org.apache.commons.math3.stat.descriptive.moment.Variance Java Examples

/**
 * Tests slice sampling of a monotonic beta distribution as an example of sampling of a bounded random variable.
 * Checks that input mean and variance are recovered by 10000 samples to a relative error of 0.5% and 2%,
 * respectively.
 */
@Test
public void testSliceSamplingOfMonotonicBetaDistribution() {
    rng.setSeed(RANDOM_SEED);

    final double alpha = 10.;
    final double beta = 1.;
    final BetaDistribution betaDistribution = new BetaDistribution(alpha, beta);
    final Function<Double, Double> betaLogPDF = betaDistribution::logDensity;
    final double mean = betaDistribution.getNumericalMean();
    final double variance = betaDistribution.getNumericalVariance();

    final double xInitial = 0.5;
    final double xMin = 0.;
    final double xMax = 1.;
    final double width = 0.1;
    final int numSamples = 10000;
    final SliceSampler betaSampler = new SliceSampler(rng, betaLogPDF, xMin, xMax, width);
    final double[] samples = Doubles.toArray(betaSampler.sample(xInitial, numSamples));

    final double sampleMean = new Mean().evaluate(samples);
    final double sampleVariance = new Variance().evaluate(samples);
    Assert.assertEquals(relativeError(sampleMean, mean), 0., 0.005);
    Assert.assertEquals(relativeError(sampleVariance, variance), 0., 0.02);
}
 

@Override
public double score(final List<? extends Cluster<T>> clusters) {
    double varianceSum = 0.0;
    for (final Cluster<T> cluster : clusters) {
        if (!cluster.getPoints().isEmpty()) {

            final Clusterable center = centroidOf(cluster);

            // compute the distance variance of the current cluster
            final Variance stat = new Variance();
            for (final T point : cluster.getPoints()) {
                stat.increment(distance(point, center));
            }
            varianceSum += stat.getResult();

        }
    }
    return varianceSum;
}
 

/**
 * Compute a covariance matrix from a matrix whose columns represent
 * covariates.
 * @param matrix input matrix (must have at least one column and two rows)
 * @param biasCorrected determines whether or not covariance estimates are bias-corrected
 * @return covariance matrix
 * @throws MathIllegalArgumentException if the matrix does not contain sufficient data
 */
protected RealMatrix computeCovarianceMatrix(RealMatrix matrix, boolean biasCorrected)
throws MathIllegalArgumentException {
    int dimension = matrix.getColumnDimension();
    Variance variance = new Variance(biasCorrected);
    RealMatrix outMatrix = new BlockRealMatrix(dimension, dimension);
    for (int i = 0; i < dimension; i++) {
        for (int j = 0; j < i; j++) {
          double cov = covariance(matrix.getColumn(i), matrix.getColumn(j), biasCorrected);
          outMatrix.setEntry(i, j, cov);
          outMatrix.setEntry(j, i, cov);
        }
        outMatrix.setEntry(i, i, variance.evaluate(matrix.getColumn(i)));
    }
    return outMatrix;
}
 

/**
 * Tests slice sampling of a peaked beta distribution as an example of sampling of a bounded random variable.
 * Checks that input mean and variance are recovered by 10000 samples to a relative error of 0.5% and 2%,
 * respectively.
 */
@Test
public void testSliceSamplingOfPeakedBetaDistribution() {
    rng.setSeed(RANDOM_SEED);

    final double alpha = 10.;
    final double beta = 4.;
    final BetaDistribution betaDistribution = new BetaDistribution(alpha, beta);
    final Function<Double, Double> betaLogPDF = betaDistribution::logDensity;
    final double mean = betaDistribution.getNumericalMean();
    final double variance = betaDistribution.getNumericalVariance();

    final double xInitial = 0.5;
    final double xMin = 0.;
    final double xMax = 1.;
    final double width = 0.1;
    final int numSamples = 10000;
    final SliceSampler betaSampler = new SliceSampler(rng, betaLogPDF, xMin, xMax, width);
    final double[] samples = Doubles.toArray(betaSampler.sample(xInitial, numSamples));

    final double sampleMean = new Mean().evaluate(samples);
    final double sampleVariance = new Variance().evaluate(samples);
    Assert.assertEquals(relativeError(sampleMean, mean), 0., 0.005);
    Assert.assertEquals(relativeError(sampleVariance, variance), 0., 0.02);
}
 

