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function [intra, inter, Qnodes, Fnodes, Onode] = mk_hhmm_topo_F1(D, all_Q_to_Qs, Ops)
% MK_HHMM_TOPO Make Hierarchical HMM topology assuming level 1 can finish
% function [intra, inter, Qnodes, Fnodes, Onode] = mk_hhmm_topo(D, all_Q_to_Qs, Ops, F1)
%
% D is the depth of the hierarchy
% If all_Q_to_Qs = 1, level i connects to all levels below, else just to i+1 [0]
% Ops are the Q parents of the observed node [Qnodes(end)]
% If F1=1, level 1 can finish (restart), else there is no F1->Q1 arc [0]
Qnodes = 1:D;
if nargin < 2, all_Q_to_Qs = 1; end
if nargin < 3, Ops = Qnodes(D); end
if nargin < 4, F1 = 0; end
if F1
Fnodes = 2*D:-1:D+1; % must number from bottom to top
Onode = 2*D+1;
ss = 2*D+1;
else
Fnodes = (2*D)-1:-1:D+1;
Onode = 2*D;
ss = 2*D;
end
intra = zeros(ss);
intra(Ops, Onode) = 1;
for d=1:D-1
if all_Q_to_Qs
intra(Qnodes(d), Qnodes(d+1:end)) = 1;
else
intra(Qnodes(d), Qnodes(d+1)) = 1;
end
end
for d=D:-1:3
intra(Fnodes(d), Fnodes(d-1)) = 1;
end
if F1
intra(Fnodes(2), Fnodes(1)) = 1;
end
if all_Q_to_Qs
for d=1:D
intra(Qnodes(d), Fnodes(d:end)) = 1;
end
else
for d=1:D
if d < D
intra(Qnodes(d), Fnodes([d d+1])) = 1;
else
intra(Qnodes(d), Fnodes(d)) = 1;
end
end
end
inter = zeros(ss);
for d=1:D
inter(Qnodes(d), Qnodes(d)) = 1;
end
for d=1:D
if d==1
inter(Fnodes(d), Qnodes(d)) = 1;
else
inter(Fnodes(d), Qnodes([d-1 d])) = 1;
end
end
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