function CPD = update_ess2(CPD, fmarginal, evidence, ns, cnodes, hidden_bitv)% UPDATE_ESS Update the Expected Sufficient Statistics of a hhmm Q node.% function CPD = update_ess(CPD, fmarginal, evidence, ns, cnodes, idden_bitv)% Figure out the node numbers associated with each parentdom = fmarginal.domain;self = dom(end); % by assumptionold_self = dom(CPD.old_self_ndx);Fself = dom(CPD.Fself_ndx);Fbelow = dom(CPD.Fbelow_ndx);Qps = dom(CPD.Qps_ndx);Qsz = CPD.Qsz;Qpsz = CPD.Qpsz;fmarg = add_ev_to_dmarginal(fmarginal, evidence, ns);% hor_counts(old_self, Qps, self),% fmarginal(old_self, Fbelow, Fself, Qps, self)% hor_counts(i,k,j) = fmarginal(i,2,1,k,j) % below has finished, self has not% ver_counts(i,k,j) = fmarginal(i,2,2,k,j) % below has finished, and so has self (reset)% Since any of i,j,k may be observed, we write% hor_counts(counts_ndx{:}) = fmarginal(fmarg_ndx{:})% where e.g., counts_ndx = {1, ':', 2} if Qps is hidden but we observe old_self=1, self=2.% To create this counts_ndx, we write counts_ndx = mk_multi_ndx(3, obs_dim, obs_val)% where counts_obs_dim = [1 3], counts_obs_val = [1 2] specifies the values of dimensions 1 and 3.counts_obs_dim = [];fmarg_obs_dim = [];obs_val = []; if hidden_bitv(self)  effQsz = Qsz;else  effQsz = 1;  counts_obs_dim = [counts_obs_dim 3];  fmarg_obs_dim = [fmarg_obs_dim 5];  obs_val = [obs_val evidence{self}];end  % e.g., D=4, d=3, Qps = all Qs above, so dom = [Q3(t-1) F4(t-1) F3(t-1) Q1(t) Q2(t) Q3(t)].% so self = Q3(t), old_self = Q3(t-1), CPD.Qps = [1 2], Qps = [Q1(t) Q2(t)]dom = fmarginal.domain;self = dom(end);old_self = dom(1);Qps = dom(length(dom)-length(CPD.Qps):end-1);Qsz = CPD.Qsizes(CPD.d);Qpsz = prod(CPD.Qsizes(CPD.Qps));% If some of the Q nodes are observed (which happens during supervised training)% the counts will only be non-zero in positions% consistent with the evidence. We put the computed marginal responsibilities% into the appropriate slots of the big counts array.% (Recall that observed discrete nodes only have a single effective value.)% (A more general, but much slower, way is to call add_evidence_to_dmarginal.)% We assume the F nodes are never observed.obs_self = ~hidden_bitv(self);obs_Qps = (~isempty(Qps)) & (~any(hidden_bitv(Qps))); % we assume that all or none of the Q parents are observedif obs_self  self_val = evidence{self};  oldself_val = evidence{old_self};endif obs_Qps  Qps_val = subv2ind(Qpsz, cat(1, evidence{Qps}));  if Qps_val == 0    keyboard  endendif CPD.d==1 % no Qps from above  if ~CPD.F1toQ1 % no F from self    % marg(Q1(t-1), F2(t-1), Q1(t))                                % F2(t-1) P(Q1(t)=j | Q1(t-1)=i)    % 1       delta(i,j)    % 2       transprob(i,j)    if obs_self      hor_counts = zeros(Qsz, Qsz);      hor_counts(oldself_val, self_val) = fmarginal.T(2);    else      marg = reshape(fmarginal.T, [Qsz 2 Qsz]);      hor_counts = squeeze(marg(:,2,:));    end  else    % marg(Q1(t-1), F2(t-1), F1(t-1), Q1(t))                                % F2(t-1) F1(t-1)  P(Qd(t)=j| Qd(t-1)=i)    % ------------------------------------------------------    % 1        1         delta(i,j)    % 2        1         transprob(i,j)    % 1        2         impossible    % 2        2         startprob(j)    if obs_self      marg = myreshape(fmarginal.T, [1 2 2 1]);      hor_counts = zeros(Qsz, Qsz);      hor_counts(oldself_val, self_val) = marg(1,2,1,1);      ver_counts = zeros(Qsz, 1);      %ver_counts(self_val) = marg(1,2,2,1);      ver_counts(self_val) = marg(1,2,2,1) + marg(1,1,2,1);    else      marg = reshape(fmarginal.T, [Qsz 2 2 Qsz]);      hor_counts = squeeze(marg(:,2,1,:));      %ver_counts = squeeze(sum(marg(:,2,2,:),1)); % sum over i      ver_counts = squeeze(sum(marg(:,2,2,:),1)) + squeeze(sum(marg(:,1,2,:),1)); % sum i,b    end  end % F1toQ1else % d ~= 1  if CPD.d < CPD.D % general case    % marg(Qd(t-1), Fd+1(t-1), Fd(t-1), Qps(t), Qd(t))                                % Fd+1(t-1) Fd(t-1)  P(Qd(t)=j| Qd(t-1)=i, Qps(t)=k)    % ------------------------------------------------------    % 1        1         delta(i,j)    % 2        1         transprob(i,k,j)    % 1        2         impossible    % 2        2         startprob(k,j)    if obs_Qps & obs_self      marg = myreshape(fmarginal.T, [1 2 2 1 1]);      k = 1;      hor_counts = zeros(Qsz, Qpsz, Qsz);      hor_counts(oldself_val, Qps_val, self_val) = marg(1, 2,1, k,1);      ver_counts = zeros(Qpsz, Qsz);      %ver_counts(Qps_val, self_val) = marg(1, 2,2, k,1);      ver_counts(Qps_val, self_val) = marg(1, 2,2, k,1) + marg(1, 1,2, k,1);    elseif obs_Qps & ~obs_self      marg = myreshape(fmarginal.T, [Qsz 2 2 1 Qsz]);      k = 1;      hor_counts = zeros(Qsz, Qpsz, Qsz);      hor_counts(:, Qps_val, :) = marg(:, 2,1, k,:);      ver_counts = zeros(Qpsz, Qsz);      %ver_counts(Qps_val, :) = sum(marg(:, 2,2, k,:), 1);      ver_counts(Qps_val, :) = sum(marg(:, 2,2, k,:), 1) + sum(marg(:, 1,2, k,:), 1);    elseif ~obs_Qps & obs_self      error('not yet implemented')    else % everything is hidden      marg = reshape(fmarginal.T, [Qsz 2 2 Qpsz Qsz]);      hor_counts = squeeze(marg(:,2,1,:,:)); % i,k,j      %ver_counts = squeeze(sum(marg(:,2,2,:,:),1)); % sum over i      ver_counts = squeeze(sum(marg(:,2,2,:,:),1)) + squeeze(sum(marg(:,1,2,:,:),1)); % sum over i,b    end  else % d == D, so no F from below    % marg(QD(t-1), FD(t-1), Qps(t), QD(t))                                % FD(t-1) P(QD(t)=j | QD(t-1)=i, Qps(t)=k)    % 1      transprob(i,k,j)     % 2      startprob(k,j)    if obs_Qps & obs_self      marg = myreshape(fmarginal.T, [1 2 1 1]);      k = 1;      hor_counts = zeros(Qsz, Qpsz, Qsz);      hor_counts(oldself_val, Qps_val, self_val) = marg(1, 1, k,1);      ver_counts = zeros(Qpsz, Qsz);      ver_counts(Qps_val, self_val) = marg(1, 2, k,1);    elseif obs_Qps & ~obs_self      marg = myreshape(fmarginal.T, [Qsz 2 1 Qsz]);      k = 1;      hor_counts = zeros(Qsz, Qpsz, Qsz);      hor_counts(:, Qps_val, :) = marg(:, 1, k,:);      ver_counts = zeros(Qpsz, Qsz);      ver_counts(Qps_val, :) = sum(marg(:, 2, k, :), 1);    elseif ~obs_Qps & obs_self      error('not yet implemented')    else % everything is hidden      marg = reshape(fmarginal.T, [Qsz 2 Qpsz Qsz]);      hor_counts = squeeze(marg(:,1,:,:));      ver_counts = squeeze(sum(marg(:,2,:,:),1)); % sum over i    end  endendCPD.sub_CPD_trans = update_ess_simple(CPD.sub_CPD_trans, hor_counts);if ~isempty(CPD.sub_CPD_start)  CPD.sub_CPD_start = update_ess_simple(CPD.sub_CPD_start, ver_counts);end