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.*;
  import edu.cmu.tetrad.graph.Node;
  import edu.cmu.tetrad.util.*;
  import org.apache.commons.math3.distribution.TDistribution;
  import org.apache.commons.math3.linear.SingularMatrixException;
  
  import java.io.PrintStream;
  import java.text.NumberFormat;
  import java.util.*;
  import java.util.concurrent.ConcurrentHashMap;
  
  import static java.lang.Math.abs;
  import static java.lang.Math.sqrt;
  
  /**
   * 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 IndTestCorrelationT 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 pValue;
  
      /**
       * 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 TDistribution tDistribution;
      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 IndTestCorrelationT(DataSet dataSet, double alpha) {
          if (!(dataSet.isContinuous())) {
              throw new IllegalArgumentException("Data set must be continuous.");
          }
  
          this.covMatrix = new CovarianceMatrix(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(dataSet);
  
          tDistribution = new TDistribution(dataSet.getNumRows() - 2);
      }
  
      /**
       * Constructs a new Fisher Z independence test with the listed arguments.
       *
       * @param data      A 2D continuous data set with no missing values.
       * @param variables A list of variables, a subset of the variables of <code>data</code>.
       * @param alpha     The significance cutoff level. p values less than alpha will be reported as dependent.
       */
      public IndTestCorrelationT(TetradMatrix data, List<Node> variables, double alpha) {
          this.dataSet = ColtDataSet.makeContinuousData(variables, data);
          this.dataSet = DataUtils.center(dataSet);
          this.covMatrix = new CovarianceMatrix(dataSet);
          this._covMatrix = covMatrix.getMatrix();
          this.variables = Collections.unmodifiableList(variables);
          this.indexMap = indexMap(variables);
          this.nameMap = mapNames(variables);
          setAlpha(alpha);
      }
  
      /**
       * Constructs a new independence test that will determine conditional independence facts using the given correlation
       * matrix and the given significance level.
       */
      public IndTestCorrelationT(ICovarianceMatrix corrMatrix, double alpha) {
          this.covMatrix = corrMatrix;
          this._covMatrix = corrMatrix.getMatrix();
          this.variables = Collections.unmodifiableList(corrMatrix.getVariables());
          this.indexMap = indexMap(variables);
          this.nameMap = mapNames(variables);
          setAlpha(alpha);
      }
  
      //==========================PUBLIC METHODS=============================//
  
      /**
       * Creates a new independence test instance for a subset of the variables.
       */
      public IndependenceTest indTestSubset(List<Node> vars) {
          if (vars.isEmpty()) {
              throw new IllegalArgumentException("Subset may not be empty.");
          }
  
          for (Node var : vars) {
              if (!variables.contains(var)) {
                  throw new IllegalArgumentException(
                          "All vars must be original vars");
              }
          }
  
          int[] indices = new int[vars.size()];
  
          for (int i = 0; i < indices.length; i++) {
              indices[i] = indexMap.get(vars.get(i));
          }
  
          ICovarianceMatrix newCovMatrix = covMatrix.getSubmatrix(indices);
  
          double alphaNew = getAlpha();
          return new IndTestCorrelationT(newCovMatrix, alphaNew);
      }
  
      /**
       * 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();
  
          TetradMatrix submatrix = DataUtils.subMatrix(_covMatrix, indexMap, x, y, z);
          r = StatUtils.partialCorrelation(submatrix);
  
          double t = Math.sqrt(n - 2) * (r / Math.sqrt(1. - r * r));
          pValue = 2.0 * (1.0 - gettDistribution().cumulativeProbability(abs(t)));
  
          boolean independent = pValue > alpha;
  
          if (verbose) {
              if (independent) {
                  TetradLogger.getInstance().log("independencies",
                          SearchLogUtils.independenceFactMsg(x, y, z, r)); //getScore()));
              } else {
                  if (pValueLogger != null) {
                      pValueLogger.println(getPValue());
                  }
  
                  TetradLogger.getInstance().log("dependencies",
                          SearchLogUtils.dependenceFactMsg(x, y, z, getPValue()));
              }
          }
  
          return independent;
      }
  
      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) {
          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 (SingularMatrixException e) {
                  System.out.println(SearchLogUtils.determinismDetected(z, x));
                  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;
      }
  
      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;
      }
  
      public void setVariables(List<Node> variables) {
          if (variables.size() != this.variables.size()) throw new IllegalArgumentException("Wrong # of variables.");
          this.variables = new ArrayList<>(variables);
          covMatrix.setVariables(variables);
      }
  
      public ICovarianceMatrix getCov() {
          return covMatrix;
      }
  
      @Override
      public List<DataSet> getDataSets() {
  
          List<DataSet> dataSets = new ArrayList<>();
  
          dataSets.add(dataSet);
  
          return dataSets;
      }
  
      @Override
      public int getSampleSize() {
          return covMatrix.getSampleSize();
      }
  
      @Override
      public List<TetradMatrix> getCovMatrices() {
          return null;
      }
  
      @Override
      public double getScore() {
          return -(getPValue() - getAlpha());
      }
  
      public TDistribution gettDistribution() {
          return tDistribution;
      }
  
      public boolean isVerbose() {
          return verbose;
      }
  
      public void setVerbose(boolean verbose) {
          this.verbose = verbose;
      }
  }
  
  
  
  
  