function [marginals, loglik] = enter_soft_evidence(engine, CPDpot, observed, pot_type, filter)% ENTER_SOFT_EVIDENCE Add the specified soft evidence to the network (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);H = length(hnodes);local_logscale = zeros(1,ss);obschild = zeros(1,ss);for i=hnodes  ocs = myintersect(children(bnet.dag, i), onodes);  assert(length(ocs)==1);  obschild(i) = ocs(1);end    t = 1;for i=hnodes  fwd{i,t} = CPDpot{i,t};  c = obschild(i);  temp = pot_to_marginal(CPDpot{c,t});   ev = dpot(i, ns(i), temp.T);  fwd{i,t} = multiply_by_pot(fwd{i,t}, ev);  [fwd{i,t}, local_logscale(i)] = normalize_pot(fwd{i,t});endlogscale(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);    c = obschild(i);    temp = pot_to_marginal(CPDpot{c,t});    ev = dpot(i, ns(i), temp.T);    fwd{i,t} = multiply_by_pot(fwd{i,t}, ev);    [fwd{i,t}, local_logscale(i)] = normalize_pot(fwd{i,t});  end  logscale(t) = sum(local_logscale);endloglik = sum(logscale);if filter  marginals = fwd;  return;endback = cell(ss,T);t = T;for i=hnodes  back{i,t} = dpot(i, ns(i));  back{i,t} = set_domain_pot(back{i,t}, i+ss);endfor t=T-1:-1:1  for i=hnodes    pot = CPDpot{i,t+1};    pot = multiply_by_pot(pot, back{i,t+1});    c = obschild(i);    temp = pot_to_marginal(CPDpot{c,t+1});    ev = dpot(i, ns(i), temp.T);    pot = multiply_by_pot(pot, ev);    back{i,t} = marginalize_pot(pot, i);    back{i,t} = normalize_pot(back{i,t});    back{i,t} = set_domain_pot(back{i,t}, i+ss);  endend% COMBINEfor t=1:T  for i=hnodes    back{i,t} = set_domain_pot(back{i,t}, i);    fwd{i,t} = multiply_by_pot(fwd{i,t}, back{i,t});    marginals{i,t} = normalize_pot(fwd{i,t});    %fwdback{i,t} = normalize_pot(multiply_pots(fwd{i,t}, back{i,t}));  endend