code: ///////////////////////////////////////////////////////////////////////////////
  // For information as to what this class does, see the Javadoc, below.       //
  // Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006,       //
  // 2007, 2008, 2009, 2010, 2014, 2015 by Peter Spirtes, Richard Scheines, Joseph   //
  // Ramsey, and Clark Glymour.                                                //
  //                                                                           //
  // This program is free software; you can redistribute it and/or modify      //
  // it under the terms of the GNU General Public License as published by      //
  // the Free Software Foundation; either version 2 of the License, or         //
  // (at your option) any later version.                                       //
  //                                                                           //
  // This program is distributed in the hope that it will be useful,           //
  // but WITHOUT ANY WARRANTY; without even the implied warranty of            //
  // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the             //
  // GNU General Public License for more details.                              //
  //                                                                           //
  // You should have received a copy of the GNU General Public License         //
  // along with this program; if not, write to the Free Software               //
  // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA //
  ///////////////////////////////////////////////////////////////////////////////
  
  package edu.cmu.tetrad.search;
  
  import edu.cmu.tetrad.graph.*;
  import edu.cmu.tetrad.util.ChoiceGenerator;
  
  import java.util.ArrayList;
  import java.util.List;
  import java.util.Set;
  
  /**
   * This class contains methods which can be used to determine whether a directed graph is in the equivalence class
   * determined by the given PAG.  See p. 300 Def. 12.1.1 of CPS for a specification.
   *
   * @author Frank Wimberly
   */
  public final class PagUtils {
  
      /**
       * This method implements step (1) of the definition.
       *
       * @return true if every vertex in gamma is in O.
       */
      public static boolean graphInPagStep0(Graph pag, Graph dag) {
  
          //(1) Every vertex in gamma is in O (measured nodes in dag)
          List<Node> pagNodes = pag.getNodes();
  
          //If there is a node in pag that's not a measured node in dag return false.
          for (Node pagNode : pagNodes) {
              if (dag.getNode(pagNode.getName()) == null) {
                  return false;
              }
              if (dag.getNode(pagNode.getName()).getNodeType() != NodeType
                      .MEASURED) {
                  return false;
              }
          }
  
          return true;
      }
  
      public static boolean graphInPagStep1(Graph pag, Graph dag) {
          //If A and B are in O, there is an edge between A and B in gamma
          //iff for every W subset of O minus {A, B}, A and B are d-connected
          //given W in [every graph] in delta (dag).
          IndTestDSep test = new IndTestDSep(pag);
  
          List<Node> V = new ArrayList<>(dag.getNodes());
  
          for (Edge edge : pag.getEdges()) {
              Node A = edge.getNode1();
              Node B = edge.getNode2();
  
              List<Node> W = new ArrayList<>(V);
              W.remove(A);
              W.remove(B);
  
              ChoiceGenerator gen = new ChoiceGenerator(W.size(), W.size());
              int[] choice;
  
              while ((choice = gen.next()) != null) {
                  List<Node> S = GraphUtils.asList(choice, W);
  
                  if (test.isDSeparated(A, B, S)) {
                      return false;
                  }
  
              }
          }
  
          return true;
      }
  
      public static boolean graphInPagStep2(Graph pag, Graph dag) {
          Set<Edge> pagEdges = pag.getEdges();
  
          for (Edge edge : pagEdges) {
              if (edge.getEndpoint1() == Endpoint.TAIL) {
                  Node A = edge.getNode1();
                  Node B = edge.getNode2();
  
                  Node Ad = dag.getNode(A.getName());
                  Node Bd = dag.getNode(B.getName());
  
                  List<Node> singletonB = new ArrayList<>();
                  singletonB.add(Bd);
                  List<Node> ancestorsOfB = dag.getAncestors(singletonB);
                  if (!ancestorsOfB.contains(Ad)) {
                      return false;
                  }
              }
          }
  
          return true;
      }
  
      public static boolean graphInPagStep3(Graph pag, Graph dag) {
          Set<Edge> pagEdges = pag.getEdges();
  
          for (Edge edge : pagEdges) {
              if (edge.getEndpoint2() == Endpoint.ARROW) {
                  Node A = edge.getNode1();
                  Node B = edge.getNode2();
  
                  Node Ad = dag.getNode(A.getName());
                  Node Bd = dag.getNode(B.getName());
  
                  if (dag.isAncestorOf(Bd, Ad)) {
                      return false;
                  }
              }
          }
  
          return true;
      }
  
      public static boolean graphInPagStep4(Graph pag, Graph dag) {
          Set<Triple> pagUnderLines = pag.getUnderLines();
  
          for (Triple underline : pagUnderLines) {
              Node A = underline.getX();
              Node B = underline.getY();
              Node C = underline.getZ();
  
              Node Ad = dag.getNode(A.getName());
              Node Bd = dag.getNode(B.getName());
              Node Cd = dag.getNode(C.getName());
  
              if (!dag.isAncestorOf(Bd, Ad) && !dag.isAncestorOf(Bd, Cd)) {
                  return false;
              }
          }
  
          return true;
      }
  
      public static boolean graphInPagStep5(Graph pag, Graph dag) {
          for (Triple triple : pag.getDottedUnderlines()) {
              Node A = triple.getX();
              Node B = triple.getY();
              Node C = triple.getZ();
  
              Node Ad = dag.getNode(A.getName());
              Node Bd = dag.getNode(B.getName());
              Node Cd = dag.getNode(C.getName());
  
              if (pag.isParentOf(A, B) && pag.isParentOf(C, B)) {
                  List<Node> commonChildrenAC = new ArrayList<>(dag.getChildren(Ad));
                  commonChildrenAC.retainAll(dag.getChildren(Cd));
  
                  for (Node Dd : commonChildrenAC) {
                      if (dag.isDescendentOf(Bd, Dd)) {
                          return false;
                      }
                  }
              }
          }
  
          return true;
      }
  }
  
  
  
  
  