/*
 * Copyright 2011 Sandia Corporation.
 * Under the terms of Contract DE-AC04-94AL85000, there is a non-exclusive
 * license for use of this work by or on behalf of the
 * U.S. Government. Redistribution and use in source and binary forms, with
 * or without modification, are permitted provided that this Notice and any
 * statement of authorship are reproduced on all copies.
 */
// .SECTION Thanks
// Thanks to Philippe Pebay from Sandia National Laboratories
// for implementing this test.

#include "vtkCorrelativeStatistics.h"
#include "vtkDataObjectCollection.h"
#include "vtkDoubleArray.h"
#include "vtkMath.h"
#include "vtkMultiBlockDataSet.h"
#include "vtkStringArray.h"
#include "vtkTable.h"
#include "vtkTimerLog.h"

#include <sstream>

//=============================================================================
int TestCorrelativeStatistics(int, char*[])
{
  int testStatus = 0;

  double mingledData[] = {
    46,
    45,
    47,
    49,
    46,
    47,
    46,
    46,
    47,
    46,
    47,
    49,
    49,
    49,
    47,
    45,
    50,
    50,
    46,
    46,
    51,
    50,
    48,
    48,
    52,
    54,
    48,
    47,
    52,
    52,
    49,
    49,
    53,
    54,
    50,
    50,
    53,
    54,
    50,
    52,
    53,
    53,
    50,
    51,
    54,
    54,
    49,
    49,
    52,
    52,
    50,
    51,
    52,
    52,
    49,
    47,
    48,
    48,
    48,
    50,
    46,
    48,
    47,
    47,
  };
  int nVals1 = 32;

  vtkDoubleArray* dataset1Arr = vtkDoubleArray::New();
  dataset1Arr->SetNumberOfComponents(1);
  dataset1Arr->SetName("M0");

  vtkDoubleArray* dataset2Arr = vtkDoubleArray::New();
  dataset2Arr->SetNumberOfComponents(1);
  dataset2Arr->SetName("M1");

  vtkDoubleArray* dataset3Arr = vtkDoubleArray::New();
  dataset3Arr->SetNumberOfComponents(1);
  dataset3Arr->SetName("M2");

  for (int i = 0; i < nVals1; ++i)
  {
    int ti = i << 1;
    dataset1Arr->InsertNextValue(mingledData[ti]);
    dataset2Arr->InsertNextValue(mingledData[ti + 1]);
    dataset3Arr->InsertNextValue(-1.);
  }

  vtkTable* datasetTable1 = vtkTable::New();
  datasetTable1->AddColumn(dataset1Arr);
  dataset1Arr->Delete();
  datasetTable1->AddColumn(dataset2Arr);
  dataset2Arr->Delete();
  datasetTable1->AddColumn(dataset3Arr);
  dataset3Arr->Delete();

  // Pairs of interest
  int nMetricPairs = 2;
  vtkStdString columnPairs[] = {
    "M0", "M1", // First pair
    "M2", "M1"  // Second pair
  };

  // Reference values
  // Means and variances for metrics 0, and 1, respectively
  double meansX1[] = { 49.21875, 49.5 };
  double varsX1[] = { 5.9828629, 7.548397 };

  // Means and variances for metrics 1 and 2, respectively
  double meansY1[] = { 49.5, -1. };
  double varsY1[] = { 7.548397, 0. };

  // Covariance matrix of (metric 0, metric 1) and (metric 1, metric 2) pairs
  double covariances1[] = { 6.14516, 0. };

  // Pearson r for each of the pairs
  double correlations1[] = { 0.914433, vtkMath::Nan() };

  // Thresholds for outlier detection
  double threshold[] = { 4., 1.8, 1.8 };

  // Set correlative statistics algorithm and its input data port
  vtkCorrelativeStatistics* cs1 = vtkCorrelativeStatistics::New();

