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.data;
  
  //import cern.colt.matrix.DoubleMatrix2D;
  import edu.cmu.tetrad.graph.Node;
  import edu.cmu.tetrad.util.*;
  import java.io.IOException;
  import java.io.ObjectInputStream;
  import java.text.NumberFormat;
  import java.util.*;
  import java.util.concurrent.RecursiveTask;
  import java.util.stream.Collectors;
  import org.apache.commons.math3.linear.RealMatrix;
  
  /**
   * Stores a covariance matrix together with variable names and sample size,
   * intended as a representation of a data set. When constructed from a
   * continuous data set, the matrix is not checked for positive definiteness;
   * however, when a covariance matrix is supplied, its positive definiteness is
   * always checked. If the sample size is less than the number of variables, the
   * positive definiteness is "spot-checked"--that is, checked for various
   * submatrices.
   *
   * @author Joseph Ramsey jdramsey@andrew.cmu.edu
   * @see edu.cmu.tetrad.data.CorrelationMatrix
   */
  public class CovarianceMatrix implements ICovarianceMatrix {
  
      static final long serialVersionUID = 23L;
  
      /**
       * The name of the covariance matrix.
       *
       * @serial May be null.
       */
      private String name;
  
      /**
       * The variables (in order) for this covariance matrix.
       *
       * @serial Cannot be null.
       */
      private List<Node> variables;
  
      /**
       * The size of the sample from which this covariance matrix was calculated.
       *
       * @serial Range > 0.
       */
      private int sampleSize;
  
      /**
       * Stored matrix data. Should be square. This may be set by derived classes,
       * but it must always be set to a legitimate covariance matrix.
       *
       * @serial Cannot be null. Must be symmetric and positive definite.
       */
      private TetradMatrix matrix;
  
      /**
       * The list of selected variables.
       *
       * @serial Cannot be null.
       */
      private Set<Node> selectedVariables = new HashSet<>();
  
      /**
       * The knowledge for this data.
       *
       * @serial Cannot be null.
       */
      private IKnowledge knowledge = new Knowledge2();
  
      private double[][] vectors = null;
  
      //=============================CONSTRUCTORS=========================//
      /**
       * Constructs a new covariance matrix from the given data set.
       *
       * @throws IllegalArgumentException if this is not a continuous data set.
       */
      public CovarianceMatrix(DataSet dataSet) {
          if (!dataSet.isContinuous()) {
              throw new IllegalArgumentException("Not a continuous data set.");
          }
  
          this.matrix = new TetradMatrix(dataSet.getNumColumns(), dataSet.getNumColumns());
  
          this.variables = Collections.unmodifiableList(dataSet.getVariables());
          this.sampleSize = dataSet.getNumRows();
  
          if (dataSet instanceof BoxDataSet) {
  
              DataBox box = ((BoxDataSet) dataSet).getDataBox().copy();
  
              if (box instanceof VerticalDoubleDataBox) {
                  if (!dataSet.getVariables().equals(variables)) {
                      throw new IllegalArgumentException();
                  }
  
                  vectors = ((VerticalDoubleDataBox) box).getVariableVectors();
  
  //                final TetradMatrix doubleData = dataSet.getDoubleData();
  //                DataUtils.remean(doubleData, means);
              }
  
          }
  
          if (vectors == null) {
              final TetradMatrix doubleData = dataSet.getDoubleData().copy();
              TetradVector means = DataUtils.means(doubleData);
              DataUtils.demean(doubleData, means);
  
              final RealMatrix realMatrix = doubleData.getRealMatrix();
  
              vectors = new double[variables.size()][];
  
              for (int i = 0; i < variables.size(); i++) {
                  vectors[i] = realMatrix.getColumnVector(i).toArray();
              }
          }
  
          TetradVector means = DataUtils.means(vectors);
  
          int NTHREADS = Runtime.getRuntime().availableProcessors() * 10;
          int _chunk = variables.size() / NTHREADS + 1;
          int minChunk = 100;
          final int chunk = _chunk < minChunk ? minChunk : _chunk;
  
          class VarianceTask extends RecursiveTask<Boolean> {
  
              private int chunk;
              private int from;
              private int to;
  
              public VarianceTask(int chunk, int from, int to) {
                  this.chunk = chunk;
                  this.from = from;
                  this.to = to;
              }
  
              @Override
              protected Boolean compute() {
                  if (to - from <= chunk) {
                      for (int i = from; i < to; i++) {
                          double d = 0.0D;
  
                          int count = 0;
  
                          double[] v1 = vectors[i];
  
                          for (int k = 0; k < sampleSize; ++k) {
                              if (Double.isNaN(v1[k])) {
                                  continue;
                              }
  
                              d += v1[k] * v1[k];
                              count++;
                          }
  
