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.IndependenceFact;
  import edu.cmu.tetrad.graph.Node;
  import edu.cmu.tetrad.util.MatrixUtils;
  import edu.cmu.tetrad.util.TetradMatrix;
  
  import java.util.*;
  
  import static java.lang.Math.sqrt;
  
  /**
   * Created by josephramsey on 4/13/14.
   */
  public class RecursivePartialCorrelation {
  
      private final TetradMatrix corr;
      private final Map<Node, Integer> nodesMap = new HashMap<>();
      private Map<IndependenceFact, Double> memory = new WeakHashMap<>();
  
      public RecursivePartialCorrelation(List<Node> nodes, TetradMatrix cov) {
          this.corr = MatrixUtils.convertCovToCorr(new TetradMatrix(cov));
          for (int i = 0; i < nodes.size(); i++) nodesMap.put(nodes.get(i), i);
      }
  
      public double corr(Node x, Node y, List<Node> z) {
          if (z.isEmpty()) return this.corr.get(nodesMap.get(x), nodesMap.get(y));
  //        if (z.size() == 1) {
  //            int _x = nodesMap.get(x);
  //            int _y = nodesMap.get(y);
  //            int _z = nodesMap.get(z.get(0));
  //
  //            double c1 = corr.get(_x, _y);
  //            double c2 = corr.get(_y, _z);
  //            double c3 = corr.get(_x, _z);
  //            return (c1 - c2 * c3) / sqrt(1 - c2 * c2) * sqrt(1 - c3 * c3);
  //        }
          IndependenceFact spec = spec(x, y, z);
          if (memory.containsKey(spec)) {
              Double corr = memory.get(spec);
              if (corr != null) return corr;
          }
          Node z0 = z.get(0);
  
  //        for (Node _z0 : z) {
  //            z0 = _z0;
  //            List<Node> _z = new ArrayList<Node>(z);
  //            _z.remove(_z0);
  //            if (memory.containsKey(spec(x, y, _z))) {
  //                break;
  //            }
  //        }
  
          List<Node> _z = new ArrayList<>(z);
          _z.remove(z0);
  
          double corr0 = corr(x, y, _z);
          double corr1 = corr(x, z0, _z);
          double corr2 = corr(z0, y, _z);
          double corr3 = (corr0 - corr1 * corr2) / sqrt(1. - corr1 * corr1) * sqrt(1. - corr2 * corr2);
  
          memory.put(spec, corr3);
  
          return corr3;
      }
  
      private IndependenceFact spec(Node x, Node y, List<Node> z) {
          return new IndependenceFact(x, y, z);
      }
  }
  
  
  
  