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function smallpot = marginalize_pot(bigpot, keep)
% MARGINALIZE_POT Marginalize a cgpot onto a smaller domain.
% smallpot = marginalize_pot(bigpot, keep)
sumover = mysetdiff(bigpot.domain, keep);
cdom = myunion(bigpot.cheaddom, bigpot.ctaildom);
csumover = myintersect(sumover, bigpot.cheaddom);
dsumover = myintersect(sumover, bigpot.ddom);
dkeep = myintersect(keep, bigpot.ddom);
ckeep = myintersect(keep, bigpot.cheaddom);
cheaddom = myintersect(keep, bigpot.cheaddom);
assert(isempty(myintersect(csumover,bigpot.ctaildom)));
ns = zeros(1, max(bigpot.domain));
ns(bigpot.ddom) = bigpot.dsizes;
ns(bigpot.cheaddom) = bigpot.cheadsizes;
ns(bigpot.ctaildom) = bigpot.ctailsizes;
if sum(ns(csumover)) > 0
for i=1:bigpot.dsize
bigpot.scgpotc{i} = marginalize_pot(bigpot.scgpotc{i}, ckeep, csumover, ns);
end
end
if (isequal(csumover, cheaddom))
bigpot.ctaildom = [];
end
% If we are not marginalizing over any discrete nodes, we are done.
if prod(ns(dsumover))==1
smallpot = scgpot(dkeep, cheaddom, bigpot.ctaildom, ns, bigpot.scgpotc);
return;
end
if (~isempty(bigpot.ctaildom))
assert(0);
return;
end
I = prod(ns(dkeep));
J = prod(ns(dsumover));
C = sum(ns(ckeep));
sum_map = find_equiv_posns(dsumover, bigpot.ddom);
keep_map = find_equiv_posns(dkeep, bigpot.ddom);
iv = zeros(1, length(bigpot.ddom)); % index vector
p1 = zeros(I,J);
A1 = zeros(C,J,I);
C1 = zeros(C,C,J,I);
for i=1:I
keep_iv = ind2subv(ns(dkeep), i);
iv(keep_map) = keep_iv;
for j=1:J
sum_iv = ind2subv(ns(dsumover), j);
iv(sum_map) = sum_iv;
k = subv2ind(ns(bigpot.ddom), iv);
pot = struct(bigpot.scgpotc{k}); % violate object privacy
p1(i,j) = pot.p;
if C > 0 % so mu1 and Sigma1 are non-empty
A1(:,j,i) = pot.A;
C1(:,:,j,i) = pot.C;
end
end
end
% Collapse the mixture of Gaussians
coef = mk_stochastic(p1); % coef must be convex combination
%keyboard
p2 = sum(p1,2);
if (all(p2 == 0))
p2 = p2 + (p2==0)*eps;
end
A = [];
S = [];
pot = cell(1,I);
ctailsize = sum(ns(bigpot.ctaildom));
tB = zeros(C, ctailsize);
for i=1:I
if C > 0
[A, S] = collapse_mog(A1(:,:,i), C1(:,:,:,i), coef(i,:));
end
p = p2(i);
pot{i} = scgcpot(C, ctailsize, p, A, tB, S);
end
smallpot = scgpot(dkeep, ckeep, bigpot.ctaildom, ns, pot);
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