function [marginal, msg, loglik] = enter_soft_ev(engine, evidence)% [marginal, msg, loglik] = smooth_evidence(engine, evidence) (pearl_dbn)[ss T] = size(evidence);bnet = bnet_from_engine(engine);bnet2 = dbn_to_bnet(bnet, T);ns = bnet2.node_sizes;hnodes = mysetdiff(1:ss, engine.onodes);hnodes = hnodes(:)';onodes2 = unroll_set(engine.onodes(:), ss, T);onodes2 = onodes2(:)';hnodes2 = unroll_set(hnodes(:), ss, T);hnodes2 = hnodes2(:)';[engine.parent_index, engine.child_index] = mk_pearl_msg_indices(bnet2);rand_init = 0;use_ev = 0;msg = init_pearl_msgs(bnet2.dag, ns, evidence, rand_init, use_ev);msg = init_pearl_dbn_ev_msgs(bnet, evidence, engine);verbose = 0;pot_type = 'd';niter = engine.max_iter;if verbose, fprintf('old smooth\n'); endfor iter=1:niter  % FORWARD  for t=1:T    if verbose, fprintf('t=%d\n', t); end        % update pi    for i=hnodes      n = i + (t-1)*ss;      ps = parents(bnet2.dag, n);      if t==1	e = bnet.equiv_class(i,1);      else	e = bnet.equiv_class(i,2);      end      msg{n}.pi = compute_pi(bnet.CPD{e}, n, ps, msg);      if verbose, fprintf('%d computes pi\n', n); disp(msg{n}.pi); end    end        % send pi msg to children     for i=hnodes      n = i + (t-1)*ss;      %cs = myintersect(children(bnet2.dag, n), hnodes2);      cs = children(bnet2.dag, n); % must use all children to get index right      for c=cs(:)'	j = engine.parent_index{c}(n); % n is c's j'th parent	pi_msg = normalise(compute_pi_msg(n, cs, msg, c, ns));	msg{c}.pi_from_parent{j} = pi_msg;	if verbose, fprintf('%d sends pi to %d\n', n, c); disp(pi_msg); end      end    end  end  % BACKWARD  for t=T:-1:1    if verbose, fprintf('t = %d\n', t); end    % update lambda    for i=hnodes      n = i + (t-1)*ss;      cs = children(bnet2.dag, n);      msg{n}.lambda = compute_lambda(n, cs, msg, ns);      if verbose, fprintf('%d computes lambda\n', n); disp(msg{n}.lambda); end    end        % send lambda msgs to hidden parents in prev slcie    for i=hnodes      n = i + (t-1)*ss;      ps = parents(bnet2.dag, n);      for p=ps(:)'	j = engine.child_index{p}(n); % n is p's j'th child	if t > 1	  e = bnet.equiv_class(i, 2);	else	  e = bnet.equiv_class(i, 1);	end	lam_msg = normalise(compute_lambda_msg(bnet.CPD{e}, n, ps, msg, p));	msg{p}.lambda_from_child{j} = lam_msg;	if verbose, fprintf('%d sends lambda to %d\n', n, p); disp(lam_msg); end      end     end      endendmarginal = cell(ss,T);lik = zeros(1,ss*T);for t=1:T  for i=hnodes    n = i + (t-1)*ss;    [bel, lik(n)] = normalise(msg{n}.pi .* msg{n}.lambda);         marginal{i,t} = bel;  endendloglik = 0;%loglik = sum(log(lik));%%%%%%%function lambda = compute_lambda(n, cs, msg, ns)% Pearl p183 eq 4.50lambda = prod_lambda_msgs(n, cs, msg, ns);%%%%%%%function pi_msg = compute_pi_msg(n, cs, msg, c, ns)% Pearl p183 eq 4.53 and 4.51pi_msg = msg{n}.pi .* prod_lambda_msgs(n, cs, msg, ns, c);%%%%%%%%%function lam = prod_lambda_msgs(n, cs, msg, ns, except)if nargin < 5, except = -1; end%lam = msg{n}.lambda_from_self(:);lam = ones(ns(n), 1);for i=1:length(cs)  c = cs(i);  if c ~= except    lam = lam .* msg{n}.lambda_from_child{i};  endend