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.data.ICovarianceMatrix;
  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.ForkJoinPoolInstance;
  import edu.cmu.tetrad.util.TetradLogger;
  import java.io.PrintStream;
  import java.util.Iterator;
  import java.util.List;
  import java.util.concurrent.RecursiveTask;
  
  /**
   * J.M. Ogarrio and P. Spirtes and J. Ramsey, "A Hybrid Causal Search Algorithm
   * for Latent Variable Models," JMLR 2016.
   *
   * @author Juan Miguel Ogarrio
   * @author ps7z
   * @author jdramsey
   */
  public final class GFciMax implements GraphSearch {
  
      // The PAG being constructed.
      private Graph graph;
  
      // The background knowledge.
      private IKnowledge knowledge = new Knowledge2();
  
      // The conditional independence test.
      private IndependenceTest independenceTest;
  
      // Flag for complete rule set, true if should use complete rule set, false otherwise.
      private boolean completeRuleSetUsed = false;
  
      // The maximum length for any discriminating path. -1 if unlimited; otherwise, a positive integer.
      private int maxPathLength = -1;
  
      // Bounds the degree of the graph.
      private int maxDegree = -1;
  
      // The logger to use.
      private TetradLogger logger = TetradLogger.getInstance();
  
      // True iff verbose output should be printed.
      private boolean verbose = false;
  
      // The covariance matrix beign searched over. Assumes continuous data.
      ICovarianceMatrix covarianceMatrix;
  
      // The sample size.
      int sampleSize;
  
      // The print stream that output is directed to.
      private PrintStream out = System.out;
  
      // True iff one-edge faithfulness is assumed. Speed up the algorith for very large searches. By default false.
      private boolean faithfulnessAssumed = true;
  
      // The score.
      private Score score;
  
      private SepsetProducer sepsets;
      private long elapsedTime;
  
      //============================CONSTRUCTORS============================//
      public GFciMax(IndependenceTest test, Score score) {
          if (score == null) {
              throw new NullPointerException();
          }
          this.sampleSize = score.getSampleSize();
          this.score = score;
          this.independenceTest = test;
      }
  
      //========================PUBLIC METHODS==========================//
      public Graph search() {
          long time1 = System.currentTimeMillis();
  
          List<Node> nodes = getIndependenceTest().getVariables();
  
          logger.log("info", "Starting FCI algorithm.");
          logger.log("info", "Independence test = " + getIndependenceTest() + ".");
  
          this.graph = new EdgeListGraphSingleConnections(nodes);
  
          Fges fges = new Fges(score);
          fges.setKnowledge(getKnowledge());
          fges.setVerbose(verbose);
          fges.setNumPatternsToStore(0);
          fges.setFaithfulnessAssumed(faithfulnessAssumed);
          fges.setMaxDegree(maxDegree);
          fges.setOut(out);
          graph = fges.search();
          Graph fgesGraph = new EdgeListGraphSingleConnections(graph);
          sepsets = new SepsetsGreedy(fgesGraph, independenceTest, null, maxDegree);
  
          graph.reorientAllWith(Endpoint.CIRCLE);
  
          for (Node b : nodes) {
              List<Node> adjacentNodes = fgesGraph.getAdjacentNodes(b);
  
              if (adjacentNodes.size() < 2) {
                  continue;
              }
  
              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]);
  
                  if (graph.isAdjacentTo(a, c) && fgesGraph.isAdjacentTo(a, c)) {
                      if (sepsets.getSepset(a, c) != null) {
                          graph.removeEdge(a, c);
                      }
                  }
              }
          }
  
  //        modifiedR0(fgesGraph);
          sepsets = new SepsetsMinScore(fgesGraph, independenceTest, maxDegree);
  
          addColliders(graph, fgesGraph);
  
          FciOrient fciOrient = new FciOrient(sepsets);
          fciOrient.setVerbose(verbose);
          fciOrient.setOut(out);
          fciOrient.setKnowledge(getKnowledge());
          fciOrient.setCompleteRuleSetUsed(completeRuleSetUsed);
          fciOrient.setMaxPathLength(maxPathLength);
          fciOrient.doFinalOrientation(graph);
  
          GraphUtils.replaceNodes(graph, independenceTest.getVariables());
  
          long time2 = System.currentTimeMillis();
  
          elapsedTime = time2 - time1;
  
          return graph;
      }
  
      @Override
      public long getElapsedTime() {
          return elapsedTime;
      }
  