/**
 * Compute a covariance matrix from a matrix whose columns represent
 * covariates.
 * @param matrix input matrix (must have at least one column and two rows)
 * @param biasCorrected determines whether or not covariance estimates are bias-corrected
 * @return covariance matrix
 * @throws MathIllegalArgumentException if the matrix does not contain sufficient data
 */
protected RealMatrix computeCovarianceMatrix(RealMatrix matrix, boolean biasCorrected)
throws MathIllegalArgumentException {
    int dimension = matrix.getColumnDimension();
    Variance variance = new Variance(biasCorrected);
    RealMatrix outMatrix = new BlockRealMatrix(dimension, dimension);
    for (int i = 0; i < dimension; i++) {
        for (int j = 0; j < i; j++) {
          double cov = covariance(matrix.getColumn(i), matrix.getColumn(j), biasCorrected);
          outMatrix.setEntry(i, j, cov);
          outMatrix.setEntry(j, i, cov);
        }
        outMatrix.setEntry(i, i, variance.evaluate(matrix.getColumn(i)));
    }
    return outMatrix;
}
 

/**
 * Compute a covariance matrix from a matrix whose columns represent
 * covariates.
 * @param matrix input matrix (must have at least one column and two rows)
 * @param biasCorrected determines whether or not covariance estimates are bias-corrected
 * @return covariance matrix
 * @throws MathIllegalArgumentException if the matrix does not contain sufficient data
 */
protected RealMatrix computeCovarianceMatrix(RealMatrix matrix, boolean biasCorrected)
throws MathIllegalArgumentException {
    int dimension = matrix.getColumnDimension();
    Variance variance = new Variance(biasCorrected);
    RealMatrix outMatrix = new BlockRealMatrix(dimension, dimension);
    for (int i = 0; i < dimension; i++) {
        for (int j = 0; j < i; j++) {
          double cov = covariance(matrix.getColumn(i), matrix.getColumn(j), biasCorrected);
          outMatrix.setEntry(i, j, cov);
          outMatrix.setEntry(j, i, cov);
        }
        outMatrix.setEntry(i, i, variance.evaluate(matrix.getColumn(i)));
    }
    return outMatrix;
}
 

/**
 * Test slice sampling of a peaked beta distribution as an example of sampling of a bounded random variable.
 * Checks that input mean and variance are recovered by 10000 samples to a relative error of 0.5% and 2%,
 * respectively.
 */
@Test
public void testSliceSamplingOfPeakedBetaDistribution() {
    rng.setSeed(RANDOM_SEED);

    final double alpha = 10.;
    final double beta = 4.;
    final BetaDistribution betaDistribution = new BetaDistribution(alpha, beta);
    final Function<Double, Double> betaLogPDF = betaDistribution::logDensity;

    final double xInitial = 0.5;
    final double xMin = 0.;
    final double xMax = 1.;
    final double width = 0.1;
    final int numSamples = 10000;
    final SliceSampler betaSampler = new SliceSampler(rng, betaLogPDF, xMin, xMax, width);
    final double[] samples = Doubles.toArray(betaSampler.sample(xInitial, numSamples));

    final double mean = betaDistribution.getNumericalMean();
    final double variance = betaDistribution.getNumericalVariance();
    final double sampleMean = new Mean().evaluate(samples);
    final double sampleVariance = new Variance().evaluate(samples);
    Assert.assertEquals(relativeError(sampleMean, mean), 0., 0.005);
    Assert.assertEquals(relativeError(sampleVariance, variance), 0., 0.02);
}
 

