function [marginal, msg, loglik] = smooth_evidence(engine, evidence)[ss T] = size(evidence);bnet = bnet_from_engine(engine);onodes = engine.onodes;hnodes = mysetdiff(1:ss, onodes);hnodes = hnodes(:)';ns = bnet.node_sizes(:);onodes2 = [onodes(:); onodes(:)+ss];ns(onodes2) = 1;	   verbose = 0;pot_type = 'd';niter = engine.max_iter;if verbose, fprintf('new smooth\n'); end% msg(i1,t1,i2,j2) (i1,t1) -> (i2,t2)%lambda_msg = cell(ss,T,ss,T);%pi_msg = cell(ss,T,ss,T);% intra_lambda_msg(i,j,t) (i,t) -> (j,t), i is child% inter_lambda_msg(i,j,t) (i,t+1) -> (j,t), i is child% inter_pi_msg(i,j,t) (i,t-1) -> (j,t), i is parentintra_lambda_msg = cell(ss,ss,T);inter_lambda_msg = cell(ss,ss,T);inter_pi_msg = cell(ss,ss,T);lambda = cell(ss,T);pi = cell(ss,T);for t=1:T  for i=1:ss    lambda{i,t} = ones(ns(i), 1);    pi{i,t} = ones(ns(i), 1);        cs = children(bnet.intra, i);    for c=cs(:)'      intra_lambda_msg{c,i,t} = ones(ns(i),1);    end        cs = children(bnet.inter, i);    for c=cs(:)'      inter_lambda_msg{c,i,t} = ones(ns(i),1);    end        ps = parents(bnet.inter, i);    for p=ps(:)'      inter_pi_msg{p,i,t} = ones(ns(i), 1); % not used for t==1    end  endend% each hidden node absorbs lambda from its observed child (if any)for t=1:T  for i=hnodes    c = engine.obschild(i);    if c > 0      if t==1	fam = family(bnet.dag, c);	e = bnet.equiv_class(c, 1);	CPDpot = CPD_to_pot(pot_type, bnet.CPD{e}, fam, bnet.node_sizes(:), bnet.cnodes(:), evidence(:,1));      else	fam = family(bnet.dag, c, 2); % within 2 slice network	e = bnet.equiv_class(c, 2);	CPDpot = CPD_to_pot(pot_type, bnet.CPD{e}, fam, bnet.node_sizes(:), bnet.cnodes(:), evidence(:,t-1:t));      end      temp = pot_to_marginal(CPDpot);      lam_msg = normalise(temp.T);      intra_lambda_msg{c,i,t} = lam_msg;    end  endendfor iter=1:engine.max_iter  % FORWARD  for t=1:T    % update pi    for i=hnodes      if t==1	e = bnet.equiv_class(i,1);	CPD = struct(bnet.CPD{e});	pi{i,t} = CPD.CPT;      else	e = bnet.equiv_class(i,2);	CPD = struct(bnet.CPD{e});	ps = parents(bnet.inter, i);	dom = [ps i+ss];	pot = dpot(dom, ns(dom), CPD.CPT);	for p=ps(:)'	  temp = dpot(p, ns(p), inter_pi_msg{p,i,t});	  pot = multiply_by_pot(pot, temp);	end	pot = marginalize_pot(pot, i+ss);	temp = pot_to_marginal(pot);	pi{i,t} = temp.T;      end      if verbose, fprintf('%d updates pi\n', i+(t-1)*ss); disp(pi{i,t}); end    end        % send pi msg to children     for i=hnodes      cs = children(bnet.inter, i);      for c=cs(:)'	pot = pi{i,t};	for k=cs(:)'	  if k ~= c	    pot = pot .* inter_lambda_msg{k,i,t};	  end	end	cs2 = children(bnet.intra, i);	for k=cs2(:)'	  pot = pot .* intra_lambda_msg{k,i,t};	end	inter_pi_msg{i,c,t+1} = normalise(pot);	if verbose, fprintf('%d sends pi to %d\n', i+(t-1)*ss, c+t*ss); disp(inter_pi_msg{i,c,t+1}); end      end    end  end  if verbose, fprintf('backwards\n'); end  % BACKWARD  for t=T:-1:1    % update lambda    for i=hnodes      pot = ones(ns(i), 1);      cs = children(bnet.inter, i);      for c=cs(:)'	pot = pot .* inter_lambda_msg{c,i,t};      end      cs = children(bnet.intra, i);      for c=cs(:)'	pot = pot .* intra_lambda_msg{c,i,t};      end      lambda{i,t} = normalise(pot);      if verbose, fprintf('%d computes lambda\n', i+(t-1)*ss); disp(lambda{i,t}); end    end        % send lambda msgs to hidden parents in prev slcie    for i=hnodes      ps = parents(bnet.inter, i);      if t > 1	e = bnet.equiv_class(i, 2);	CPD = struct(bnet.CPD{e});	fam = [ps i+ss];	for p=ps(:)'	  pot = dpot(fam, ns(fam), CPD.CPT);	  temp = dpot(i+ss, ns(i), lambda{i,t});	  pot = multiply_by_pot(pot, temp);	  for k=ps(:)'	    if k ~= p	      temp = dpot(k, ns(k), inter_pi_msg{k,i,t});	      pot = multiply_by_pot(pot, temp);	    end	  end	  pot = marginalize_pot(pot, p);	  temp = pot_to_marginal(pot);	  inter_lambda_msg{i,p,t-1} = normalise(temp.T);	  if verbose, fprintf('%d sends lambda to %d\n', i+(t-1)*ss, p+(t-2)*ss); disp(inter_lambda_msg{i,p,t-1}); end	end      end    end  endendmarginal = cell(ss,T);for t=1:T  for i=hnodes    marginal{i,t} = normalise(pi{i,t} .* lambda{i,t});       endendloglik = 0;msg.inter_pi_msg = inter_pi_msg;msg.inter_lambda_msg = inter_lambda_msg;msg.intra_lambda_msg = intra_lambda_msg;