  // First verify that absence of input does not cause trouble
  cout << "## Verifying that absence of input does not cause trouble... ";
  cs1->Update();
  cout << "done.\n";

  // Prepare first test with data
  cs1->SetInputData(vtkStatisticsAlgorithm::INPUT_DATA, datasetTable1);
  datasetTable1->Delete();

  // Select Column Pairs of Interest ( Learn Mode )
  // 1.1: a valid pair
  cs1->AddColumnPair("M0", "M1");
  // 1.2: the same valid pair, just reversed -- should thus be ignored
  cs1->AddColumnPair("M1", "M0");
  // 2: another valid pair
  cs1->AddColumnPair("M2", "M1");
  // 3: an invalid pair
  cs1->AddColumnPair("M1", "M3");

  // Test Learn, Derive, Test, and Assess options
  cs1->SetLearnOption(true);
  cs1->SetDeriveOption(true);
  cs1->SetAssessOption(true);
  cs1->SetTestOption(true);
  cs1->Update();

  // Get output data and meta tables
  vtkTable* outputData1 = cs1->GetOutput(vtkStatisticsAlgorithm::OUTPUT_DATA);
  vtkMultiBlockDataSet* outputMetaDS1 = vtkMultiBlockDataSet::SafeDownCast(
    cs1->GetOutputDataObject(vtkStatisticsAlgorithm::OUTPUT_MODEL));
  vtkTable* outputPrimary1 = vtkTable::SafeDownCast(outputMetaDS1->GetBlock(0));
  vtkTable* outputDerived1 = vtkTable::SafeDownCast(outputMetaDS1->GetBlock(1));
  vtkTable* outputTest1 = cs1->GetOutput(vtkStatisticsAlgorithm::OUTPUT_TEST);

  cout << "## Calculated the following primary statistics for first data set:\n";
  for (vtkIdType r = 0; r < outputPrimary1->GetNumberOfRows(); ++r)
  {
    cout << "   ";
    for (int i = 0; i < outputPrimary1->GetNumberOfColumns(); ++i)
    {
      cout << outputPrimary1->GetColumnName(i) << "=" << outputPrimary1->GetValue(r, i).ToString()
           << "  ";
    }

    // Verify some of the calculated primary statistics
    double testMeanX = outputPrimary1->GetValueByName(r, "Mean X").ToDouble();
    if (fabs(testMeanX - meansX1[r]) > 1.e-6)
    {
      vtkGenericWarningMacro("Incorrect mean for X");
      testStatus = 1;
    }

    double testMeanY = outputPrimary1->GetValueByName(r, "Mean Y").ToDouble();
    if (fabs(testMeanY - meansY1[r]) > 1.e-6)
    {
      vtkGenericWarningMacro("Incorrect mean for Y");
      testStatus = 1;
    }
    cout << "\n";
  }

  cout << "\n## Calculated the following derived statistics for first data set:\n";
  for (vtkIdType r = 0; r < outputDerived1->GetNumberOfRows(); ++r)
  {
    cout << "   ";
    for (int i = 0; i < outputDerived1->GetNumberOfColumns(); ++i)
    {
      cout << outputDerived1->GetColumnName(i) << "=" << outputDerived1->GetValue(r, i).ToString()
           << "  ";
    }

    // Verify some of the calculated derived statistics
    double testMeanX = outputPrimary1->GetValueByName(r, "Mean X").ToDouble();
    double testMeanY = outputPrimary1->GetValueByName(r, "Mean Y").ToDouble();

    double testVarX = outputDerived1->GetValueByName(r, "Variance X").ToDouble();
    if (fabs(testVarX - varsX1[r]) > 1.e-5)
    {
      vtkGenericWarningMacro("Incorrect variance for X");
      testStatus = 1;
    }

    double testVarY = outputDerived1->GetValueByName(r, "Variance Y").ToDouble();
    if (fabs(testVarY - varsY1[r]) > 1.e-5)
    {
      vtkGenericWarningMacro("Incorrect variance for Y");
      testStatus = 1;
    }

