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.GraphUtils;
  import edu.cmu.tetrad.graph.Node;
  import edu.cmu.tetrad.regression.Regression;
  import edu.cmu.tetrad.regression.RegressionDataset;
  import edu.cmu.tetrad.regression.RegressionResult;
  import edu.cmu.tetrad.util.RandomUtil;
  import edu.cmu.tetrad.util.StatUtils;
  import edu.cmu.tetrad.util.TetradLogger;
  import edu.cmu.tetrad.util.TetradMatrix;
  
  import java.util.ArrayList;
  import java.util.Arrays;
  import java.util.List;
  
  /**
   * Calculates independence from pooled residuals.
   *
   * @author Joseph Ramsey
   */
  public final class IndTestFisherZConcatenateResiduals implements IndependenceTest {
  
  
      /**
       * The variables of the covariance matrix, in order. (Unmodifiable list.)
       */
      private List<Node> variables;
  
      private ArrayList<Regression> regressions;
  
      private List<DataSet> dataSets;
  
      /**
       * The significance level of the independence tests.
       */
      private double alpha;
      /**
       * The value of the Fisher's Z statistic associated with the last calculated partial correlation.
       */
  //    private double fisherZ;
  
      private double pValue = Double.NaN;
      private boolean verbose = false;
  
  //    private DataSet concatenatedData;
  
      //==========================CONSTRUCTORS=============================//
  
      public IndTestFisherZConcatenateResiduals(List<DataSet> dataSets, double alpha) {
          System.out.println("# data sets = " + dataSets.size());
          this.dataSets = dataSets;
  
          regressions = new ArrayList<>();
  
          for (DataSet dataSet : dataSets) {
              DataSet _dataSet = new BoxDataSet(new DoubleDataBox(dataSet.getDoubleData().toArray()),
                      dataSets.get(0).getVariables());
  
              regressions.add(new RegressionDataset(_dataSet));
          }
  
          setAlpha(alpha);
  
  //        this.concatenatedData = DataUtils.concatenate(dataSets);
  
          this.variables = dataSets.get(0).getVariables();
  
          List<DataSet> dataSets2 = new ArrayList<>();
  
          for (int i = 0; i < dataSets.size(); i++) {
              DataSet dataSet = ColtDataSet.makeContinuousData(variables, dataSets.get(i).getDoubleData());
              dataSets2.add(dataSet);
          }
  
          this.dataSets = dataSets2;
      }
  
      //==========================PUBLIC METHODS=============================//
  
      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) {
  
          x = getVariable(variables, x.getName());
          z = GraphUtils.replaceNodes(z, variables);
  
          // Calculate the residual of x and y conditional on z for each data set and concatenate them.
          double[] residualsX = residuals(x, z);
          double[] residualsY = residuals(y, z);
  
          List<Double> residualsXFiltered = new ArrayList<>();
          List<Double> residualsYFiltered = new ArrayList<>();
  
          // This is the way of dealing with missing values; residuals are only correlated
          // for data sets in which both residuals exist.
          for (int i = 0; i < residualsX.length; i++) {
              if (!Double.isNaN(residualsX[i]) && !Double.isNaN(residualsY[i])) {
                  residualsXFiltered.add(residualsX[i]);
                  residualsYFiltered.add(residualsY[i]);
              }
          }
  
          residualsX = new double[residualsXFiltered.size()];
          residualsY = new double[residualsYFiltered.size()];
  
          for (int i = 0; i < residualsXFiltered.size(); i++) {
              residualsX[i] = residualsXFiltered.get(i);
              residualsY[i] = residualsYFiltered.get(i);
          }
  
  
          if (residualsX.length != residualsY.length) throw new IllegalArgumentException("Missing values handled.");
          int sampleSize = residualsX.length;
  
