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 cern.colt.matrix.DoubleMatrix1D;
  import cern.colt.matrix.DoubleMatrix2D;
  import cern.colt.matrix.impl.DenseDoubleMatrix2D;
  import cern.colt.matrix.linalg.Algebra;
  import cern.jet.math.Functions;
  import edu.cmu.tetrad.data.DataSet;
  import edu.cmu.tetrad.data.ICovarianceMatrix;
  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.NumberFormatUtil;
  import edu.cmu.tetrad.util.RandomUtil;
  import edu.cmu.tetrad.util.TetradLogger;
  import edu.cmu.tetrad.util.TetradMatrix;
  
  import java.text.NumberFormat;
  import java.util.ArrayList;
  import java.util.Arrays;
  import java.util.Collections;
  import java.util.List;
  
  /**
   * Checks independence of X _||_ Y | Z for variables X and Y and list Z of variables. Partial correlations are
   * calculated using generalized inverses, so linearly dependent variables do not throw exceptions. Must supply a
   * continuous data set; don't know how to do this with covariance or correlation matrices.
   *
   * @author Joseph Ramsey
   * @author Frank Wimberly adapted IndTestCramerT for Fisher's Z
   */
  public final class IndTestRegression implements IndependenceTest {
  
      /**
       * The correlation matrix.
       */
      private final DoubleMatrix2D data;
  
      /**
       * The variables of the correlation matrix, in order. (Unmodifiable list.)
       */
      private final List<Node> variables;
  
      /**
       * The significance level of the independence tests.
       */
      private double alpha;
  
      /**
       * The cutoff value for 'alpha' area in the two tails of the partial correlation distribution function.
       */
      private double thresh = Double.NaN;
  
      /**
       * The last calculated partial correlation, needed to calculate relative strength.
       */
      private double storedR = 0.;
  
      /**
       * The value of the Fisher's Z statistic associated with the las calculated partial correlation.
       */
      private double fishersZ;
  
      /**
       * The standard number formatter for Tetrad.
       */
      private static NumberFormat nf = NumberFormatUtil.getInstance().getNumberFormat();
      private DataSet dataSet;
      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 IndTestRegression(DataSet dataSet, double alpha) {
          if (!(alpha >= 0 && alpha <= 1)) {
              throw new IllegalArgumentException("Alpha mut be in [0, 1]");
          }
  
          this.dataSet = dataSet;
          this.data = new DenseDoubleMatrix2D(dataSet.getDoubleData().toArray());
          this.variables = Collections.unmodifiableList(dataSet.getVariables());
          setAlpha(alpha);
      }
  
      //==========================PUBLIC METHODS=============================//
  
      /**
       * Creates a new IndTestCramerT instance for a subset of the variables.
       */
      public IndependenceTest indTestSubset(List vars) {
  //        if (vars.isEmpty()) {
  //            throw new IllegalArgumentException("Subset may not be empty.");
  //        }
  //
  //        for (int i = 0; i < vars.size(); i++) {
  //            if (!variables.contains(vars.get(i))) {
  //                throw new IllegalArgumentException(
  //                        "All vars must be original vars");
  //            }
  //        }
  //
  //        double[][] m = new double[vars.size()][vars.size()];
  //
  //        for (int i = 0; i < vars.size(); i++) {
  //            for (int j = 0; j < vars.size(); j++) {
  //                double val = data.getValue(variables.indexOf(vars.get(i)),
  //                        variables.indexOf(vars.get(j)));
  //                m[i][j] = val;
  //            }
  //        }
  //
  //        int sampleSize = covMatrix().getN();
  //        CorrelationMatrix newCorrMatrix = new CorrelationMatrix(vars, m,
  //                sampleSize);
  //
  //        double alphaNew = getAlternativePenalty();
  //        IndependenceTest newIndTest = new IndTestCramerT(newCorrMatrix,
  //                alphaNew);
  //        return newIndTest;
  //
          return null;
      }
  
      /**
       * Determines whether variable x is independent of variable y given a list of conditioning variables z.
       *
       * @param xVar  the one variable being compared.
       * @param yVar  the second variable being compared.
       * @param zList the list of conditioning variables.
       * @return true iff x _||_ y | z.
       * @throws RuntimeException if a matrix singularity is encountered.
       */
      public boolean isIndependent(Node xVar, Node yVar, List<Node> zList) {
          if (zList == null) {
              throw new NullPointerException();
          }
  
          for (Node node : zList) {
              if (node == null) {
                  throw new NullPointerException();
              }
          }
  
          List<Node> regressors = new ArrayList<>();
          regressors.add(dataSet.getVariable(yVar.getName()));
  
          for (Node zVar : zList) {
              regressors.add(dataSet.getVariable(zVar.getName()));
          }
  