                          double v = d;
                          v /= (count - 1);
  
                          matrix.set(i, i, v);
  
                          if (v == 0) {
                              System.out.println("    Zero variance! " + variables.get(i));
                          }
                      }
  
                      return true;
                  } else {
                      int mid = (to + from) / 2;
  
                      VarianceTask left = new VarianceTask(chunk, from, mid);
                      VarianceTask right = new VarianceTask(chunk, mid, to);
  
                      left.fork();
                      right.compute();
                      left.join();
  
                      return true;
                  }
              }
          }
  
          class RestOfThemTask extends RecursiveTask<Boolean> {
  
              private int chunk;
              private int from;
              private int to;
  
              public RestOfThemTask(int chunk, int from, int to) {
                  this.chunk = chunk;
                  this.from = from;
                  this.to = to;
              }
  
              @Override
              protected Boolean compute() {
                  if (to - from <= chunk) {
                      for (int i = from; i < to; i++) {
                          for (int j = 0; j < i; j++) {
  
                              double d = 0.0D;
  
                              double[] v1 = vectors[i];
                              double[] v2 = vectors[j];
                              int count = 0;
  
                              for (int k = 0; k < sampleSize; k++) {
                                  if (Double.isNaN(v1[k])) {
                                      continue;
                                  }
                                  if (Double.isNaN(v2[k])) {
                                      continue;
                                  }
  
                                  d += v1[k] * v2[k];
                                  count++;
                              }
  
                              double v = d;
                              v /= (count - 1);
  
                              matrix.set(i, j, v);
                              matrix.set(j, i, v);
                          }
                      }
  
                      return true;
                  } else {
                      int mid = (to + from) / 2;
  
                      RestOfThemTask left = new RestOfThemTask(chunk, from, mid);
                      RestOfThemTask right = new RestOfThemTask(chunk, mid, to);
  
                      left.fork();
                      right.compute();
                      left.join();
  
                      return true;
                  }
              }
          }
  
          VarianceTask task = new VarianceTask(chunk, 0, variables.size());
          ForkJoinPoolInstance.getInstance().getPool().invoke(task);
  
          RestOfThemTask task2 = new RestOfThemTask(chunk, 0, variables.size());
          ForkJoinPoolInstance.getInstance().getPool().invoke(task2);
  
          DataUtils.demean(vectors, means);
  
          this.variables = Collections.unmodifiableList(dataSet.getVariables());
          this.sampleSize = dataSet.getNumRows();
      }
  
      /**
       * Protected constructor to construct a new covariance matrix using the
       * supplied continuous variables and the the given symmetric, positive
       * definite matrix and sample size. The number of variables must equal the
       * dimension of the array.
       *
       * @param variables the list of variables (in order) for the covariance
       * matrix.
       * @param matrix an square array of containing covariances.
       * @param sampleSize the sample size of the data for these covariances.
       * @throws IllegalArgumentException if the given matrix is not symmetric (to
       * a tolerance of 1.e-5) and positive definite, if the number of variables
       * does not equal the dimension of m, or if the sample size is not positive.
       */
      public CovarianceMatrix(List<Node> variables, TetradMatrix matrix,
              int sampleSize) {
          if (variables.size() != matrix.rows() && variables.size() != matrix.columns()) {
              throw new IllegalArgumentException("# variables not equal to matrix dimension.");
          }
  
          this.variables = Collections.unmodifiableList(variables);
          this.sampleSize = sampleSize;
          this.matrix = matrix;
          checkMatrix();
      }
  
      /**
       * Copy constructor.
       */
      public CovarianceMatrix(CovarianceMatrix covMatrix) {
          this(covMatrix.variables, covMatrix.matrix,
                  covMatrix.sampleSize);
      }
  
      public CovarianceMatrix(ICovarianceMatrix covMatrix) {
          this(covMatrix.getVariables(), covMatrix.getMatrix(),
                  covMatrix.getSampleSize());
      }
  
      /**
       * Generates a simple exemplar of this class to test serialization.
       */
      public static ICovarianceMatrix serializableInstance() {
          List<Node> variables = new ArrayList<>();
          Node x = new ContinuousVariable("X");
          variables.add(x);
          TetradMatrix matrix = TetradAlgebra.identity(1);
          return new CovarianceMatrix(variables, matrix, 100);
      }
  
      //============================PUBLIC METHODS=========================//
      /**
       * @return the list of variables (unmodifiable).
       */
      public final List<Node> getVariables() {
          return this.variables;
      }
  
      /**
       * @return the variable names, in order.
       */
      public final List<String> getVariableNames() {
          List<String> names = new ArrayList<>();
  
          for (int i = 0; i < getVariables().size(); i++) {
              Node variable = getVariables().get(i);
              names.add(variable.getName());
          }
  
          return names;
      }
  
      /**
       * @return the variable name at the given index.
       */
      public final String getVariableName(int index) {
          if (index >= getVariables().size()) {
              throw new IllegalArgumentException("Index out of range: " + index);
          }
  
