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function [transprob, termprob] = remove_hhmm_end_state(A)
% REMOVE_END_STATE Infer transition and termination probabilities from automaton with an end state
% [transprob, termprob] = remove_end_state(A)
%
% A(i,k,j) = Pr( i->j | Qps=k), where i in 1:Q, j in 1:(Q+1), and Q+1 is the end state
% This implements the equation in footnote 3 of my NIPS 01 paper,
% transprob(i,k,j) = \tilde{A}_k(i,j)
% termprob(k,j) = \tau_k(j)
%
% For the top level, the k index is missing.
Q = size(A,1);
toplevel = (ndims(A)==2);
if toplevel
Qk = 1;
A = reshape(A, [Q 1 Q+1]);
else
Qk = size(A, 2);
end
transprob = A(:, :, 1:Q);
term = A(:,:,Q+1)'; % term(k,j) = P(Qj -> end | k)
termprob = term;
%termprob = zeros(Qk, Q, 2);
%termprob(:,:,2) = term;
%termprob(:,:,1) = 1-term;
for k=1:Qk
for i=1:Q
for j=1:Q
denom = (1-termprob(k,i));
denom = denom + (denom==0)*eps;
transprob(i,k,j) = transprob(i,k,j) / denom;
end
end
end
if toplevel
termprob = squeeze(termprob);
transprob = squeeze(transprob);
end
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