/**
 * Test slice sampling of a monotonic beta distribution as an example of sampling of a bounded random variable.
 * Checks that input mean and variance are recovered by 10000 samples to a relative error of 0.5% and 2%,
 * respectively.
 */
@Test
public void testSliceSamplingOfMonotonicBetaDistribution() {
    rng.setSeed(RANDOM_SEED);

    final double alpha = 10.;
    final double beta = 1.;
    final BetaDistribution betaDistribution = new BetaDistribution(alpha, beta);
    final Function<Double, Double> betaLogPDF = betaDistribution::logDensity;

    final double xInitial = 0.5;
    final double xMin = 0.;
    final double xMax = 1.;
    final double width = 0.1;
    final int numSamples = 10000;
    final SliceSampler betaSampler = new SliceSampler(rng, betaLogPDF, xMin, xMax, width);
    final double[] samples = Doubles.toArray(betaSampler.sample(xInitial, numSamples));

    final double mean = betaDistribution.getNumericalMean();
    final double variance = betaDistribution.getNumericalVariance();
    final double sampleMean = new Mean().evaluate(samples);
    final double sampleVariance = new Variance().evaluate(samples);
    Assert.assertEquals(relativeError(sampleMean, mean), 0., 0.005);
    Assert.assertEquals(relativeError(sampleVariance, variance), 0., 0.02);
}
 

/**
 * Compute a covariance matrix from a matrix whose columns represent
 * covariates.
 * @param matrix input matrix (must have at least one column and two rows)
 * @param biasCorrected determines whether or not covariance estimates are bias-corrected
 * @return covariance matrix
 * @throws MathIllegalArgumentException if the matrix does not contain sufficient data
 */
protected RealMatrix computeCovarianceMatrix(RealMatrix matrix, boolean biasCorrected)
throws MathIllegalArgumentException {
    int dimension = matrix.getColumnDimension();
    Variance variance = new Variance(biasCorrected);
    RealMatrix outMatrix = new BlockRealMatrix(dimension, dimension);
    for (int i = 0; i < dimension; i++) {
        for (int j = 0; j < i; j++) {
          double cov = covariance(matrix.getColumn(i), matrix.getColumn(j), biasCorrected);
          outMatrix.setEntry(i, j, cov);
          outMatrix.setEntry(j, i, cov);
        }
        outMatrix.setEntry(i, i, variance.evaluate(matrix.getColumn(i)));
    }
    return outMatrix;
}
 

/**
 * JIRA: MATH-691
 */
@Test
public void testOverrideVarianceWithMathClass() {
    double[] scores = {1, 2, 3, 4};
    SummaryStatistics stats = new SummaryStatistics();
    stats.setVarianceImpl(new Variance(false)); //use "population variance"
    for(double i : scores) {
      stats.addValue(i);
    }
    Assert.assertEquals((new Variance(false)).evaluate(scores),stats.getVariance(), 0); 
}
 

/**
 * Get a random point from the {@link Cluster} with the largest distance variance.
 *
 * @param clusters the {@link Cluster}s to search
 * @return a random point from the selected cluster
 */
private T getPointFromLargestVarianceCluster(final Collection<Cluster<T>> clusters) {

    double maxVariance = Double.NEGATIVE_INFINITY;
    Cluster<T> selected = null;
    for (final Cluster<T> cluster : clusters) {
        if (!cluster.getPoints().isEmpty()) {

            // compute the distance variance of the current cluster
            final T center = cluster.getCenter();
            final Variance stat = new Variance();
            for (final T point : cluster.getPoints()) {
                stat.increment(point.distanceFrom(center));
            }
            final double variance = stat.getResult();

            // select the cluster with the largest variance
            if (variance > maxVariance) {
                maxVariance = variance;
                selected = cluster;
            }

        }
    }

    // did we find at least one non-empty cluster ?
    if (selected == null) {
        throw new ConvergenceException(LocalizedFormats.EMPTY_CLUSTER_IN_K_MEANS);
    }

    // extract a random point from the cluster
    final List<T> selectedPoints = selected.getPoints();
    return selectedPoints.remove(random.nextInt(selectedPoints.size()));

