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.graph.Node;
  import edu.cmu.tetrad.util.TetradMatrix;
  import edu.cmu.tetrad.util.TetradVector;
  import org.apache.commons.math3.linear.LUDecomposition;
  import org.apache.commons.math3.linear.RealMatrix;
  import org.apache.commons.math3.stat.correlation.Covariance;
  import org.apache.commons.math3.util.FastMath;
  
  import java.util.ArrayList;
  import java.util.List;
  
  import static java.lang.Math.PI;
  import static java.lang.Math.log;
  
  /**
   * Implements the continuous BIC score for FGS.
   *
   * @author Joseph Ramsey
   */
  public class SemBicScoreImages3 implements ISemBicScore, Score {
  
      // The variables of the covariance matrix.
      private List<Node> variables;
  
      // Sample sizes of each data set.
      private int[] sampleSizes;
  
      // Total sample size.
      private final int N;
  
      // The penalty penaltyDiscount.
      private double penaltyDiscount = 1.0;
  
      // True if verbose output should be sent to out.
      private boolean verbose = false;
  
      // Covariances for each of the input data sets.
      private List<TetradMatrix> covs = new ArrayList<>();
  
      /**
       * Constructs the score using a covariance matrix.
       */
      public SemBicScoreImages3(List<DataSet> dataSets) {
          sampleSizes = new int[dataSets.size()];
          int N = 0;
  
          for (int i = 0; i < dataSets.size(); i++) {
              DataSet dataSet = dataSets.get(i);
              covs.add(cov(dataSet));
              sampleSizes[i] = dataSet.getNumRows();
              N += sampleSizes[i];
          }
  
          this.variables = dataSets.get(0).getVariables();
          this.N = N;
      }
  
      @Override
      public double localScoreDiff(int x, int y, int[] z) {
          return localScore(y, append(z, x)) - localScore(y, z);
      }
  
      @Override
      public double localScoreDiff(int x, int y) {
          return localScore(y, x) - localScore(y);
      }
  
      /**
       * Calculates the sample likelihood and BIC score for i given its parents in a simple SEM model
       */
      public double localScore(int i, int... parents) {
          return score1(i, parents);
      }
  
      /**
       * Specialized scoring method for a single parent. Used to speed up the effect edges search.
       */
      public double localScore(int i, int parent) {
          return localScore(i, new int[]{parent});
      }
  
      /**
       * Specialized scoring method for no parents. Used to speed up the effect edges search.
       */
      public double localScore(int i) {
          return localScore(i, new int[0]);
      }
  
      public double getPenaltyDiscount() {
          return penaltyDiscount;
      }
  
      @Override
      public boolean isEffectEdge(double bump) {
          return bump > -0.25 * getPenaltyDiscount() * log(N);
      }
  
      public DataSet getDataSet() {
          throw new UnsupportedOperationException();
      }
  
      public boolean isVerbose() {
          return verbose;
      }
  
      public void setVerbose(boolean verbose) {
          this.verbose = verbose;
      }
  
      @Override
      public List<Node> getVariables() {
          return variables;
      }
  
      public boolean getAlternativePenalty() {
          return false;
      }
  
      public void setAlternativePenalty(double alpha) {
          //
      }
  
      @Override
      public void setPenaltyDiscount(double value) {
          this.penaltyDiscount = value;
      }
  
      @Override
      public int getSampleSize() {
          return N;
      }
  
  
      @Override
      public Node getVariable(String targetName) {
          for (Node node : variables) {
              if (node.getName().equals(targetName)) {
                  return node;
              }
          }
  
          return null;
      }
  
      @Override
      public int getMaxDegree() {
          return 1000;
      }
  
      @Override
      public boolean determines(List<Node> z, Node y) {
          return false;
      }
  
      private double score1(int i, int[] parents) {
          int p = parents.length;
  
          double lik = 0.0;
          int dof = 0;
  
