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function [cpdag] = dag_to_cpdag1(dags)
% 2
% (also works with a cell array of dags, returning a cell array of cpdags)
% DAG_TO_CPDAG produce a N*N matrix which values respect :
%
% If the edge is compelled then 1 on the edge.
% If the edge is reversible then 1 on the edge and 1 in the reverse edge.
%
% Make sure that the entry is a DAG.
%
% See D.M. Chickering: "Learning Equivalence Classes of Bayesian-Network Structures".
%
%
% francois.olivier.c.h@gmail.com, philippe.leray@univ-nantes.fr
if ~iscell(dags)
dag=cell(1,1);
dag{1}=dags;
else
dag=dags;
end
for da=1:length(dag)
cpdags{da} = abs(label_edges(dag{da}));
end
if ~iscell(dags)
cpdag=cpdags{1};
else
cpdag=cpdags;
end
%%==============================================================================
function [label] = label_edges(dag)
% LABEL-EDGES produce a N*N matrix which values are
% +1 if the edge is compelled or
% -1 if the edge is reversible.
% Make sure that the entry is a DAG.
%
% francois.olivier.c.h@gmail.com
N=length(dag);
[order xedge yedge] = order_edges(dag);
label = 2*dag; % all edges as unknown
NbEdges = length(xedge) ;
%xedge=x, yedge=y, %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for Edge=1:NbEdges,
xlow=xedge(Edge);
ylow=yedge(Edge);
if label(xlow,ylow)==2
fin = 0;
%wcompelled = find(label(:,xlow)~=2);
wcompelled = find(label(:,xlow)==1);
parenty = find(label(:,ylow)~=0);
%sonsy = find(label(ylow,:)~=0);
for s = 1:length(wcompelled)
w = wcompelled(s);
if ~ismember(w,parenty)
label(xlow,ylow)=1;
label(ylow,xlow)=0; %
label(parenty,ylow)=1;
label(ylow,parenty)=0; %
%label(ylow,sonsy)=1; %
%label(sonsy,ylow)=0; %
fin = 1;
elseif fin == 0
label(w,ylow)=1;
%label(ylow,w)=0; %
end
end
if fin == 0
parentx = [xlow ; find(label(:,xlow)~=0)];
if ~isempty(mysetdiff(parenty,parentx))
%label(xlow,ylow)=1; %
%label(ylow,xlow)=0; %
label(find(label(:,ylow)==2),ylow)=1;
label(ylow,find(label(ylow,:)==2))=1; %
else
label(xlow,ylow)=-1;
label(ylow,xlow)=-1; %
ttp = find(label(:,ylow)==2);
label(ttp,ylow)=-1;
label(ylow,ttp)=-1; %
end
end
end
end
%%%========================================================================================
function [order, x, y] = order_edges(dag)
% ORDER_EDGES produce a total (natural) ordering over the edges in a DAG.
% Make sure that the entry is a DAG.
%
% francois.olivier.c.h@gmail.com
%
% 2 mai 2003
if acyclic(dag)==0
error('Requires an acyclic graph');
end
N=length(dag);
order = zeros(N,N);
node_order = topological_sort(dag);
[tmp oo] = sort(node_order);
dag2=dag(node_order,node_order);
[x y]=find(flipud(dag2)==1);
nb_edges=length(x);
if nb_edges~=0
order(sub2ind([N N],N+1-x,y))=1:nb_edges ;
end
order=order(oo,oo);
x=node_order(N+1-x);
y=node_order(y);
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