    double testCovariance = outputDerived1->GetValueByName(r, "Covariance").ToDouble();
    if (fabs(testCovariance - covariances1[r]) > 1.e-5)
    {
      vtkGenericWarningMacro("Incorrect covariance");
      testStatus = 1;
    }

    double testPearsonR = outputDerived1->GetValueByName(r, "Pearson r").ToDouble();
    // Special treatment as some values of Pearson r are Nan, resulting in an exception on VS for <
    vtkTypeBool isNanTest = vtkMath::IsNan(testPearsonR);
    vtkTypeBool isNanCorr = vtkMath::IsNan(correlations1[r]);
    if (isNanTest || isNanCorr)
    {
      if (isNanTest != isNanCorr)
      {
        vtkGenericWarningMacro("Incorrect correlation coefficient");
        testStatus = 1;
      }
    }
    else if (fabs(testPearsonR - correlations1[r]) > 1.e-6)
    {
      vtkGenericWarningMacro("Incorrect correlation coefficient");
      testStatus = 1;
    }

    // Test regression lines if linear regression is valid
    if (outputDerived1->GetValueByName(r, "Linear Correlation").ToString() == "valid")
    {
      double testSlopeYX = outputDerived1->GetValueByName(r, "Slope Y/X").ToDouble();
      double testInterceptYX = outputDerived1->GetValueByName(r, "Intercept Y/X").ToDouble();
      if (fabs(testSlopeYX * testMeanX + testInterceptYX - testMeanY) > 1.e-8)
      {
        vtkGenericWarningMacro("Incorrect linear regression of Y on X");
        testStatus = 1;
      }

      double testSlopeXY = outputDerived1->GetValueByName(r, "Slope X/Y").ToDouble();
      double testInterceptXY = outputDerived1->GetValueByName(r, "Intercept X/Y").ToDouble();
      if (fabs(testSlopeXY * testMeanY + testInterceptXY - testMeanX) > 1.e-8)
      {
        vtkGenericWarningMacro("Incorrect linear regression of X on Y");
        testStatus = 1;
      }
    }

    cout << "\n";
  }

  // Check some results of the Test option
  cout << "\n## Calculated the following Jarque-Bera-Srivastava statistics:\n";
  for (vtkIdType r = 0; r < outputTest1->GetNumberOfRows(); ++r)
  {
    cout << "   ";
    for (int i = 0; i < outputTest1->GetNumberOfColumns(); ++i)
    {
      cout << outputTest1->GetColumnName(i) << "=" << outputTest1->GetValue(r, i).ToString()
           << "  ";
    }

    cout << "\n";
  }

  // Search for outliers to check results of Assess option
  cout << "\n## Searching for outliers with respect to various criteria:\n";
  int assessIdx[] = { 3, 4, 5 };
  int testIntValue[] = { 3, 3, 4 };
  for (int i = 0; i < 3; ++i)
  {
    cerr << "   For |" << outputData1->GetColumnName(assessIdx[i]) << "| > " << threshold[i]
         << ", found the following outliers:\n";

    int nOutliers = 0;

    for (vtkIdType r = 0; r < outputData1->GetNumberOfRows(); ++r)
    {
      double assessed = outputData1->GetValue(r, assessIdx[i]).ToDouble();
      if (fabs(assessed) > threshold[i])
      {
        ++nOutliers;

        cout << "     (" << outputData1->GetValueByName(r, columnPairs[0]).ToDouble() << ","
             << outputData1->GetValueByName(r, columnPairs[1]).ToDouble() << "): " << assessed
             << "\n";
      }
    } // r

    // Verify that number of found outliers is correct
    if (nOutliers != testIntValue[i])
    {
      vtkGenericWarningMacro(
        "Expected " << testIntValue[i] << " outliers, found " << nOutliers << ".");
      testStatus = 1;
    }
  }

