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function [PDAGs, nodes] = mk_nbrs_of_pdag_add(cpdag,engine)
% MK_NBRS_OF_PDAG_ADD Make the superior inclusion boundary of CPDAG.
% [PDAGs, nodes] = mk_nbrs_of_pdag_add(CPDAG)
%
% PDAGs{i} is the i'th neighbor of CPDAG0 generated by INSERT(X,Y,T) with
% nodes{i,1:2}=[X Y]
% nodes{i,3}=T
%
% See D.M. Chickering 2002 : "Optimal Structure Identification with Greedy Search".
%
% philippe.leray@univ-nantes.fr, francois.olivier.c.h@gmail.com
% 24 july 2003
compteur=0 ;
N=length(cpdag);
G=pdag_to_dag(cpdag);
if nargin==1,
bnet_tmp=mk_bnet(pdag_to_dag(cpdag),2*ones(N,1));
bnet_tmp=mk_bnet(G,2*ones(N,1));
engine_tmp=struct(jtree_inf_engine(bnet_tmp));
clear bnet_tmp
else
engine_tmp=struct(engine);
end
cliques=engine_tmp.cliques;
nbcliques=length(cliques);
clear engine_tmp;
% find in the PDAG all the X Y not connected
[LX LY]=find((cpdag|cpdag')+eye(N)==0);
nlinks=length(LX); % here is a bug when nlinks is zeros, for i=1:nlinks fail 31-37 added by hanbin
if nlinks==0
[i,j]=find(cpdag);k=unidrnd(size(i,1),1);
cpdag(i(k),j(k))=0;
[LX LY]=find((cpdag|cpdag')+eye(N)==0);
nlinks=length(LX);
end
for i=1:nlinks
X=LX(i);
Y=LY(i);
% Neighbors of Y
NY = myintersect(find(cpdag(:,Y)), find(cpdag(Y,:)));
% Adjacents of X
AX = myunion(find(cpdag(:,X)), find(cpdag(X,:)));
% Neighbors of Y adjacent to X
NAYX = myintersect(NY,AX);
% Neighbors of Y NOT adjacent to X
NNAYX = mysetdiff(NY, NAYX);
% this function recursively "walks" (dfs) in the graph representation of NNA powerset
liste=NNAYX;
if ~isempty(liste)
premier=liste(1);
dernier=liste(end);
end;
current_set=[];
fini=0;
evite2 = 0 ;
while ~fini
isclique=0;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Test 1
% is [NAYX current_set] a clique ?
if isempty(current_set)
NAYXT=NAYX;
elseif isempty(NAYX)
NAYXT=current_set;
else
NAYXT = union(NAYX,current_set);
end
% if isempty(NAYXT),isclique=1;end
isclique = isempty(NAYXT) | ismemberclique(NAYXT,cliques) ;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% End Test 1
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Test 2
% is there exist a partially directed path Y...X in PDAG \ NAYXT ?
if isclique
if evite2
test2=1 ;
else
%%%% calcul test 2
L2 = setdiff(1:N,NAYXT);
test2=~partialconnected(cpdag(L2,L2),find(L2==Y),find(L2==X));
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% End Test 2
if test2
evitet2=1;
% avoid testing INSERT(X,Y,[]) and INSERT(Y,X,[]) if pa(Y)=pa(X)
test0=1 ;
if (X>Y)
if length(current_set)==0
PaX=setdiff(find(cpdag(X,:)),find(cpdag(:,X)));
PaY=setdiff(find(cpdag(Y,:)),find(cpdag(:,Y)));
test0=(length(setdiff(PaX,PaY))~=0);
end
end
if test0
%fprintf(' INSERT(%d,%d,',X,Y); fprintf('%d',current_set);
%fprintf(')\n');
compteur=compteur+1;
nodes{compteur,1}=X;
nodes{compteur,2}=Y;
nodes{compteur,3}=current_set;
ptmp=cpdag;
ptmp(X,Y)=1;
ptmp(current_set,Y)=1;
ptmp(Y,current_set)=0;
PDAGs{compteur}=ptmp;
end
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Next Set to test ...
% what is the net set in the powerset ?
if length(liste)==0
fini=1 ; next_set=[];
elseif length(current_set)==0
next_set=[premier]; % first node after the root []
else
actuel=current_set(end);
if actuel==dernier
if length(current_set)==1
fini=1; % no more node ...
else
ancien=current_set(end-1); % new "branch"
next_set=[current_set(1:end-2) liste(find(liste==ancien)+1)];
end
else % new node in the "branch"
if ~isclique
if length(current_set)==1
fini=1; % no more node ...
else
ancien=current_set(end-1); % new "branch"
next_set=[current_set(1:end-2) liste(find(liste==ancien)+1)];
evite2=0;
end
else
next_set=[current_set liste(find(liste==actuel)+1)];
end
end
end
current_set=next_set;
end
end
%%%%%%%%%
function resu = ismemberclique(v,cliques)
finiclique = 0 ; resu=0 ;
cl=1; ncl=length(cliques) ;
while (~finiclique) & (cl<=ncl);
if ismember(v,cliques{cl})
resu=1;
finiclique=1 ;
end
cl=cl+1;
end
%%%%%%%%%
function resu = partialconnected(G,Y,X)
tmp=expm(G);
resu = (tmp(Y,X)~=0);
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