      /**
       * The maximum of parents any nodes can have in output pattern.
       *
       * @param maxDegree -1 for unlimited.
       */
      public void setMaxDegree(int maxDegree) {
          if (maxDegree < -1) {
              throw new IllegalArgumentException(
                      "Depth must be -1 (unlimited) or >= 0: " + maxDegree);
          }
  
          this.maxDegree = maxDegree;
      }
  
      /**
       * The maximum of parents any nodes can have in output pattern.
       *
       * @return -1 for unlimited.
       */
      public int getMaxDegree() {
          return maxDegree;
      }
  
      // Due to Spirtes.
      public void modifiedR0(Graph fgesGraph) {
          graph.reorientAllWith(Endpoint.CIRCLE);
          fciOrientbk(knowledge, graph, graph.getNodes());
  
          List<Node> nodes = graph.getNodes();
  
          for (Node b : nodes) {
              List<Node> adjacentNodes = graph.getAdjacentNodes(b);
  
              if (adjacentNodes.size() < 2) {
                  continue;
              }
  
              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]);
  
                  if (fgesGraph.isDefCollider(a, b, c)) {
                      graph.setEndpoint(a, b, Endpoint.ARROW);
                      graph.setEndpoint(c, b, Endpoint.ARROW);
                  } else if (fgesGraph.isAdjacentTo(a, c) && !graph.isAdjacentTo(a, c)) {
                      List<Node> sepset = sepsets.getSepset(a, c);
  
                      if (sepset != null && !sepset.contains(b)) {
                          graph.setEndpoint(a, b, Endpoint.ARROW);
                          graph.setEndpoint(c, b, Endpoint.ARROW);
                      }
                  }
              }
          }
      }
  
      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;
      }
  
      /**
       * @return the maximum length of any discriminating path, or -1 of
       * unlimited.
       */
      public int getMaxPathLength() {
          return 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;
      }
  
      public ICovarianceMatrix getCovMatrix() {
          return covarianceMatrix;
      }
  
      public ICovarianceMatrix getCovarianceMatrix() {
          return covarianceMatrix;
      }
  
      public void setCovarianceMatrix(ICovarianceMatrix covarianceMatrix) {
          this.covarianceMatrix = covarianceMatrix;
      }
  
      public PrintStream getOut() {
          return out;
      }
  
      public void setOut(PrintStream out) {
          this.out = out;
      }
  
      public void setIndependenceTest(IndependenceTest independenceTest) {
          this.independenceTest = independenceTest;
      }
  
      public void setFaithfulnessAssumed(boolean faithfulnessAssumed) {
          this.faithfulnessAssumed = faithfulnessAssumed;
      }
  
      //===========================================PRIVATE METHODS=======================================//
      /**
       * Orients according to background knowledge
       */
      private void fciOrientbk(IKnowledge knowledge, Graph graph, List<Node> variables) {
          logger.log("info", "Starting BK Orientation.");
  
          for (Iterator<KnowledgeEdge> it = knowledge.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 = knowledge.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.");
      }
  
      private void addColliders(Graph graph, final Graph fgesGraph) {
          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, 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, fgesGraph, nodes.get(i));
                      }
  
                      return true;
                  } else {
                      int mid = (to + from) / 2;
  
                      Task left = new Task(nodes, graph, from, mid);
                      Task right = new Task(nodes, graph, mid, to);
  
                      left.fork();
                      right.compute();
                      left.join();
  
                      return true;
                  }
              }
          }
  
          Task task = new Task(nodes, graph, 0, nodes.size());
  
          ForkJoinPoolInstance.getInstance().getPool().invoke(task);
      }
  
      private void doNode(Graph graph, Graph fgesGraph, 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]);
  
  //            if (fgesGraph.isAdjacentTo(a, c) && !graph.isAdjacentTo(a, c)) {
              // S actually has to be non-null here, but the compiler doesn't know that.
              List<Node> S = sepsets.getSepset(a, c);
              if (S != null && !S.contains(b)) {
                  graph.setEndpoint(a, b, Endpoint.ARROW);
                  graph.setEndpoint(c, b, Endpoint.ARROW);
              }
          }
  //        }
      }
  }
  