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.DataSet;
  import edu.cmu.tetrad.data.DataUtils;
  import edu.cmu.tetrad.data.ICovarianceMatrix;
  import edu.cmu.tetrad.graph.Node;
  import edu.cmu.tetrad.util.*;
  
  import java.io.PrintStream;
  import java.text.NumberFormat;
  import java.util.*;
  import java.util.concurrent.ConcurrentHashMap;
  
  /**
   * Checks conditional independence of variable in a continuous data set using Fisher's Z test. See Spirtes, Glymour, and
   * Scheines, "Causation, Prediction and Search," 2nd edition, page 94.
   *
   * @author Joseph Ramsey
   * @author Frank Wimberly adapted IndTestCramerT for Fisher's Z
   */
  public final class IndTestDrton implements IndependenceTest {
  
      /**
       * The covariance matrix.
       */
      private final ICovarianceMatrix covMatrix;
  
      /**
       * The matrix out of the cov matrix.
       */
      private final TetradMatrix _covMatrix;
  
      /**
       * The variables of the covariance matrix, in order. (Unmodifiable list.)
       */
      private List<Node> variables;
  
      /**
       * The significance level of the independence tests.
       */
      private double alpha;
  
      /**
       * The value of the Fisher's Z statistic associated with the las calculated partial correlation.
       */
      private double fisherZ;
  
      /**
       * Formats as 0.0000.
       */
      private static NumberFormat nf = NumberFormatUtil.getInstance().getNumberFormat();
  
      /**
       * Stores a reference to the dataset being analyzed.
       */
      private DataSet dataSet;
  
      private PrintStream pValueLogger;
      private Map<Node, Integer> indexMap;
      private Map<String, Node> nameMap;
      private boolean verbose = false;
  
      //==========================CONSTRUCTORS=============================//
  
      /**
       * Constructs a new Independence test which checks independence facts based on the correlation matrix implied by the
       * given data set (must be continuous). The given significance level is used.
       *
       * @param dataSet A data set containing only continuous columns.
       * @param alpha   The alpha level of the test.
       */
      public IndTestDrton(DataSet dataSet, double alpha) {
          if (!(dataSet.isContinuous())) {
              throw new IllegalArgumentException("Data set must be continuous.");
          }
  
          this.covMatrix = DataUtils.covarianceNonparanormalDrton(dataSet);
          this._covMatrix = covMatrix.getMatrix();
          List<Node> nodes = covMatrix.getVariables();
  
          this.variables = Collections.unmodifiableList(nodes);
          this.indexMap = indexMap(variables);
          this.nameMap = mapNames(variables);
          setAlpha(alpha);
  
          this.dataSet = DataUtils.center(this.dataSet);
      }
  
      //==========================PUBLIC METHODS=============================//
  
      /**
       * Creates a new independence test instance for a subset of the variables.
       */
  
      public IndependenceTest indTestSubset(List<Node> vars) {
          throw new UnsupportedOperationException();
      }
  
      /**
       * Determines whether variable x is independent of variable y given a list of conditioning variables z.
       *
       * @param x the one variable being compared.
       * @param y the second variable being compared.
       * @param z the list of conditioning variables.
       * @return true iff x _||_ y | z.
       * @throws RuntimeException if a matrix singularity is encountered.
       */
      public boolean isIndependent(Node x, Node y, List<Node> z) {
          double r;
          int n = sampleSize();
  
          if (z.isEmpty()) {
              Integer xi = indexMap.get(x);
              Integer yi = indexMap.get(y);
  
              if (xi == null || yi == null) {
                  xi = indexMap.get(nameMap.get(x.getName()));
                  yi = indexMap.get(nameMap.get(y.getName()));
  
                  if (xi == null || yi == null) {
                      throw new IllegalArgumentException("Node not in map");
                  }
              }
  
              double a = _covMatrix.get(xi, xi);
              double b = _covMatrix.get(xi, yi);
              double d = _covMatrix.get(yi, yi);
  
              r = -b / Math.sqrt(a * d);
          } else {
              TetradMatrix submatrix = DataUtils.subMatrix(_covMatrix, indexMap, x, y, z);
              r = StatUtils.partialCorrelation(submatrix);
          }
  
          // Either dividing by a zero standard deviation (in which case it's dependent) or doing a regression
  //        // (effectively) with a multicolliarity.. or missing values in the data!
  //        if (Double.isNaN(engine)) {
  //
  //            // Maybe it's missing values. Try calculating engine using just the rows in the data set
  //            // (if it exists) with defined values for all compared variables.
  //            if (dataSet != null) {
  //                int[] vars = new int[2 + z.size()];
  //
  //                vars[0] = variables.indexOf(x);
  //                vars[1] = variables.indexOf(y);
  //
  //                for (int k = 0; k < z.size(); k++) {
  //                    vars[2 + k] = variables.indexOf(z.get(k));
  //                }
  //
  //                int[] _n = new int[1];
  //
  //                TetradMatrix submatrix = DataUtils.covMatrixForDefinedRows(dataSet, vars, _n);
  //
  //                engine = StatUtils.partialCorrelation(submatrix);
  //            }
  //
  //            if (Double.isNaN(engine)) {
  //                return false;
  //            }
  //        }
  
  
          if (r > 1.) r = 1.;
          if (r < -1.) r = -1.;
  
