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function marginal = marginal_family(engine, i, t)
% MARGINAL_FAMILY Compute the marginal on the specified family (ff)
% marginal = marginal_family(engine, i, t)
if engine.filter
error('can''t currently use marginal_family when filtering with ff');
end
if nargin < 3, t = 1; end
% The method is similar to the following HMM equation:
% xi(i,j,t) = normalise( alpha(i,t) * transmat(i,j) * obsmat(j,t+1) * beta(j,t+1) )
% where xi(i,j,t) = Pr(Q(t)=i, Q(t+1)=j | y(1:T))
bnet = bnet_from_engine(engine);
ss = length(bnet.intra);
if myismember(i, engine.onodes)
ps = parents(bnet.dag, i);
p = ps(1);
marginal = pot_to_marginal(engine.marginals{ps(1),t});
fam = ([ps i]) + (t-1)*ss;
elseif t==1
marginal = pot_to_marginal(engine.marginals{i,t});
fam = i + (t-1)*ss;
else
pot = engine.CPDpot{i,t};
c = engine.obschild(i);
if c>0
pot = multiply_by_pot(pot, engine.CPDpot{c,t});
end
pot = multiply_by_pot(pot, engine.back{i,t});
ps = parents(bnet.dag, i+ss);
for p=ps(:)'
pot = multiply_by_pot(pot, engine.fwd{p,t-1});
end
marginal = pot_to_marginal(normalize_pot(pot));
fam = ([ps i+ss]) + (t-2)*ss;
end
% we convert the domain to the unrolled numbering system
% so that update_ess extracts the right evidence.
marginal.domain = fam;
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