          Node variable = getVariables().get(index);
          return variable.getName();
      }
  
      /**
       * @return the dimension of the covariance matrix.
       */
      public final int getDimension() {
          return variables.size();
      }
  
      /**
       * The size of the sample used to calculated this covariance matrix.
       *
       * @return The sample size (> 0).
       */
      public final int getSampleSize() {
          return this.sampleSize;
      }
  
      /**
       * Gets the name of the covariance matrix.
       */
      public final String getName() {
          return this.name;
      }
  
      /**
       * Sets the name of the covariance matrix.
       */
      public final void setName(String name) {
          this.name = name;
      }
  
      /**
       * @return the knowledge associated with this data.
       */
      public final IKnowledge getKnowledge() {
          return this.knowledge.copy();
      }
  
      /**
       * Associates knowledge with this data.
       */
      public final void setKnowledge(IKnowledge knowledge) {
          if (knowledge == null) {
              throw new NullPointerException();
          }
  
          this.knowledge = knowledge.copy();
      }
  
      /**
       * @return a submatrix of the covariance matrix with variables in the given
       * order.
       */
      public final ICovarianceMatrix getSubmatrix(int[] indices) {
          List<Node> submatrixVars = new LinkedList<>();
  
          for (int indice : indices) {
              submatrixVars.add(variables.get(indice));
          }
  
          TetradMatrix cov = matrix.getSelection(indices, indices);
          return new CovarianceMatrix(submatrixVars, cov, getSampleSize());
      }
  
      public final ICovarianceMatrix getSubmatrix(List<String> submatrixVarNames) {
          String[] varNames = new String[submatrixVarNames.size()];
  
          for (int i = 0; i < submatrixVarNames.size(); i++) {
              varNames[i] = submatrixVarNames.get(i);
          }
  
          return getSubmatrix(varNames);
      }
  
      /**
       * @return a submatrix of this matrix, with variables in the given order.
       */
      public final CovarianceMatrix getSubmatrix(String[] submatrixVarNames) {
          List<Node> submatrixVars = new LinkedList<>();
  
          for (String submatrixVarName : submatrixVarNames) {
              submatrixVars.add(getVariable(submatrixVarName));
          }
  
          if (!getVariables().containsAll(submatrixVars)) {
              throw new IllegalArgumentException(
                      "The variables in the submatrix "
                      + "must be in the original matrix: original=="
                      + getVariables() + ", sub==" + submatrixVars);
          }
  
          for (int i = 0; i < submatrixVars.size(); i++) {
              if (submatrixVars.get(i) == null) {
                  throw new NullPointerException(
                          "The variable name at index " + i + " is null.");
              }
          }
  
          int[] indices = new int[submatrixVars.size()];
          for (int i = 0; i < indices.length; i++) {
              indices[i] = getVariables().indexOf(submatrixVars.get(i));
          }
  
          TetradMatrix cov = matrix.getSelection(indices, indices);
          return new CovarianceMatrix(submatrixVars, cov, getSampleSize());
      }
  
      /**
       * @return the value of element (i,j) in the matrix
       */
      public final double getValue(int i, int j) {
          return matrix.get(i, j);
      }
  
      public void setMatrix(TetradMatrix matrix) {
          this.matrix = matrix;
          checkMatrix();
      }
  
      public final void setSampleSize(int sampleSize) {
          if (sampleSize <= 0) {
              throw new IllegalArgumentException("Sample size must be > 0.");
          }
  
          this.sampleSize = sampleSize;
      }
  
      /**
       * @return the size of the square matrix.
       */
      public final int getSize() {
          return matrix.rows();
      }
  
      /**
       * @return a the covariance matrix (not a copy).
       */
      public final TetradMatrix getMatrix() {
          return matrix;
      }
  
      public final void select(Node variable) {
          if (variables.contains(variable)) {
              getSelectedVariables().add(variable);
          }
      }
  
      public final void clearSelection() {
          getSelectedVariables().clear();
      }
  
      public final boolean isSelected(Node variable) {
          if (variable == null) {
              throw new NullPointerException("Null variable. Try again.");
          }
  
          return getSelectedVariables().contains(variable);
      }
  
      public final List<String> getSelectedVariableNames() {
          List<String> selectedVariableNames = new LinkedList<>();
  
          for (Node variable : selectedVariables) {
              selectedVariableNames.add(variable.getName());
          }
  
          return selectedVariableNames;
      }
  
      /**
       * Prints out the matrix
       */
      public final String toString() {
          NumberFormat nf = NumberFormatUtil.getInstance().getNumberFormat();
  
