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function smallpot = marginalize_pot(bigpot, keep, maximize, useC)
% MARGINALIZE_POT Marginalize a cpot onto a smaller domain.
% smallpot = marginalize_pot(bigpot, keep, maximize, useC)
%
% The maximize argument is ignored - maxing out a Gaussian is the same as summing it out,
% since the mode and mean are equal.
% The useC argument is ignored.
node_sizes = sparse(1, max(bigpot.domain));
node_sizes(bigpot.domain) = bigpot.sizes;
sum_over = mysetdiff(bigpot.domain, keep);
if sum(node_sizes(sum_over))==0 % isempty(sum_over)
%smallpot = bigpot;
smallpot = cpot(keep, node_sizes(keep), bigpot.g, bigpot.h, bigpot.K);
else
[h1, h2, K11, K12, K21, K22] = partition_matrix_vec(bigpot.h, bigpot.K, sum_over, keep, node_sizes);
n = length(h1);
K11inv = inv(K11);
g = bigpot.g + 0.5*(n*log(2*pi) - log(det(K11)) + h1'*K11inv*h1);
if length(h2) > 0 % ~isempty(keep) % we are are actually keeping something
A = K21*K11inv;
h = h2 - A*h1;
K = K22 - A*K12;
else
h = [];
K = [];
end
smallpot = cpot(keep, node_sizes(keep), g, h, K);
end
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