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.                                                //
  //                                                                           //
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  // it under the terms of the GNU General Public License as published by      //
  // the Free Software Foundation; either version 2 of the License, or         //
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  // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the             //
  // GNU General Public License for more details.                              //
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  // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA //
  ///////////////////////////////////////////////////////////////////////////////
  
  package edu.cmu.tetrad.search;
  
  import edu.cmu.tetrad.data.IKnowledge;
  import edu.cmu.tetrad.data.Knowledge2;
  import edu.cmu.tetrad.data.KnowledgeEdge;
  import edu.cmu.tetrad.graph.*;
  import edu.cmu.tetrad.util.ChoiceGenerator;
  import edu.cmu.tetrad.util.DepthChoiceGenerator;
  import edu.cmu.tetrad.util.ForkJoinPoolInstance;
  import edu.cmu.tetrad.util.TetradLogger;
  
  import java.util.*;
  import java.util.concurrent.ConcurrentHashMap;
  import java.util.concurrent.RecursiveTask;
  
  
  /**
   * Extends Erin Korber's implementation of the Fast Causal Inference algorithm (found in FCI.java) with Jiji Zhang's
   * Augmented FCI rules (found in sec. 4.1 of Zhang's 2006 PhD dissertation, "Causal Inference and Reasoning in Causally
   * Insufficient Systems").
   * <p>
   * This class is based off a copy of FCI.java taken from the repository on 2008/12/16, revision 7306. The extension is
   * done by extending doFinalOrientation() with methods for Zhang's rules R5-R10 which implements the augmented search.
   * (By a remark of Zhang's, the rule applications can be staged in this way.)
   *
   * @author Joseph Ramsey
   * @author Vineet Rhagu
   */
  public final class FciMax implements GraphSearch {
  
      /**
       * The PAG being constructed.
       */
      private Graph graph;
  
      /**
       * The SepsetMap being constructed.
       */
      private SepsetMap sepsets;
  
      /**
       * The background knowledge.
       */
      private IKnowledge knowledge = new Knowledge2();
  
      /**
       * The variables to search over (optional)
       */
      private List<Node> variables = new ArrayList<>();
  
      private IndependenceTest independenceTest;
  
      /**
       * flag for complete rule set, true if should use complete rule set, false otherwise.
       */
      private boolean completeRuleSetUsed = false;
  
      /**
       * True iff the possible dsep search is done.
       */
      private boolean possibleDsepSearchDone = true;
  
      /**
       * The maximum length for any discriminating path. -1 if unlimited; otherwise, a positive integer.
       */
      private int maxPathLength = -1;
  
      /**
       * The depth for the fast adjacency search.
       */
      private int depth = -1;
  
      /**
       * Elapsed time of last search.
       */
      private long elapsedTime;
  
      /**
       * The logger to use.
       */
      private TetradLogger logger = TetradLogger.getInstance();
  
      /**
       * True iff verbose output should be printed.
       */
      private boolean verbose = false;
  
      /**
       * An initial graph if there is one.
       */
      private Graph initialGraph;
  
      /**
       * Max path length for the possible dsep search.
       */
      private int possibleDsepDepth = -1;
  
  
      //============================CONSTRUCTORS============================//
  
      /**
       * Constructs a new FCI search for the given independence test and background knowledge.
       */
      public FciMax(IndependenceTest independenceTest) {
          if (independenceTest == null || knowledge == null) {
              throw new NullPointerException();
          }
  
          this.independenceTest = independenceTest;
          this.variables.addAll(independenceTest.getVariables());
      }
  
      //========================PUBLIC METHODS==========================//
  
      public int getDepth() {
          return depth;
      }
  
      public void setDepth(int depth) {
          if (depth < -1) {
              throw new IllegalArgumentException(
                      "Depth must be -1 (unlimited) or >= 0: " + depth);
          }
  
          this.depth = depth;
      }
  
      public long getElapsedTime() {
          return this.elapsedTime;
      }
  
      public Graph search() {
          FasConcurrent fas = new FasConcurrent(initialGraph, getIndependenceTest());
          fas.setVerbose(verbose);
          return search(fas);
      }
  
      public void setInitialGraph(Graph initialGraph) {
          this.initialGraph = initialGraph;
      }
  
      public Graph search(IFas fas) {
          logger.log("info", "Starting FCI algorithm.");
          logger.log("info", "Independence test = " + getIndependenceTest() + ".");
          fas.setVerbose(verbose);
  
          fas.setKnowledge(getKnowledge());
          fas.setDepth(depth);
          fas.setVerbose(verbose);
          this.graph = fas.search();
          this.sepsets = fas.getSepsets();
  
          graph.reorientAllWith(Endpoint.CIRCLE);
  
