essentialGraph.cpp

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 *       - Pierre-Henri WUILLEMIN(_at_LIP6)                                 *
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#include <agrum/BN/algorithms/essentialGraph.h>
 
#ifdef GUM_NO_INLINE
#  include <agrum/BN/algorithms/essentialGraph_inl.h>
#endif   // GU%_NO_INLINE
 
namespace gum {
  EssentialGraph::EssentialGraph(const DAGmodel& m) : _dagmodel_(&m) { _buildEssentialGraph_(); }
 
  EssentialGraph::EssentialGraph(const DAGmodel& m, const PDAG& mg) : _dagmodel_(&m), _pdag_(mg) {}
 
  EssentialGraph::EssentialGraph(const EssentialGraph& g) {
    _dagmodel_ = g._dagmodel_;
    _buildEssentialGraph_();
  }
 
  EssentialGraph& EssentialGraph::operator=(const EssentialGraph& g) {
    if (&g != this) {
      _dagmodel_ = g._dagmodel_;
      _buildEssentialGraph_();
    }
    return *this;
  }
 
  EssentialGraph::~EssentialGraph() = default;
 
  void EssentialGraph::_buildEssentialGraph_() {
    MixedGraph mg;   // during the process, the graph may not be a PDAG
    _pdag_.clear();
    if (_dagmodel_ == nullptr) return;
 
    for (const auto& node: _dagmodel_->nodes()) {
      mg.addNodeWithId(node);
      _pdag_.addNodeWithId(node);
    }
    for (const auto& arc: _dagmodel_->arcs()) {
      mg.addArc(arc.tail(), arc.head());
    }
 
    std::vector< Arc > v;
    do {
      v.clear();
      for (const auto x: _dagmodel_->topologicalOrder())
        for (const auto y: mg.children(x))
          if (!_strongly_protected_(mg, x, y)) v.emplace_back(x, y);
 
      for (const auto& arc: v) {
        mg.eraseArc(arc);
        mg.addEdge(arc.tail(), arc.head());
      }
    } while (!v.empty());
 
    for (const auto& arc: mg.arcs()) {
      _pdag_.addArc(arc.tail(), arc.head());
    }
    for (const auto& edge: mg.edges()) {
      _pdag_.addEdge(edge.first(), edge.second());
    }
 
    for (auto id: _pdag_)
      _pdag_.setName(id, _dagmodel_->variable(id).name());
  }
 
  bool EssentialGraph::_strongly_protected_(NodeId a, NodeId b) const {
    return _strongly_protected_(_pdag_, a, b);
  }
 
  bool EssentialGraph::_strongly_protected_(MixedGraph mg, NodeId a, NodeId b) {
    // testing a->b from
    // A Characterization of Markov Equivalence Classes for Acyclic Digraphs (2001)
    //  Steen A. Andersson, David Madigan, and Michael D. Perlman*
 
    // condition (a)
    for (const auto& c: mg.parents(a)) {
      if (!mg.existsArc(c, b)) { return true; }
    }
 
 
    for (const auto& c: mg.parents(b)) {
      if (c == a) { continue; }
      // condition (c)
      if (mg.existsArc(a, c)) { return true; }
 
      // condition (b) knowing that a can not be a parent of c (condition below)
      if (!mg.existsEdge(a, c) && !mg.existsArc(c, a)) { return true; }
    }
 
    // condition (d)
    bool oneFound = false;
    for (const auto& c: mg.parents(b)) {
      if (c == a) { continue; }
      // condition (d)
      if (mg.existsEdge(c, a)) {
        if (oneFound) {   // this is the second found
          return true;
        }
        oneFound = true;
      }
    }
 
    return false;
  }
 
  std::string EssentialGraph::toDot() const {
    std::stringstream output;
    std::stringstream nodeStream;
    std::stringstream edgeStream;
    List< NodeId >    treatedNodes;
    output << "digraph \"no_name\" {\n";
    nodeStream << "node [shape = ellipse];\n";
    std::string tab = "  ";
    if (_dagmodel_ != nullptr) {
      for (const auto node: _pdag_.nodes()) {
        nodeStream << std::format("{}{}[label=\"{}\"];",
                                  tab,
                                  node,
                                  _dagmodel_->variable(node).name());
 
        for (const auto nei: _pdag_.neighbours(node))
          if (!treatedNodes.exists(nei))
            edgeStream << std::format("{}{} -> {} [dir=none];\n", tab, node, nei);
 
        for (const auto chi: _pdag_.children(node))
          edgeStream << std::format("{}{} -> {} [color=red];\n", tab, node, chi);
 
        treatedNodes.insert(node);
      }
    }
    output << nodeStream.str() << '\n' << edgeStream.str() << '\n' << "}\n";
 
    return output.str();
  }
 
  UndiGraph EssentialGraph::skeleton() const {
    UndiGraph skel;
    for (const auto& n: nodes())
      skel.addNodeWithId(n);
    for (const auto& edge: edges())
      skel.addEdge(edge.first(), edge.second());
    for (const auto& arc: arcs())
      skel.addEdge(arc.tail(), arc.head());
    if (_dagmodel_ != nullptr)
      for (auto id: skel)
        skel.setName(id, _dagmodel_->variable(id).name());
    return skel;
  }
}   // namespace gum