  // Test with a slight variation of initial data set (to test model aggregation)
  int nVals2 = 32;

  vtkDoubleArray* dataset4Arr = vtkDoubleArray::New();
  dataset4Arr->SetNumberOfComponents(1);
  dataset4Arr->SetName("M0");

  vtkDoubleArray* dataset5Arr = vtkDoubleArray::New();
  dataset5Arr->SetNumberOfComponents(1);
  dataset5Arr->SetName("M1");

  vtkDoubleArray* dataset6Arr = vtkDoubleArray::New();
  dataset6Arr->SetNumberOfComponents(1);
  dataset6Arr->SetName("M2");

  for (int i = 0; i < nVals2; ++i)
  {
    int ti = i << 1;
    dataset4Arr->InsertNextValue(mingledData[ti] + 1.);
    dataset5Arr->InsertNextValue(mingledData[ti + 1]);
    dataset6Arr->InsertNextValue(1.);
  }

  vtkTable* datasetTable2 = vtkTable::New();
  datasetTable2->AddColumn(dataset4Arr);
  dataset4Arr->Delete();
  datasetTable2->AddColumn(dataset5Arr);
  dataset5Arr->Delete();
  datasetTable2->AddColumn(dataset6Arr);
  dataset6Arr->Delete();

  // Set correlative statistics algorithm and its input data port
  vtkCorrelativeStatistics* cs2 = vtkCorrelativeStatistics::New();
  cs2->SetInputData(vtkStatisticsAlgorithm::INPUT_DATA, datasetTable2);

  // Select all valid column pairs as pairs of interest
  for (int i = 0; i < nMetricPairs; ++i)
  {
    cs2->AddColumnPair(columnPairs[2 * i], columnPairs[2 * i + 1]);
  }

  // Update with Learn option only
  cs2->SetLearnOption(true);
  cs2->SetDeriveOption(false);
  cs2->SetTestOption(false);
  cs2->SetAssessOption(false);
  cs2->Update();

  // Get output meta tables
  vtkMultiBlockDataSet* outputMetaDS2 = vtkMultiBlockDataSet::SafeDownCast(
    cs2->GetOutputDataObject(vtkStatisticsAlgorithm::OUTPUT_MODEL));
  vtkTable* outputPrimary2 = vtkTable::SafeDownCast(outputMetaDS2->GetBlock(0));

  cout << "\n## Calculated the following primary statistics for second data set:\n";
  for (vtkIdType r = 0; r < outputPrimary2->GetNumberOfRows(); ++r)
  {
    cout << "   ";
    for (int i = 0; i < outputPrimary2->GetNumberOfColumns(); ++i)
    {
      cout << outputPrimary2->GetColumnName(i) << "=" << outputPrimary2->GetValue(r, i).ToString()
           << "  ";
    }
    cout << "\n";
  }

  // Test model aggregation by adding new data to engine which already has a model
  cs1->SetInputData(vtkStatisticsAlgorithm::INPUT_DATA, datasetTable2);
  vtkMultiBlockDataSet* model = vtkMultiBlockDataSet::New();
  model->ShallowCopy(outputMetaDS1);
  cs1->SetInputData(vtkStatisticsAlgorithm::INPUT_MODEL, model);

  // Clean up
  model->Delete();
  datasetTable2->Delete();
  cs2->Delete();

  // Update with Learn and Derive options only
  cs1->SetLearnOption(true);
  cs1->SetDeriveOption(true);
  cs1->SetTestOption(false);
  cs1->SetAssessOption(false);
  cs1->Update();

  // Updated reference values
  // Means and variances for metrics 0 and 1, respectively
  double meansX0[] = { 49.71875, 49.5 };
  double varsX0[] = { 6.1418651, 7.548397 * 62. / 63. };