          double fisherZ = Math.sqrt(n - z.size() - 3.0) *
                  0.5 * (Math.log(1.0 + r) - Math.log(1.0 - r));
  
          this.fisherZ = fisherZ;
  
          if (Double.isNaN(fisherZ)) {
              return true;
          }
  
          double pValue = 2.0 * (1.0 - RandomUtil.getInstance().normalCdf(0, 1, Math.abs(fisherZ)));
  
          return pValue > alpha;
      }
  
      public boolean isIndependent(Node x, Node y, Node... z) {
          return isIndependent(x, y, Arrays.asList(z));
      }
  
      public boolean isDependent(Node x, Node y, List<Node> z) {
          return !isIndependent(x, y, z);
      }
  
      public boolean isDependent(Node x, Node y, Node... z) {
          List<Node> zList = Arrays.asList(z);
          return isDependent(x, y, zList);
      }
  
      /**
       * @return the probability associated with the most recently computed independence test.
       */
      public double getPValue() {
          return 2.0 * (1.0 - RandomUtil.getInstance().normalCdf(0, 1, Math.abs(fisherZ)));
      }
  
      /**
       * Sets the significance level at which independence judgments should be made.  Affects the cutoff for partial
       * correlations to be considered statistically equal to zero.
       */
      public void setAlpha(double alpha) {
          if (alpha < 0.0 || alpha > 1.0) {
              throw new IllegalArgumentException("Significance out of range.");
          }
  
          this.alpha = alpha;
      }
  
      /**
       * Gets the getModel significance level.
       */
      public double getAlpha() {
          return this.alpha;
      }
  
      /**
       * @return the list of variables over which this independence checker is capable of determinine independence
       * relations-- that is, all the variables in the given graph or the given data set.
       */
      public List<Node> getVariables() {
          return this.variables;
      }
  
      /**
       * @return the variable with the given name.
       */
      public Node getVariable(String name) {
          return nameMap.get(name);
      }
  
      /**
       * @return the list of variable varNames.
       */
      public List<String> getVariableNames() {
          List<Node> variables = getVariables();
          List<String> variableNames = new ArrayList<>();
          for (Node variable1 : variables) {
              variableNames.add(variable1.getName());
          }
          return variableNames;
      }
  
      /**
       * If <code>isDeterminismAllowed()</code>, deters to IndTestFisherZD; otherwise throws
       * UnsupportedOperationException.
       */
      public boolean determines(List<Node> z, Node x) throws UnsupportedOperationException {
          int[] parents = new int[z.size()];
  
          for (int j = 0; j < parents.length; j++) {
              parents[j] = covMatrix.getVariables().indexOf(z.get(j));
          }
  
          int i = covMatrix.getVariables().indexOf(x);
  
          TetradMatrix matrix2D = covMatrix.getMatrix();
          double variance = matrix2D.get(i, i);
  
          if (parents.length > 0) {
  
              // Regress z onto i, yielding regression coefficients b.
              TetradMatrix Czz = matrix2D.getSelection(parents, parents);
              TetradMatrix inverse;
  
              try {
                  inverse = Czz.inverse();
              } catch (Exception e) {
                  return true;
              }
  
              TetradVector Cyz = matrix2D.getColumn(i);
              Cyz = Cyz.viewSelection(parents);
              TetradVector b = inverse.times(Cyz);
  
              variance -= Cyz.dotProduct(b);
          }
  
          return variance < 1e-20;
      }
  
      /**
       * @return the data set being analyzed.
       */
      public DataSet getData() {
          return dataSet;
      }
  
      @Override
      public ICovarianceMatrix getCov() {
          return null;
      }
  
      @Override
      public List<DataSet> getDataSets() {
          return null;
      }
  
      @Override
      public int getSampleSize() {
          return 0;
      }
  
      @Override
      public List<TetradMatrix> getCovMatrices() {
          return null;
      }
  
      @Override
      public double getScore() {
          return -(getPValue() - getAlpha());
      }
  
      public void shuffleVariables() {
          ArrayList<Node> nodes = new ArrayList<>(this.variables);
          Collections.shuffle(nodes);
          this.variables = Collections.unmodifiableList(nodes);
      }
  
      /**
       * @return a string representation of this test.
       */
      public String toString() {
          return "Fisher's Z, alpha = " + nf.format(getAlpha());
      }
  
      public void setPValueLogger(PrintStream pValueLogger) {
          this.pValueLogger = pValueLogger;
      }
  
      //==========================PRIVATE METHODS============================//
  
      private int sampleSize() {
          return covMatrix().getSampleSize();
      }
  
      private ICovarianceMatrix covMatrix() {
          return covMatrix;
      }
  
      private Map<String, Node> mapNames(List<Node> variables) {
          Map<String, Node> nameMap = new ConcurrentHashMap<>();
  
          for (Node node : variables) {
              nameMap.put(node.getName(), node);
          }
  
          return nameMap;
      }
  
      private Map<Node, Integer> indexMap(List<Node> variables) {
          Map<Node, Integer> indexMap = new ConcurrentHashMap<>();
  
          for (int i = 0; i < variables.size(); i++) {
              indexMap.put(variables.get(i), i);
          }
  
          return indexMap;
      }
  
      @Override
      public boolean isVerbose() {
          return verbose;
      }
  
      @Override
      public void setVerbose(boolean verbose) {
          this.verbose = verbose;
      }
  }
  
  
  
  