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'); end

for 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
    
  end
end


marginal = 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;
  end
end

loglik = 0;
%loglik = sum(log(lik));



%%%%%%%

function lambda = compute_lambda(n, cs, msg, ns)
% Pearl p183 eq 4.50
lambda = prod_lambda_msgs(n, cs, msg, ns);

%%%%%%%

function pi_msg = compute_pi_msg(n, cs, msg, c, ns)
% Pearl p183 eq 4.53 and 4.51
pi_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};
  end
end