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function dag = cpdag_to_dag(cpdags)
% dags = cpdag_to_dag(cpdags)
%
% CPDAG_TO_DAG produce a N*N matrix of a dag which instantiate cpdag.
% (also works with a cell array of cpdags, returning a cell array of dags)
% make sur that your entry is a completed PDAG
% this function can't be use instead of PDAG_TO_DAG
%
% see Chickering (2002) : Learning equivalence classes of bayesian networks, JMLR2, pp475-479
%
% francois.olivier.c.h@gmail.com, philippe.leray@univ-nantes.fr
% 31 march 2006
if ~iscell(cpdags)
cpdag=cell(1,1);
cpdag{1}=cpdags;
else
cpdag=cpdags;
end
for da=1:length(cpdag)
N=length(cpdag{da});
dag=cpdag{da};
unprocessed = find_nodes_in_undirected_component(dag);
while ~isempty(unprocessed)
nbr_parents = [];
for i=1:length(unprocessed)
nbr_parents(end+1)=length(parents(dag-dag.*dag',unprocessed(i))); %nbr_parents(end+1)=length(parents(dag,unprocessed(i)));
end
[tmp, idx] = max(nbr_parents);
node = unprocessed(idx);
dag(parents(dag.*dag',node),node)=0; %dag(parents(dag,node),node)=0;
%dag(myintersect(parents(dag,node),unprocessed), node)=0; % Wei Lu
unprocessed = find_nodes_in_undirected_component(dag);
end
dags{da}=dag;
end
if ~iscell(cpdags)
dag=dags{1};
else
dag=dags;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function unprocessed = find_nodes_in_undirected_component(dag)
undirected_edges = dag.*dag';
[unprocessed, tmp] = find(undirected_edges);
unprocessed = unique(unprocessed);
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