% Make an HMM with discrete observations%   X1 -> X2%   |     | %   v     v%   Y1    Y2 intra = zeros(2);intra(1,2) = 1;inter = zeros(2);inter(1,1) = 1;n = 2;Q = 2; % num hidden statesO = 2; % num observable symbolsns = [Q O];dnodes = 1:2;onodes = [2];eclass1 = [1 2];eclass2 = [3 2];bnet = mk_dbn(intra, inter, ns, 'discrete', dnodes, 'eclass1', eclass1, 'eclass2', eclass2, ...	      'observed', onodes);rand('state', 0);prior1 = normalise(rand(Q,1));transmat1 = mk_stochastic(rand(Q,Q));obsmat1 = mk_stochastic(rand(Q,O));bnet.CPD{1} = tabular_CPD(bnet, 1, prior1);bnet.CPD{2} = tabular_CPD(bnet, 2, obsmat1);bnet.CPD{3} = tabular_CPD(bnet, 3, transmat1);T = 5; % fixed length sequencesengine = {};engine{end+1} = jtree_unrolled_dbn_inf_engine(bnet, T);engine{end+1} = hmm_inf_engine(bnet);engine{end+1} = smoother_engine(hmm_2TBN_inf_engine(bnet));engine{end+1} = smoother_engine(jtree_2TBN_inf_engine(bnet));if 1%engine{end+1} = frontier_inf_engine(bnet); % brokenengine{end+1} = bk_inf_engine(bnet, 'clusters', {[1]});engine{end+1} = jtree_dbn_inf_engine(bnet);endinf_time = cmp_inference_dbn(bnet, engine, T);ncases = 2;max_iter = 2;[learning_time, CPD, LL, cases] = cmp_learning_dbn(bnet, engine, T, 'ncases', ncases, 'max_iter', max_iter);% Compare to HMM toolboxdata = zeros(ncases, T);for i=1:ncases  %data(i,:) = cat(2, cases{i}{onodes,:});  data(i,:) = cell2num(cases{i}(onodes,:));end[LL2, prior2, transmat2, obsmat2] = dhmm_em(data, prior1, transmat1, obsmat1, 'max_iter', max_iter);e = 1;assert(approxeq(prior2, CPD{e,1}.CPT))assert(approxeq(obsmat2, CPD{e,2}.CPT))assert(approxeq(transmat2, CPD{e,3}.CPT))assert(approxeq(LL2, LL{e}))