          StringBuilder buf = new StringBuilder();
  
          // Build the variable names
          buf.append(getVariableNames().stream().collect(Collectors.joining("\t")));
  
          int numVars = getVariableNames().size();
          buf.append("\n");
  
          for (int j = 0; j < numVars; j++) {
              for (int i = 0; i <= j; i++) {
                  buf.append(nf.format(getValue(i, j)));
  
                  // Don't add ending tab to each data line, data reader will validate this extra tab as missing value
                  // This is the fix to issue #525: https://github.com/cmu-phil/tetrad/issues/525
                  if (i < j) {
                      buf.append("\t");
                  }
              }
              buf.append("\n");
          }
  
  //        buf.append("\nCovariance matrix:");
  //        buf.append("\n\tVariables = ").append(getVariable());
  //        buf.append("\n\tSample size = ").append(getSampleSize());
  //        buf.append("\n");
  //        buf.append(MatrixUtils.toString(matrixC.toArray()));
  //
  //        if (getKnowledge() != null && !getKnowledge().isEmpty()) {
  //            buf.append(getKnowledge());
  //        }
          return buf.toString();
      }
  
      @Override
      public boolean isContinuous() {
          return true;
      }
  
      @Override
      public boolean isDiscrete() {
          return false;
      }
  
      @Override
      public boolean isMixed() {
          return false;
      }
  
      public void setVariables(List<Node> variables) {
          if (variables.size() != this.variables.size()) {
              throw new IllegalArgumentException("Wrong # of variables.");
          }
          for (int i = 0; i < variables.size(); i++) {
              if (!variables.get(i).getName().equals(variables.get(i).getName())) {
                  throw new IllegalArgumentException("Variable in index " + (i + 1) + " does not have the same name "
                          + "as the variable being substituted for it.");
              }
              this.variables = variables;
          }
      }
  
      @Override
      public TetradMatrix getSelection(int[] rows, int[] cols) {
          return matrix.getSelection(rows, cols);
      }
  
      //========================PRIVATE METHODS============================//
      public Node getVariable(String name) {
          for (int i = 0; i < getVariables().size(); i++) {
              Node variable = getVariables().get(i);
              if (name.equals(variable.getName())) {
                  return variable;
              }
          }
  
          return null;
      }
  
      @Override
      public DataModel copy() {
          return null;
      }
  
      @Override
      public void setValue(int i, int j, double v) {
          if (i == j) {
              matrix.set(i, j, v);
          } else {
              matrix.set(i, j, v);
              matrix.set(j, i, v);
          }
      }
  
      @Override
      public void removeVariables(List<String> remaining) {
          ICovarianceMatrix cov = getSubmatrix(remaining);
          this.matrix = cov.getMatrix();
          this.variables = cov.getVariables();
          clearSelection();
      }
  
      private Set<Node> getSelectedVariables() {
          return selectedVariables;
      }
  
      /**
       * Checks the sample size, variable, and matrix information.
       */
      private void checkMatrix() {
          for (Node variable : variables) {
              if (variable == null) {
                  throw new NullPointerException();
              }
          }
  
          if (sampleSize < 1) {
              throw new IllegalArgumentException(
                      "Sample size must be at least 1.");
          }
  
  //        for (int i = 0; i < matrix.rows(); i++) {
  //            for (int j = 0; j < matrix.columns(); j++) {
  //                if (Double.isNaN(matrix.get(i, j))) {
  //                    throw new IllegalArgumentException("Please remove or impute missing values.");
  //                }
  //            }
  //        }
      }
  
      /**
       * Adds semantic checks to the default deserialization method. This method
       * must have the standard signature for a readObject method, and the body of
       * the method must begin with "s.defaultReadObject();". Other than that, any
       * semantic checks can be specified and do not need to stay the same from
       * version to version. A readObject method of this form may be added to any
       * class, even if Tetrad sessions were previously saved out using a version
       * of the class that didn't include it. (That's what the
       * "s.defaultReadObject();" is for. See J. Bloch, Effective Java, for help.
       *
       * @throws java.io.IOException
       * @throws ClassNotFoundException
       */
      private void readObject(ObjectInputStream s)
              throws IOException, ClassNotFoundException {
          s.defaultReadObject();
  
          if (getVariables() == null) {
              throw new NullPointerException();
          }
  
  //        if (matrixC != null) {
  //            matrix = new TetradMatrix(matrixC.toArray());
  //            matrixC = null;
  //        }
          if (knowledge == null) {
              throw new NullPointerException();
          }
  
          if (sampleSize < -1) {
              throw new IllegalStateException();
          }
  
          if (selectedVariables == null) {
              selectedVariables = new HashSet<>();
          }
      }
  }
  