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.CovarianceMatrix;
  import edu.cmu.tetrad.data.DataSet;
  import edu.cmu.tetrad.data.ICovarianceMatrix;
  import edu.cmu.tetrad.graph.Node;
  import edu.cmu.tetrad.util.NumberFormatUtil;
  import edu.cmu.tetrad.util.RandomUtil;
  import edu.cmu.tetrad.util.TetradMatrix;
  
  import java.text.NumberFormat;
  import java.util.*;
  import java.util.concurrent.ConcurrentHashMap;
  
  import static java.lang.Math.abs;
  
  /**
   * 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 IndTestPartialCorrelation implements IndependenceTest {
  
      /**
       * 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 pValue;
  
      /**
       * Formats as 0.0000.
       */
      private static NumberFormat nf = NumberFormatUtil.getInstance().getNumberFormat();
  
      /**
       * Stores a reference to the dataset being analyzed.
       */
      private DataSet dataSet;
  
      private int sampleSize;
  
      CovarianceMatrix cov;
  
      private boolean verbose = false;
  
  
      //==========================CONSTRUCTORS=============================//
  
      public IndTestPartialCorrelation(DataSet data, double alpha) {
          this.dataSet = data;
          this.alpha = alpha;
          this.sampleSize = data.getNumRows();
          this.variables = new ArrayList<>(data.getVariables());
          this.cov = new CovarianceMatrix(data);
      }
  
      //==========================PUBLIC METHODS=============================//
  
      /**
       * Creates a new independence test instance for a subset of the variables.
       */
      public IndependenceTest indTestSubset(List<Node> vars) {
          throw new UnsupportedOperationException();
      }
  
      public boolean isIndependent(Node x, Node y, List<Node> z) {
          return indepCollection(x, y, alpha);
      }
  
      private boolean indepCollection(Node x, Node y, double alpha) {
          TetradMatrix submatrix = cov.getMatrix();
  
          TetradMatrix inverse;
  
          try {
              inverse = submatrix.inverse();
          } catch (Exception e) {
              throw new IllegalArgumentException();
          }
  
          int i = variables.indexOf(x);
          int j = variables.indexOf(y);
  
          double a = -1.0 * inverse.get(i, j);
          double v0 = inverse.get(i, i);
          double v1 = inverse.get(j, j);
          double b = Math.sqrt(v0 * v1);
  
          double r = a / b;
  
          double fisherZ = Math.sqrt(cov.getSampleSize() - 3 - (variables.size() - 2)) * 0.5 * (Math.log(1.0 + r) - Math.log(1.0 - r));
          double p = 2.0 * (1.0 - RandomUtil.getInstance().normalCdf(0, 1, abs(fisherZ)));
          return p > alpha;
  
      }
  
      private List<Node> listVars(int[] indices, List<Node> vars) {
          List<Node> nodes = new ArrayList<>();
  
          for (int i : indices) {
              nodes.add(vars.get(i));
          }
  
          return nodes;
      }
  
      /**
       * @return the submatrix of m with variables in the order of the x variables.
       */
      public static TetradMatrix subMatrix(ICovarianceMatrix m, List<Node> x, List<Node> y, List<Node> z) {
          List<Node> variables = m.getVariables();
          TetradMatrix _covMatrix = m.getMatrix();
  
          // Create index array for the given variables.
          int[] indices = new int[x.size() + y.size() + z.size()];
  
          for (int i = 0; i < x.size(); i++) {
              indices[i] = variables.indexOf(x.get(i));
          }
  
          for (int i = 0; i < y.size(); i++) {
              indices[x.size() + i] = variables.indexOf(y.get(i));
          }
  
          for (int i = 0; i < z.size(); i++) {
              indices[x.size() + y.size() + i] = variables.indexOf(z.get(i));
          }
  
  //        System.out.println(Arrays.toString(indices));
  
          // Extract submatrix of correlation matrix using this index array.
          TetradMatrix submatrix = _covMatrix.getSelection(indices, indices);
  
          return submatrix;
      }
  
      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 pValue;
      }
  
      /**
       * 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) {
          throw new UnsupportedOperationException();
      }
  
      /**
       * @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 {
          throw new UnsupportedOperationException();
      }
  
      /**
       * @return the data set being analyzed.
       */
      public DataSet getData() {
          return dataSet;
      }
  
      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());
      }
  
      //==========================PRIVATE METHODS============================//
  
      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;
      }
  
      public ICovarianceMatrix getCov() {
          throw new UnsupportedOperationException();
      }
  
      @Override
      public List<DataSet> getDataSets() {
  
          List<DataSet> dataSets = new ArrayList<>();
  
          dataSets.add(dataSet);
  
          return dataSets;
      }
  
      @Override
      public int getSampleSize() {
          return sampleSize;
      }
  
      @Override
      public List<TetradMatrix> getCovMatrices() {
          return null;
      }
  
      @Override
      public double getScore() {
          return getPValue();
      }
  
  
      @Override
      public boolean isVerbose() {
          return verbose;
      }
  
      @Override
      public void setVerbose(boolean verbose) {
          this.verbose = verbose;
      }
  }
  
  
  
  