Daniel@0: function smallpot = marginalize_pot(bigpot, keep)
Daniel@0: % MARGINALIZE_POT Marginalize a cgpot onto a smaller domain.
Daniel@0: % smallpot = marginalize_pot(bigpot, keep)
Daniel@0: 
Daniel@0: sumover = mysetdiff(bigpot.domain, keep);
Daniel@0: csumover = myintersect(sumover, bigpot.cdom);
Daniel@0: dsumover = myintersect(sumover, bigpot.ddom);
Daniel@0: dkeep = myintersect(keep, bigpot.ddom);
Daniel@0: ckeep = myintersect(keep, bigpot.cdom);
Daniel@0: %ns = sparse(1, max(bigpot.domain)); % must be full, so I is an integer
Daniel@0: ns = zeros(1, max(bigpot.domain));
Daniel@0: ns(bigpot.ddom) = bigpot.dsizes;
Daniel@0: ns(bigpot.cdom) = bigpot.csizes;
Daniel@0: 
Daniel@0: % sum(ns(csumover))==0 is like isempty(csumover) but handles observed nodes.
Daniel@0: % Similarly, prod(ns(dsumover))==1 is like isempty(dsumover)
Daniel@0: 
Daniel@0: % Marginalize the cts parts.
Daniel@0: % If we are in canonical form, we stay that way, since moment form might not exist.
Daniel@0: % Besides, we would like to minimize the number of conversions.
Daniel@0: if sum(ns(csumover)) > 0
Daniel@0:   if bigpot.subtype == 'm'
Daniel@0:     for i=1:bigpot.dsize
Daniel@0:       bigpot.mom{i} = marginalize_pot(bigpot.mom{i}, ckeep);
Daniel@0:     end
Daniel@0:   else
Daniel@0:     for i=1:bigpot.dsize
Daniel@0:       bigpot.can{i} = marginalize_pot(bigpot.can{i}, ckeep);
Daniel@0:     end
Daniel@0:   end
Daniel@0: end
Daniel@0: 
Daniel@0: % If we are not marginalizing over any discrete nodes, we are done.
Daniel@0: if prod(ns(dsumover))==1
Daniel@0:   smallpot = cgpot(dkeep, ckeep, ns, bigpot.can, bigpot.mom, bigpot.subtype);
Daniel@0:   return;
Daniel@0: end
Daniel@0: 
Daniel@0: % To marginalize the discrete parts, we must be in moment form.
Daniel@0: bigpot = cg_can_to_mom(bigpot);
Daniel@0: 
Daniel@0: I = prod(ns(dkeep));
Daniel@0: J = prod(ns(dsumover));
Daniel@0: C = sum(ns(ckeep));
Daniel@0: 
Daniel@0: % Reshape bigpot into the form mu1(:,j,i), where i is in dkeep, j is in dsumover
Daniel@0: T1 = zeros(I,J);
Daniel@0: mu1 = zeros(C,J,I);
Daniel@0: Sigma1 = zeros(C,C,J,I);
Daniel@0: sum_map = find_equiv_posns(dsumover, bigpot.ddom);
Daniel@0: keep_map = find_equiv_posns(dkeep, bigpot.ddom);
Daniel@0: iv = zeros(1, length(bigpot.ddom)); % index vector
Daniel@0: for i=1:I
Daniel@0:   keep_iv = ind2subv(ns(dkeep), i);
Daniel@0:   iv(keep_map) = keep_iv;
Daniel@0:   for j=1:J
Daniel@0:     sum_iv = ind2subv(ns(dsumover), j);
Daniel@0:     iv(sum_map) = sum_iv;
Daniel@0:     k = subv2ind(ns(bigpot.ddom), iv);
Daniel@0:     mom = struct(bigpot.mom{k}); % violate object privacy
Daniel@0:     T1(i,j) = exp(mom.logp);
Daniel@0:     if C > 0 % so mu1 and Sigma1 are non-empty
Daniel@0:       mu1(:,j,i) = mom.mu;
Daniel@0:       Sigma1(:,:,j,i) = mom.Sigma;
Daniel@0:     end
Daniel@0:   end
Daniel@0: end
Daniel@0: 
Daniel@0: % Collapse the mixture of Gaussians
Daniel@0: coef = mk_stochastic(T1); % coef must be convex combination
Daniel@0: T2 = sum(T1,2);
Daniel@0: T2 = T2 + (T2==0)*eps;
Daniel@0: %if C > 0, disp('collapsing onto '); disp(leep); end
Daniel@0: mu = [];
Daniel@0: Sigma = [];
Daniel@0: mom = cell(1,I);
Daniel@0: for i=1:I
Daniel@0:   if C > 0
Daniel@0:     [mu, Sigma] = collapse_mog(mu1(:,:,i), Sigma1(:,:,:,i), coef(i,:));
Daniel@0:   end
Daniel@0:   logp = log(T2(i));
Daniel@0:   mom{i} = mpot(ckeep, ns(ckeep), logp, mu, Sigma);
Daniel@0: end
Daniel@0: 
Daniel@0: smallpot = cgpot(dkeep, ckeep, ns, [], mom, 'm');
Daniel@0: