ev, fam)% add_ev is an optional argument; if 1, we will "inflate" the marginal of observed nodes% to their original size, adding 0s to the positions which contradict the evidence   if nargin < 3, t = 1; endif nargin < 4, add_ev = 0; endif nargin < 5, fam = 0; endbnet = bnet_from_engine(engine);ss = length(bnet.intra);if t==1 | t==engine.T  slice = t;  nodes2 = nodes;elseif mysubset(nodes, engine.persist)  slice = t-1;  nodes2 = nodes+ss;else  slice = t;  nodes2 = nodes;end%disp(['computing marginal on ' num2str(nodes) ' t = ' num2str(t) ' fam = ' num2str(fam)]);if t==engine.T  c = clq_containing_nodes(engine.jtree_engine1, nodes2, fam);else  c = clq_containing_nodes(engine.jtree_engine, nodes2, fam);endif c == -1  error(['no clique contains ' nodes2])end%disp(['using ' num2str(nodes2) ' slice = ' num2str(slice) ' clq = ' num2str(c)]);bigpot = engine.clpot{c, slice};pot = marginalize_pot(bigpot, nodes2, engine.maximize);%pot = normalize_pot(pot);marginal = pot_to_marginal(pot);% we convert the domain to the unrolled numbering system% so that add_ev_to_dmarginal (maybe called in update_ess) extracts the right evidence.marginal.domain = nodes+(t-1)*ss;if add_ev  marginal = add_ev_to_dmarginal(marginal, engine.evidence, engine.node_sizes);end