          SepsetProducer sp = new SepsetsMaxPValuePossDsep(graph, independenceTest, null, depth, maxPathLength);
  
          // The original FCI, with or without JiJi Zhang's orientation rules
          if (isPossibleDsepSearchDone()) {
              addColliders(graph);
  
              for (Edge edge : new ArrayList<>(graph.getEdges())) {
                  Node x = edge.getNode1();
                  Node y = edge.getNode2();
  
                  List<Node> sepset = sp.getSepset(x, y);
  
                  if (sepset != null) {
                      graph.removeEdge(x, y);
                      sepsets.set(x, y, sepset);
                  }
              }
  
              // Reorient all edges as o-o.
              graph.reorientAllWith(Endpoint.CIRCLE);
          }
  
          addColliders(graph);
  
          // Step CI C (Zhang's step F3.)
          long time5 = System.currentTimeMillis();
  
          long time6 = System.currentTimeMillis();
          logger.log("info", "Step CI C: " + (time6 - time5) / 1000. + "s");
  
          final FciOrient fciOrient = new FciOrient(new SepsetsSet(this.sepsets, independenceTest));
  
          fciOrient.setCompleteRuleSetUsed(completeRuleSetUsed);
          fciOrient.setMaxPathLength(maxPathLength);
          fciOrient.setKnowledge(knowledge);
          fciOrient.doFinalOrientation(graph);
          graph.setPag(true);
  
          return graph;
      }
  
      private void addColliders(Graph graph) {
          final Map<Triple, Double> scores = new ConcurrentHashMap<>();
  
          List<Node> nodes = graph.getNodes();
  
          class Task extends RecursiveTask<Boolean> {
              int from;
              int to;
              int chunk = 20;
              List<Node> nodes;
              Graph graph;
  
              public Task(List<Node> nodes, Graph graph, Map<Triple, Double> scores, int from, int to) {
                  this.nodes = nodes;
                  this.graph = graph;
                  this.from = from;
                  this.to = to;
              }
  
              @Override
              protected Boolean compute() {
                  if (to - from <= chunk) {
                      for (int i = from; i < to; i++) {
                          doNode(graph, scores, nodes.get(i));
                      }
  
                      return true;
                  } else {
                      int mid = (to + from) / 2;
  
                      Task left = new Task(nodes, graph, scores, from, mid);
                      Task right = new Task(nodes, graph, scores, mid, to);
  
                      left.fork();
                      right.compute();
                      left.join();
  
                      return true;
                  }
              }
          }
  
          Task task = new Task(nodes, graph, scores, 0, nodes.size());
  
          ForkJoinPoolInstance.getInstance().getPool().invoke(task);
  
          List<Triple> tripleList = new ArrayList<>(scores.keySet());
  
          // Most independent ones first.
          Collections.sort(tripleList, new Comparator<Triple>() {
  
              @Override
              public int compare(Triple o1, Triple o2) {
                  return Double.compare(scores.get(o2), scores.get(o1));
              }
          });
  
          for (Triple triple : tripleList) {
              Node a = triple.getX();
              Node b = triple.getY();
              Node c = triple.getZ();
  
              graph.setEndpoint(a, b, Endpoint.ARROW);
              graph.setEndpoint(c, b, Endpoint.ARROW);
          }
      }
  
      private void doNode(Graph graph, Map<Triple, Double> scores, Node b) {
          List<Node> adjacentNodes = graph.getAdjacentNodes(b);
  
          if (adjacentNodes.size() < 2) {
              return;
          }
  
          ChoiceGenerator cg = new ChoiceGenerator(adjacentNodes.size(), 2);
          int[] combination;
  
          while ((combination = cg.next()) != null) {
              Node a = adjacentNodes.get(combination[0]);
              Node c = adjacentNodes.get(combination[1]);
  
              // Skip triples that are shielded.
              if (graph.isAdjacentTo(a, c)) {
                  continue;
              }
  
              List<Node> adja = graph.getAdjacentNodes(a);
              double score = Double.POSITIVE_INFINITY;
              List<Node> S = null;
  
              DepthChoiceGenerator cg2 = new DepthChoiceGenerator(adja.size(), -1);
              int[] comb2;
  
              while ((comb2 = cg2.next()) != null) {
                  List<Node> s = GraphUtils.asList(comb2, adja);
                  independenceTest.isIndependent(a, c, s);
                  double _score = independenceTest.getScore();
  
                  if (_score < score) {
                      score = _score;
                      S = s;
                  }
              }
  
              List<Node> adjc = graph.getAdjacentNodes(c);
  