          for (int k = 0; k < covs.size(); k++) {
              TetradMatrix cov = covs.get(k);
              int[] parentsPlus = append(parents, i);
              final int a = sampleSizes[k];
              final double lik1 = gaussianLikelihood(cov.getSelection(parentsPlus, parentsPlus), a);
              final double lik2 = gaussianLikelihood(cov.getSelection(parents, parents), a);
              lik += lik1 - lik2;
              dof += p + 1;
          }
  
          return 2.0 * lik - getPenaltyDiscount() * dof * log(N); //getPriorForStructure(p, 2);
      }
  
      public double score2(int i, int[] parents) {
          double lik = 0.0;
  
          for (int k = 0; k < covs.size(); k++) {
              final int a = sampleSizes[k];
              TetradMatrix cov = covs.get(k);
              double residualVariance = cov.get(i, i);
              TetradMatrix covxx = cov.getSelection(parents, parents);
              TetradMatrix covxxInv = covxx.inverse();
              TetradVector covxy = cov.getSelection(parents, new int[]{i}).getColumn(0);
              TetradVector b = covxxInv.times(covxy);
              residualVariance -= covxy.dotProduct(b);
              lik += - (a / 2.0) * log(residualVariance) - (a / 2.0) - (a / 2.0) * log(2 * PI);
          }
  
  //        System.out.println(lik);
  
          return 2.0 * lik - getPenaltyDiscount() * (parents.length + 1) * log(N);
      }
  
      private TetradMatrix cov(DataSet x) {
          TetradMatrix M = x.getDoubleData();
          RealMatrix covarianceMatrix = new Covariance(M.getRealMatrix(), true).getCovarianceMatrix();
          return new TetradMatrix(covarianceMatrix, covarianceMatrix.getRowDimension(), covarianceMatrix.getColumnDimension());
      }
  
      private int h(int p) {
          return p * (p + 1) / 2;
      }
  
      private double getPriorForStructure(int numParents, double e) {
          int vm = variables.size() - 1;
          return numParents * log(e / (vm)) + (vm - numParents) * log(1.0 - (e / (vm)));
      }
  
      private double gaussianLikelihood(TetradMatrix sigma, int n) {
          if (sigma.columns() == 0 || n == 0) return 0;
          int k = sigma.columns();
          return -0.5 * n * log(sigma.det()) - 0.5 * n * k - 0.5 * n * k * log(2.0 * PI);
      }
  
      private double logdet(TetradMatrix m) {
          RealMatrix M = m.getRealMatrix();
          final double tol = 1e-9;
          RealMatrix LT = new org.apache.commons.math3.linear.CholeskyDecomposition(M, tol, tol).getLT();
  
          double sum = 0.0;
  
          for (int i = 0; i < LT.getRowDimension(); i++) {
              sum += FastMath.log(LT.getEntry(i, i));
          }
  
          return 2.0 * sum;
      }
  
      private double logdet2(TetradMatrix m) {
          if (m.rows() == 0) return 0.0;
  
          RealMatrix M = m.getRealMatrix();
          final LUDecomposition luDecomposition = new LUDecomposition(M);
          RealMatrix L = luDecomposition.getL();
          RealMatrix U = luDecomposition.getU();
          RealMatrix P = luDecomposition.getP();
  
  //        System.out.println(new TetradMatrix(L.multiply(U)));
  //        System.out.println(new TetradMatrix(m));
  //        System.out.println(new TetradMatrix(L));
  //        System.out.println(new TetradMatrix(U));
  //        System.out.println(new TetradMatrix(P));
  
          double sum = 0.0;
  
          for (int i = 0; i < L.getRowDimension(); i++) {
              sum += FastMath.log(L.getEntry(i, i));
          }
  
          for (int i = 0; i < U.getRowDimension(); i++) {
              sum += FastMath.log(U.getEntry(i, i));
          }
  
  //        for (int i = 0; i < P.getRowDimension(); i++) {
  //            sum += log(P.getEntry(i, i));
  //        }
  
          return sum;
      }
  
      private int[] append(int[] parents, int i) {
          int[] all = new int[parents.length + 1];
          System.arraycopy(parents, 0, all, 0, parents.length);
          all[all.length - 1] = i;
          return all;
      }
  }
  
  
  
  