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function [PDAGs, nodes] = mk_nbrs_of_pdag_del(cpdag,engine)
% MK_NBRS_OF_PDAG_ADD Make the inferior inclusion boundary of CPDAG.
% [PDAGs, nodes] = mk_nbrs_of_pdag_del(CPDAG)
%
% PDAGs{i} is the i'th neighbor of CPDAG0 generated by DELETE(X,Y,H) with
% nodes{i,1:2}=[X Y]
% nodes{i,3}=H
%
% See D.M. Chickering 2002 : "Optimal Structure Identification with Greedy Search".
%
% philippe.leray@univ-nantes.fr
% 25 july 2003
compteur=0;
N=length(cpdag);
if nargin==1,
bnet_tmp=mk_bnet(pdag_to_dag(cpdag),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;
verbose=0;
if verbose
fprintf('---- Les cliques (maximales) du DAG\n');
for i=1:nbcliques,
disp(cliques{i});
end
fprintf('---- Variables \n');
end
% find in the PDAG all the X Y connected
[LX LY]=find(cpdag==1);
nlinks=length(LX);
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);
% this function recursively "walks" (dfs) in the graph representation of NA powerset
if verbose
X, Y, NY, AX, NAYX
fprintf('---- NA Powerset\n\n');
end
liste=NAYX;
if ~isempty(liste)
premier=liste(1);
dernier=liste(end);
end
current_set=[];
fini=0;
evite2 = 0 ;
while ~fini
if verbose
% sert uniquement � l'affichage pour le prog de test ...
if isempty(current_set)
fprintf('\t H = []\n\n');
else
fprintf('\t H = '); disp(current_set);
end
end
isclique=0;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Test 1
% is [NAYX \ current_set] a clique ?
if isempty(current_set)
NAYXH=NAYX;
elseif isempty(NAYX)
NAYXH=current_set;
else
NAYXH = mysetdiff(NAYX,current_set);
end
if isempty(NAYXH)
if verbose
fprintf('\t\t NA(Y,X) \\ T = \t[]\n\n');
end
elseif verbose
fprintf('\t\t NA(Y,X) \\ T ='); disp(NAYXH);
end
isclique = isempty(NAYXH) | ismemberclique(NAYXH,cliques) ;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% End Test 1
if isclique
% avoid testing INSERT(X,Y,H) and INSERT(Y,X,H) if X--Y
test0=1 ;
if (X>Y)
test0=~cpdag(Y,X);
if verbose&~test0
fprintf(' (inutile de tester %d %d ',X,Y); fprintf('%d',current_set);
fprintf(')\n');
end
end
if test0
if verbose
fprintf(' ==DELETE(%d,%d,',X,Y); fprintf('%d',current_set);
fprintf(')\n');
end
compteur=compteur+1;
nodes{compteur,1}=X;
nodes{compteur,2}=Y;
nodes{compteur,3}=current_set;
ptmp=cpdag;
ptmp(X,Y)=0;
ptmp(Y,X)=0;
ptmp(current_set,Y)=0;
ptmp(Y,current_set)=1;
ptmp(current_set(find(cpdag(X,current_set)==1)),X)=0;
PDAGs{compteur}=ptmp;
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
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