          // return a judgement of whether these concatenated residuals are independent.
          double r = StatUtils.correlation(residualsX, residualsY);
  
          if (r > 1.) r = 1.;
          if (r < -1.) r = -1.;
  
          double fisherZ = Math.sqrt(sampleSize - z.size() - 3.0) *
                  0.5 * (Math.log(1.0 + r) - Math.log(1.0 - r));
  
          if (Double.isNaN(fisherZ)) {
              return false;
  //            throw new IllegalArgumentException("The Fisher's Z " +
  //                    "score for independence fact " + x + " _||_ " + y + " | " +
  //                    z + " is undefined. r = " + r);
          }
  
          double pvalue = 2.0 * (1.0 - RandomUtil.getInstance().normalCdf(0, 1, Math.abs(fisherZ)));
          this.pValue = pvalue;
          boolean independent = pvalue > alpha;
  
          if (verbose) {
              if (independent) {
                  TetradLogger.getInstance().log("independencies",
                          SearchLogUtils.independenceFactMsg(x, y, z, getPValue()));
                  System.out.println(SearchLogUtils.independenceFactMsg(x, y, z, getPValue()));
              } else {
                  TetradLogger.getInstance().log("dependencies",
                          SearchLogUtils.dependenceFactMsg(x, y, z, getPValue()));
              }
          }
  
          return independent;
  
      }
  
  
      private double[] residuals(Node node, List<Node> parents) {
          List<Double> _residuals = new ArrayList<>();
  
          Node target = dataSets.get(0).getVariable(node.getName());
  
          List<Node> regressors = new ArrayList<>();
  
          for (Node _regressor : parents) {
              Node variable = dataSets.get(0).getVariable(_regressor.getName());
              regressors.add(variable);
          }
  
  
          for (int m = 0; m < dataSets.size(); m++) {
              RegressionResult result = regressions.get(m).regress(target, regressors);
              double[] residualsSingleDataset = result.getResiduals().toArray();
  
              double mean = StatUtils.mean(residualsSingleDataset);
              for (int i2 = 0; i2 < residualsSingleDataset.length; i2++) {
                  residualsSingleDataset[i2] = residualsSingleDataset[i2] - mean;
              }
  
              for (double d : residualsSingleDataset) {
                  _residuals.add(d);
              }
          }
  
          double[] _f = new double[_residuals.size()];
  
  
          for (int k = 0; k < _residuals.size(); k++) {
              _f[k] = _residuals.get(k);
          }
  
          return _f;
      }
  
      private Node getVariable(List<Node> variables, String name) {
          for (Node node : variables) {
              if (name.equals(node.getName())) {
                  return node;
              }
          }
  
          return null;
      }
  
      public boolean isIndependent(Node x, Node y, Node... z) {
          List<Node> zList = Arrays.asList(z);
          return isIndependent(x, y, zList);
      }
  
      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 this.pValue;
  //        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;
  //        this.thresh = Double.NaN;
      }
  
      /**
       * 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) {
          for (int i = 0; i < getVariables().size(); i++) {
              Node variable = getVariables().get(i);
              if (variable.getName().equals(name)) {
                  return variable;
              }
          }
  
          return null;
      }
  
      /**
       * @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;
      }
  
      /**
       * @throws UnsupportedOperationException
       */
      public boolean determines(List z, Node x) throws UnsupportedOperationException {
          throw new UnsupportedOperationException();
      }
  
      /**
       * @throws UnsupportedOperationException
       */
      public DataSet getData() {
          return DataUtils.concatenate(dataSets);
      }
  
      @Override
      public ICovarianceMatrix getCov() {
          List<DataSet> _dataSets = new ArrayList<>();
  
          for (DataSet d : dataSets) {
              _dataSets.add(DataUtils.standardizeData(d));
          }
  
          return new CovarianceMatrix(DataUtils.concatenate(_dataSets));
      }
  
      @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());
      }
  
  
      /**
       * @return a string representation of this test.
       */
      public String toString() {
          return "Fisher Z, Concatenating Residuals";
      }
  
      public boolean isVerbose() {
          return verbose;
      }
  
      public void setVerbose(boolean verbose) {
          this.verbose = verbose;
      }
  }
  
  
  