              DepthChoiceGenerator cg3 = new DepthChoiceGenerator(adjc.size(), -1);
              int[] comb3;
  
              while ((comb3 = cg3.next()) != null) {
                  List<Node> s = GraphUtils.asList(comb3, adjc);
                  independenceTest.isIndependent(c, a, s);
                  double _score = independenceTest.getScore();
  
                  if (_score < score) {
                      score = _score;
                      S = s;
                  }
              }
  
              // S actually has to be non-null here, but the compiler doesn't know that.
              if (S != null && !S.contains(b)) {
                  scores.put(new Triple(a, b, c), score);
              }
          }
      }
  
      public SepsetMap getSepsets() {
          return this.sepsets;
      }
  
      public IKnowledge getKnowledge() {
          return knowledge;
      }
  
      public void setKnowledge(IKnowledge knowledge) {
          if (knowledge == null) {
              throw new NullPointerException();
          }
  
          this.knowledge = knowledge;
      }
  
      /**
       * @return true if Zhang's complete rule set should be used, false if only R1-R4 (the rule set of the original FCI)
       * should be used. False by default.
       */
      public boolean isCompleteRuleSetUsed() {
          return completeRuleSetUsed;
      }
  
      /**
       * @param completeRuleSetUsed set to true if Zhang's complete rule set should be used, false if only R1-R4 (the rule
       *                            set of the original FCI) should be used. False by default.
       */
      public void setCompleteRuleSetUsed(boolean completeRuleSetUsed) {
          this.completeRuleSetUsed = completeRuleSetUsed;
      }
  
      public boolean isPossibleDsepSearchDone() {
          return possibleDsepSearchDone;
      }
  
      public void setPossibleDsepSearchDone(boolean possibleDsepSearchDone) {
          this.possibleDsepSearchDone = possibleDsepSearchDone;
      }
  
      /**
       * @return the maximum length of any discriminating path, or -1 of unlimited.
       */
      public int getMaxPathLength() {
          return maxPathLength == Integer.MAX_VALUE ? -1 : maxPathLength;
      }
  
      /**
       * @param maxPathLength the maximum length of any discriminating path, or -1 if unlimited.
       */
      public void setMaxPathLength(int maxPathLength) {
          if (maxPathLength < -1) {
              throw new IllegalArgumentException("Max path length must be -1 (unlimited) or >= 0: " + maxPathLength);
          }
  
          this.maxPathLength = maxPathLength;
      }
  
      /**
       * True iff verbose output should be printed.
       */
      public boolean isVerbose() {
          return verbose;
      }
  
      public void setVerbose(boolean verbose) {
          this.verbose = verbose;
      }
  
      /**
       * The independence test.
       */
      public IndependenceTest getIndependenceTest() {
          return independenceTest;
      }
  
      //===========================PRIVATE METHODS=========================//
  
      /**
       * Orients according to background knowledge
       */
      private void fciOrientbk(IKnowledge bk, Graph graph, List<Node> variables) {
          logger.log("info", "Starting BK Orientation.");
  
          for (Iterator<KnowledgeEdge> it =
               bk.forbiddenEdgesIterator(); it.hasNext(); ) {
              KnowledgeEdge edge = it.next();
  
              //match strings to variables in the graph.
              Node from = SearchGraphUtils.translate(edge.getFrom(), variables);
              Node to = SearchGraphUtils.translate(edge.getTo(), variables);
  
  
              if (from == null || to == null) {
                  continue;
              }
  
              if (graph.getEdge(from, to) == null) {
                  continue;
              }
  
              // Orient to*->from
              graph.setEndpoint(to, from, Endpoint.ARROW);
              graph.setEndpoint(from, to, Endpoint.CIRCLE);
              logger.log("knowledgeOrientation", SearchLogUtils.edgeOrientedMsg("Knowledge", graph.getEdge(from, to)));
          }
  
          for (Iterator<KnowledgeEdge> it =
               bk.requiredEdgesIterator(); it.hasNext(); ) {
              KnowledgeEdge edge = it.next();
  
              //match strings to variables in this graph
              Node from = SearchGraphUtils.translate(edge.getFrom(), variables);
              Node to = SearchGraphUtils.translate(edge.getTo(), variables);
  
              if (from == null || to == null) {
                  continue;
              }
  
              if (graph.getEdge(from, to) == null) {
                  continue;
              }
  
              graph.setEndpoint(to, from, Endpoint.TAIL);
              graph.setEndpoint(from, to, Endpoint.ARROW);
              logger.log("knowledgeOrientation", SearchLogUtils.edgeOrientedMsg("Knowledge", graph.getEdge(from, to)));
          }
  
          logger.log("info", "Finishing BK Orientation.");
      }
  }
  
  
  
  
  