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function CPT = CPD_to_CPT(CPD)
% CPD_TO_CPT Convert the discrete CPD to tabular form (noisyor)
% CPT = CPD_to_CPT(CPD)
%
% CPT(U1,...,Un, X) = Pr(X|U1,...,Un) where the Us are the parents (excluding leak).
if ~isempty(CPD.CPT)
CPT = CPD.CPT; % remember to flush cache if params change (e.g., during learning)
return;
end
q = [CPD.leak_inhibit CPD.inhibit(:)'];
% q(i) is the prob. that the i'th parent will be inhibited (flipped from 1 to 0).
% q(1) is the leak inhibition probability, and length(q) = n + 1.
if length(q)==1
CPT = [q 1-q];
return;
end
n = length(q);
Bn = ind2subv(2*ones(1,n), 1:(2^n))-1; % all n bit vectors, with the left most column toggling fastest (LSB)
CPT = zeros(2^n, 2);
% Pr(X=0 | U_1 .. U_n) = prod_{i: U_i = on} q_i = prod_i q_i ^ U_i = exp(u' * log(q_i))
% This method is problematic when q contains zeros
Q = repmat(q(:)', 2^n, 1);
Q(logical(~Bn)) = 1;
CPT(:,1) = prod(Q,2);
CPT(:,2) = 1-CPT(:,1);
CPT = reshape(CPT(2:2:end), 2*ones(1,n)); % skip cases in which the leak is off
CPD.CPT = CPT;
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