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function [marginals, loglik] = enter_soft_evidence(engine, CPDpot, observed, pot_type, filter)
% ENTER_SOFT_EVIDENCE Add the specified soft evidence to the network (bk_ff)
% [marginals, loglik] = enter_soft_evidence(engine, CPDpot, observed, pot_type, filter)
assert(pot_type == 'd');
[ss T] = size(CPDpot);
fwd = cell(ss,T);
hnodes = engine.hnodes(:)';
onodes = engine.onodes(:)';
bnet = bnet_from_engine(engine);
ns = bnet.node_sizes;
onodes2 = [onodes onodes+ss];
ns(onodes2) = 1;
logscale = zeros(1,T);
local_logscale = zeros(1,length(hnodes));
t = 1;
for i=hnodes
fwd{i,t} = CPDpot{i,t};
end
for i=onodes
p = parents(bnet.dag, i);
assert(length(p)==1);
ev = marginalize_pot(CPDpot{i,t}, p);
fwd{p,t} = multiply_by_pot(fwd{p,t}, ev);
end
for i=hnodes
[fwd{i,t}, local_logscale(i)] = normalize_pot(fwd{i,t});
end
logscale(t) = sum(local_logscale);
for t=2:T
for i=hnodes
ps = parents(bnet.dag, i+ss);
assert(all(ps<=ss)); % in previous slice
prior = CPDpot{i,t};
for p=ps(:)'
prior = multiply_by_pot(prior, fwd{p,t-1});
end
fwd{i,t} = marginalize_pot(prior, i+ss);
fwd{i,t} = set_domain_pot(fwd{i,t}, i);
end
for i=onodes
p = parents(bnet.dag, i);
assert(length(p)==1);
temp = pot_to_marginal(CPDpot{i,t});
ev = dpot(p, ns(p), temp.T);
fwd{p,t} = multiply_by_pot(fwd{p,t}, ev);
end
for i=hnodes
[fwd{i,t}, local_logscale(i)] = normalize_pot(fwd{i,t});
end
logscale(t) = sum(local_logscale);
end
marginals = fwd;
loglik = sum(logscale);
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