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function [m, pot] = marginal_family(engine, query)
% MARGINAL_NODES Compute the marginal on the family of the specified node (jtree_limid)
% [m, pot] = marginal_family(engine, query)
%
% query should be a single decision node, or [] (to compute global max expected utility)
bnet = bnet_from_engine(engine);
if isempty(query)
compute_meu = 1;
d = bnet.decision_nodes(1); % pick an arbitrary root to collect to
fam = []; % marginalize root pot down to a point
else
compute_meu = 0;
d = query;
assert(myismember(d, bnet.decision_nodes));
fam = family(bnet.dag, d);
end
clpot = init_clpot(bnet, engine.cliques, engine.clq_ass_to_node, engine.evidence, engine.exclude);
% collect to root (clique containing d)
C = length(engine.cliques);
seppot = cell(C, C); % separators are implicitely initialized to 1s
for n=engine.postorder{d}(1:end-1)
for p=parents(engine.rooted_jtree{d}, n)
%clpot{p} = divide_by_pot(clpot{n}, seppot{p,n}); % dividing by 1 is redundant
seppot{p,n} = marginalize_pot(clpot{n}, engine.separator{p,n});
clpot{p} = multiply_by_pot(clpot{p}, seppot{p,n});
end
end
root = engine.clq_ass_to_node(d);
assert(root == engine.postorder{d}(end));
pot = marginalize_pot(clpot{root}, fam);
m = pot_to_marginal(pot);
%%%%%%%%%%%
function clpot = init_clpot(bnet, cliques, clq_ass_to_node, evidence, exclude)
% Set the clique potentials to all 1s
C = length(cliques);
clpot = cell(1, C);
ns = bnet.node_sizes;
for i=1:C
clpot{i} = upot(cliques{i}, ns(cliques{i}));
end
N = length(bnet.dag);
nodes = mysetdiff(1:N, exclude);
for n=nodes(:)'
fam = family(bnet.dag, n);
e = bnet.equiv_class(n);
c = clq_ass_to_node(n);
pot = convert_to_pot(bnet.CPD{e}, 'u', ns, fam, evidence);
clpot{c} = multiply_by_pot(clpot{c}, pot);
end
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