  // Means and variances for metrics 1 and 2, respectively
  double meansY0[] = { 49.5, 0. };
  double varsY0[] = { 7.548397 * 62. / 63., 64. / 63. };

  // Pearson r for each of the two pairs
  double correlations0[] = { 0.895327, 0. };

  // Get output meta tables
  outputMetaDS1 = vtkMultiBlockDataSet::SafeDownCast(
    cs1->GetOutputDataObject(vtkStatisticsAlgorithm::OUTPUT_MODEL));
  outputPrimary1 = vtkTable::SafeDownCast(outputMetaDS1->GetBlock(0));
  outputDerived1 = vtkTable::SafeDownCast(outputMetaDS1->GetBlock(1));

  cout << "\n## Calculated the following primary statistics for aggregated (first + second) data "
          "set:\n";
  for (vtkIdType r = 0; r < outputPrimary1->GetNumberOfRows(); ++r)
  {
    cout << "   ";
    for (int i = 0; i < outputPrimary1->GetNumberOfColumns(); ++i)
    {
      cout << outputPrimary1->GetColumnName(i) << "=" << outputPrimary1->GetValue(r, i).ToString()
           << "  ";
    }

    // Verify some of the calculated primary statistics
    if (outputPrimary1->GetValueByName(r, "Cardinality").ToInt() != nVals1 + nVals2)
    {
      vtkGenericWarningMacro("Incorrect cardinality");
      testStatus = 1;
    }

    if (fabs(outputPrimary1->GetValueByName(r, "Mean X").ToDouble() - meansX0[r]) > 1.e-6)
    {
      vtkGenericWarningMacro("Incorrect mean for X");
      testStatus = 1;
    }

    if (fabs(outputPrimary1->GetValueByName(r, "Mean Y").ToDouble() - meansY0[r]) > 1.e-6)
    {
      vtkGenericWarningMacro("Incorrect mean for Y");
      testStatus = 1;
    }
    cout << "\n";
  }

  cout << "\n## Calculated the following derived statistics for aggregated (first + second) data "
          "set:\n";
  for (vtkIdType r = 0; r < outputDerived1->GetNumberOfRows(); ++r)
  {
    cout << "   ";
    for (int i = 0; i < outputDerived1->GetNumberOfColumns(); ++i)
    {
      cout << outputDerived1->GetColumnName(i) << "=" << outputDerived1->GetValue(r, i).ToString()
           << "  ";
    }

    // Verify some of the calculated derived statistics
    if (fabs(outputDerived1->GetValueByName(r, "Variance X").ToDouble() - varsX0[r]) > 1.e-5)
    {
      vtkGenericWarningMacro("Incorrect variance for X");
      testStatus = 1;
    }

    if (fabs(outputDerived1->GetValueByName(r, "Variance Y").ToDouble() - varsY0[r]) > 1.e-5)
    {
      vtkGenericWarningMacro("Incorrect variance for Y");
      testStatus = 1;
    }

    if (fabs(outputDerived1->GetValueByName(r, "Pearson r").ToDouble() - correlations0[r]) > 1.e-6)
    {
      vtkGenericWarningMacro("Incorrect correlation coefficient");
      testStatus = 1;
    }
    cout << "\n";
  }

  // Clean up
  cs1->Delete();

  // ************** Pseudo-random sample to exercise Jarque-Bera-Srivastava test *********
  int nVals = 10000;

