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');endif 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;