function undag = moralize( dag, flag, gnames )
% function undag = moralize( dag, flag, gnames )
% ARGS: dag = adjacency matrix
%       flag = whether to print comments or not
%       gnames = names of nodes for printing
% RET:  undag = undirected acyclic graph that has been moralized
% 
% dag =
%         1->2
%      0     1     1     0     0     0     0     0
% 2->1 0     0     0     1     0     0     0     0
%      0     0     0     0     1     0     1     0
%      0     0     0     0     0     1     0     0
%      0     0     0     0     0     1     0     1
%      0     0     0     0     0     0     0     0
%      0     0     0     0     0     0     0     1
% undag =
%      A->B  C  D  E  F  G  H
%    A 0  1  1  0  0  0  0  0
% B->A 1  0  0  1  0  0  0  0
%    C 1  0  0  0  1  0  1  0
%    D 0  1  0  0  1  1  0  0
%    E 0  0  1  1  0  1  1  1
%    F 0  0  0  1  1  0  0  0
%    G 0  0  1  0  1  0  0  1
%    H 0  0  0  0  1  0  1  0
if nargin < 2, flag = 0; end;
N = length(dag);
for i=1:N,
  parents = find(dag(:,i));
  % drop directionality
  len = length(parents);
  for p=1:len
    thisp = parents(p);
    dag(i,thisp) = 1;
  end;
  % marry the parents
  for p=1:len
    thisp = parents(p);
    otherp = parents(~ismember(parents,thisp));
    if ~isempty(otherp)
      dag(thisp,otherp) = 1;
      if flag == 1,
        input(sprintf('married node %d(%s) with...',thisp,char(gnames(thisp))));
        for o=1:length(otherp),
        disp(sprintf('   ... %d(%s)',otherp(o),char(gnames(otherp(o)))));
        end; % end_for
      end; % end_flag
    end;
  end; 
end;
undag = dag;