  // Pre-set Pearson correlation coefficients
  double rhoXZ1 = .8; // X and Y1 are highly linearly correlated
  double rhoXZ2 = .2; // X and Y2 are weakly linearly correlated
  double rorXZ1 = sqrt(1. - rhoXZ1 * rhoXZ1);
  double rorXZ2 = sqrt(1. - rhoXZ2 * rhoXZ2);

  vtkDoubleArray* datasetNormalX = vtkDoubleArray::New();
  datasetNormalX->SetNumberOfComponents(1);
  datasetNormalX->SetName("N(0,1)_1");

  vtkDoubleArray* datasetNormalY = vtkDoubleArray::New();
  datasetNormalY->SetNumberOfComponents(1);
  datasetNormalY->SetName("N(0,1)_2");

  vtkDoubleArray* datasetNormalZ1 = vtkDoubleArray::New();
  datasetNormalZ1->SetNumberOfComponents(1);
  std::ostringstream z1Name;
  z1Name << rhoXZ1 << " N(0,1)_1 + " << rorXZ1 << " N(0,1)_2";
  datasetNormalZ1->SetName(z1Name.str().c_str());

  vtkDoubleArray* datasetNormalZ2 = vtkDoubleArray::New();
  datasetNormalZ2->SetNumberOfComponents(1);
  std::ostringstream z2Name;
  z2Name << rhoXZ2 << " N(0,1)_1 + " << rorXZ2 << " N(0,1)_2";
  datasetNormalZ2->SetName(z2Name.str().c_str());

  vtkDoubleArray* datasetNormalZ3 = vtkDoubleArray::New();
  datasetNormalZ3->SetNumberOfComponents(1);
  datasetNormalZ3->SetName("5 N(0,1)_1 - 2");

  vtkDoubleArray* datasetUniform = vtkDoubleArray::New();
  datasetUniform->SetNumberOfComponents(1);
  datasetUniform->SetName("Standard Uniform");

  vtkDoubleArray* datasetLaplace = vtkDoubleArray::New();
  datasetLaplace->SetNumberOfComponents(1);
  datasetLaplace->SetName("Standard Laplace");

  // Seed random number generator
  vtkMath::RandomSeed(static_cast<int>(vtkTimerLog::GetUniversalTime()));

  // Generate pseudo-random vectors
  double x, y, z1, z2, z3;
  for (int i = 0; i < nVals; ++i)
  {
    x = vtkMath::Gaussian();
    y = vtkMath::Gaussian();
    z1 = rhoXZ1 * x + rorXZ1 * y;
    z2 = rhoXZ2 * x + rorXZ2 * y;
    z3 = 5. * x - 2.;
    datasetNormalX->InsertNextValue(x);
    datasetNormalY->InsertNextValue(y);
    datasetNormalZ1->InsertNextValue(z1);
    datasetNormalZ2->InsertNextValue(z2);
    datasetNormalZ3->InsertNextValue(z3);
    datasetUniform->InsertNextValue(vtkMath::Random());
    double u = vtkMath::Random() - .5;
    datasetLaplace->InsertNextValue((u < 0. ? 1. : -1.) * log(1. - 2. * fabs(u)));
  }

  vtkTable* testTable = vtkTable::New();
  testTable->AddColumn(datasetNormalX);
  datasetNormalX->Delete();
  testTable->AddColumn(datasetNormalY);
  datasetNormalY->Delete();
  testTable->AddColumn(datasetNormalZ1);
  datasetNormalZ1->Delete();
  testTable->AddColumn(datasetNormalZ2);
  datasetNormalZ2->Delete();
  testTable->AddColumn(datasetNormalZ3);
  datasetNormalZ3->Delete();
  testTable->AddColumn(datasetUniform);
  datasetUniform->Delete();
  testTable->AddColumn(datasetLaplace);
  datasetLaplace->Delete();

  // Set descriptive statistics algorithm and its input data port
  vtkCorrelativeStatistics* cs4 = vtkCorrelativeStatistics::New();
  cs4->SetInputData(vtkStatisticsAlgorithm::INPUT_DATA, testTable);
  testTable->Delete();

