% Check that adding soft evidence to a hidden node is equivalent to evaluating its leaf CPD.% Make an HMMT = 3; Q = 2; O = 2; cts_obs = 0; param_tying = 0;bnet = mk_hmm_bnet(T, Q, O, cts_obs, param_tying);N = 2*T;onodes = bnet.observed;hnodes = mysetdiff(1:N, onodes);for i=1:N  bnet.CPD{i} = tabular_CPD(bnet, i);endev = sample_bnet(bnet);evidence = cell(1,N);evidence(onodes) = ev(onodes);engine = jtree_inf_engine(bnet);[engine, ll] = enter_evidence(engine, evidence);query = 1;m = marginal_nodes(engine, query);% Make a Markov chain with the same backbonebnet2 = mk_markov_chain_bnet(T, Q);for i=1:T  S = struct(bnet.CPD{hnodes(i)}); % violate object privacy  bnet2.CPD{i} = tabular_CPD(bnet2, i, S.CPT);end% Evaluate the observed leaves of the HMMsoft_ev = cell(1,T);for i=1:T  S = struct(bnet.CPD{onodes(i)}); % violate object privacy  dist = S.CPT(:, evidence{onodes(i)});  soft_ev{i} = dist;end% Use the leaf potentials as soft evidenceengine2 = jtree_inf_engine(bnet2);[engine2, ll2] = enter_evidence(engine2, cell(1,T), 'soft', soft_ev);m2 = marginal_nodes(engine2, query);assert(approxeq(m2.T, m.T))assert(approxeq(ll2, ll))% marginal on node 1 without evidence[engine2, ll2] = enter_evidence(engine2, cell(1,T));m2 = marginal_nodes(engine2, 1);% add soft evidencesoft_ev=cell(1,T);soft_ev{1}=[0.7 0.3]; [engine2, ll2] = enter_evidence(engine2, cell(1,T), 'soft', soft_ev);m3 = marginal_nodes(engine2, 1);assert(approxeq(normalise(m2.T .* [0.7 0.3]'), m3.T))