          Regression regression = new RegressionDataset(dataSet);
          RegressionResult result = null;
  
          try {
              result = regression.regress(xVar, regressors);
          } catch (Exception e) {
              return false;
          }
  
          double p = result.getP()[1];
  
          boolean independent = p > alpha;
  
          if (verbose) {
              if (independent) {
                  TetradLogger.getInstance().log("independencies", SearchLogUtils.independenceFactMsg(xVar, yVar, zList, p));
              } else {
                  TetradLogger.getInstance().log("dependencies", SearchLogUtils.dependenceFactMsg(xVar, yVar, zList, p));
              }
          }
  
  
          return independent;
      }
  
      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 2.0 * (1.0 - RandomUtil.getInstance().normalCdf(0, 1, Math.abs(fishersZ)));
      }
  
      /**
       * 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) {
          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 variable : variables) {
              variableNames.add(variable.getName());
          }
  
          return variableNames;
      }
  
      public String toString() {
          return "Linear Regression Test, alpha = " + nf.format(getAlpha());
      }
  
      //==========================PRIVATE METHODS============================//
  
  //    /**
  //     * Return the p-value of the last calculated independence fact.
  //     *
  //     * @return this p-value.  When accessed through the IndependenceChecker
  //     *         interface, this p-value should only be considered to be a
  //     *         relative strength.
  //     */
  //    private double getRelativeStrength() {
  //
  //        // precondition:  pdf is the most recently used partial
  //        // correlation distribution function, and storedR is the most
  //        // recently calculated partial correlation.
  //        return 2.0 * Integrator.getArea(npdf, Math.abs(storedR), 9.0, 100);
  //    }
  
  //    /**
  //     * Computes that value x such that P(abs(N(0,1) > x) < alpha.  Note that
  //     * this is a two sided test of the null hypothesis that the Fisher's Z
  //     * value, which is distributed as N(0,1) is not equal to 0.0.
  //     */
  //    private double cutoffGaussian() {
  //        npdf = new NormalPdf();
  //        final double upperBound = 9.0;
  //        final double delta = 0.001;
  //        //        double alpha = this.alpha/2.0;    //Two sided test
  //        return CutoffFinder.getCutoff(npdf, upperBound, alpha, delta);
  //    }
  
  //    private int sampleSize() {
  //        return data.rows();
  //    }
  
      public boolean determines(List<Node> zList, Node xVar) {
          if (zList == null) {
              throw new NullPointerException();
          }
  
          for (Node node : zList) {
              if (node == null) {
                  throw new NullPointerException();
              }
          }
  
          int size = zList.size();
          int[] zCols = new int[size];
  
          int xIndex = getVariables().indexOf(xVar);
  
          for (int i = 0; i < zList.size(); i++) {
              zCols[i] = getVariables().indexOf(zList.get(i));
          }
  
          int[] zRows = new int[data.rows()];
          for (int i = 0; i < data.rows(); i++) {
              zRows[i] = i;
          }
  
          DoubleMatrix2D Z = data.viewSelection(zRows, zCols);
          DoubleMatrix1D x = data.viewColumn(xIndex);
          DoubleMatrix2D Zt = new Algebra().transpose(Z);
          DoubleMatrix2D ZtZ = new Algebra().mult(Zt, Z);
          DoubleMatrix2D G = new DenseDoubleMatrix2D(new TetradMatrix(ZtZ.toArray()).inverse().toArray());
  
          // Bug in Colt? Need to make a copy before multiplying to avoid
          // a ClassCastException.
          DoubleMatrix2D Zt2 = Zt.like();
          Zt2.assign(Zt);
          DoubleMatrix2D GZt = new Algebra().mult(G, Zt2);
  
          DoubleMatrix1D b_x = new Algebra().mult(GZt, x);
  
          DoubleMatrix1D xPred = new Algebra().mult(Z, b_x);
  
          DoubleMatrix1D xRes = xPred.copy().assign(x, Functions.minus);
  
          double SSE = xRes.aggregate(Functions.plus, Functions.square);
          boolean determined = SSE < 0.0001;
  
          if (determined) {
              StringBuilder sb = new StringBuilder();
              sb.append("Determination found: ").append(xVar).append(
                      " is determined by {");
  
              for (int i = 0; i < zList.size(); i++) {
                  sb.append(zList.get(i));
  
                  if (i < zList.size() - 1) {
                      sb.append(", ");
                  }
              }
  
              sb.append("}");
  
              TetradLogger.getInstance().log("independencies", sb.toString());
          }
  
          return determined;
      }
  
      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();
      }
  
      public boolean isVerbose() {
          return verbose;
      }
  
      public void setVerbose(boolean verbose) {
          this.verbose = verbose;
      }
  }
  
  
  
  
  