  // Select Column Pairs of Interest ( Learn Mode )
  cs4->AddColumnPair("N(0,1)_1", "N(0,1)_2");
  cs4->AddColumnPair("N(0,1)_2", "5 N(0,1)_1 - 2");
  cs4->AddColumnPair("N(0,1)_1", z1Name.str().c_str());
  cs4->AddColumnPair("N(0,1)_1", z2Name.str().c_str());
  cs4->AddColumnPair("N(0,1)_1", "Standard Uniform");
  cs4->AddColumnPair("Standard Laplace", "N(0,1)_2");
  cs4->AddColumnPair("Standard Uniform", "Standard Laplace");

  // Test Learn, Derive, and Test options only
  cs4->SetLearnOption(true);
  cs4->SetDeriveOption(true);
  cs4->SetTestOption(true);
  cs4->SetAssessOption(false);
  cs4->Update();

  // Get output data and meta tables
  vtkMultiBlockDataSet* outputMetaCS4 = vtkMultiBlockDataSet::SafeDownCast(
    cs4->GetOutputDataObject(vtkStatisticsAlgorithm::OUTPUT_MODEL));
  vtkTable* outputPrimary4 = vtkTable::SafeDownCast(outputMetaCS4->GetBlock(0));
  vtkTable* outputDerived4 = vtkTable::SafeDownCast(outputMetaCS4->GetBlock(1));
  vtkTable* outputTest4 = cs4->GetOutput(vtkStatisticsAlgorithm::OUTPUT_TEST);

  cout << "\n## Calculated the following primary statistics for pseudo-random variables (n="
       << nVals << "):\n";
  for (vtkIdType r = 0; r < outputPrimary4->GetNumberOfRows(); ++r)
  {
    cout << "   ";
    for (int i = 0; i < outputPrimary4->GetNumberOfColumns(); ++i)
    {
      cout << outputPrimary4->GetColumnName(i) << "=" << outputPrimary4->GetValue(r, i).ToString()
           << "  ";
    }

    cout << "\n";
  }

  cout << "\n## Calculated the following derived statistics for pseudo-random variables (n="
       << nVals << "):\n";
  for (vtkIdType r = 0; r < outputDerived4->GetNumberOfRows(); ++r)
  {
    cout << "   ";
    for (int i = 0; i < outputDerived4->GetNumberOfColumns(); ++i)
    {
      cout << outputDerived4->GetColumnName(i) << "=" << outputDerived4->GetValue(r, i).ToString()
           << "  ";
    }

    cout << "\n";
  }

  // Check some results of the Test option
  cout << "\n## Calculated the following Jarque-Bera-Srivastava statistics for pseudo-random "
          "variables (n="
       << nVals;

#ifdef USE_GNU_R
  int nNonGaussian = 3;
  int nRejected = 0;
  double alpha = .01;

  cout << ", null hypothesis: binormality, significance level=" << alpha;
#endif // USE_GNU_R

  cout << "):\n";

  // Loop over Test table
  for (vtkIdType r = 0; r < outputTest4->GetNumberOfRows(); ++r)
  {
    cout << "   ";
    for (int c = 0; c < outputTest4->GetNumberOfColumns(); ++c)
    {
      cout << outputTest4->GetColumnName(c) << "=" << outputTest4->GetValue(r, c).ToString()
           << "  ";
    }

#ifdef USE_GNU_R
    // Check if null hypothesis is rejected at specified significance level
    double p = outputTest4->GetValueByName(r, "P").ToDouble();
    // Must verify that p value is valid (it is set to -1 if R has failed)
    if (p > -1 && p < alpha)
    {
      cout << "N.H. rejected";

      ++nRejected;
    }
#endif // USE_GNU_R

    cout << "\n";
  }

#ifdef USE_GNU_R
  if (nRejected < nNonGaussian)
  {
    vtkGenericWarningMacro("Rejected only "
      << nRejected << " null hypotheses of binormality whereas " << nNonGaussian
      << " variable pairs are not Gaussian");
    testStatus = 1;
  }
#endif // USE_GNU_R

  // Clean up
  cs4->Delete();

  return testStatus;
}