}
 

@Test
public void testSummaryConsistency() {
    final DescriptiveStatistics dstats = new DescriptiveStatistics();
    final SummaryStatistics sstats = new SummaryStatistics();
    final int windowSize = 5;
    dstats.setWindowSize(windowSize);
    final double tol = 1E-12;
    for (int i = 0; i < 20; i++) {
        dstats.addValue(i);
        sstats.clear();
        double[] values = dstats.getValues();
        for (int j = 0; j < values.length; j++) {
            sstats.addValue(values[j]);
        }
        TestUtils.assertEquals(dstats.getMean(), sstats.getMean(), tol);
        TestUtils.assertEquals(new Mean().evaluate(values), dstats.getMean(), tol);
        TestUtils.assertEquals(dstats.getMax(), sstats.getMax(), tol);
        TestUtils.assertEquals(new Max().evaluate(values), dstats.getMax(), tol);
        TestUtils.assertEquals(dstats.getGeometricMean(), sstats.getGeometricMean(), tol);
        TestUtils.assertEquals(new GeometricMean().evaluate(values), dstats.getGeometricMean(), tol);
        TestUtils.assertEquals(dstats.getMin(), sstats.getMin(), tol);
        TestUtils.assertEquals(new Min().evaluate(values), dstats.getMin(), tol);
        TestUtils.assertEquals(dstats.getStandardDeviation(), sstats.getStandardDeviation(), tol);
        TestUtils.assertEquals(dstats.getVariance(), sstats.getVariance(), tol);
        TestUtils.assertEquals(new Variance().evaluate(values), dstats.getVariance(), tol);
        TestUtils.assertEquals(dstats.getSum(), sstats.getSum(), tol);
        TestUtils.assertEquals(new Sum().evaluate(values), dstats.getSum(), tol);
        TestUtils.assertEquals(dstats.getSumsq(), sstats.getSumsq(), tol);
        TestUtils.assertEquals(new SumOfSquares().evaluate(values), dstats.getSumsq(), tol);
        TestUtils.assertEquals(dstats.getPopulationVariance(), sstats.getPopulationVariance(), tol);
        TestUtils.assertEquals(new Variance(false).evaluate(values), dstats.getPopulationVariance(), tol);
    }
}
 

/**
 * Attempt to get an idea of segment mean variance near copy neutral.
 *
 * @param segments Never {@code null}
 * @return variance of segment mean (in CR space) of segments that are "close enough" to copy neutral.
 *   Zero if no segments are "close enough"
 */
private double calculateVarianceOfCopyNeutralSegmentMeans(final List<ACNVModeledSegment> segments, final double meanBiasInCR) {
    Utils.nonNull(segments);

    // Only consider values "close enough" to copy neutral (CR == 1).
    final double neutralCR = 1 + meanBiasInCR;
    final double[] neutralSegmentMeans = segments.stream()
            .mapToDouble(ACNVModeledSegment::getSegmentMeanInCRSpace)
            .filter(m -> Math.abs(m - neutralCR) < CLOSE_ENOUGH_TO_COPY_NEUTRAL_IN_CR).toArray();
    return new Variance().evaluate(neutralSegmentMeans);
}
 

/**
 * Get a random point from the {@link Cluster} with the largest distance variance.
 *
 * @param clusters the {@link Cluster}s to search
 * @return a random point from the selected cluster
 * @throws ConvergenceException if clusters are all empty
 */
private T getPointFromLargestVarianceCluster(final Collection<Cluster<T>> clusters)
throws ConvergenceException {

    double maxVariance = Double.NEGATIVE_INFINITY;
    Cluster<T> selected = null;
    for (final Cluster<T> cluster : clusters) {
        if (!cluster.getPoints().isEmpty()) {

            // compute the distance variance of the current cluster
            final T center = cluster.getCenter();
            final Variance stat = new Variance();
            for (final T point : cluster.getPoints()) {
                stat.increment(point.distanceFrom(center));
            }
            final double variance = stat.getResult();

            // select the cluster with the largest variance
            if (variance > maxVariance) {
                maxVariance = variance;
                selected = cluster;
            }

        }
    }

    // did we find at least one non-empty cluster ?
    if (selected == null) {
        throw new ConvergenceException(LocalizedFormats.EMPTY_CLUSTER_IN_K_MEANS);
    }

    // extract a random point from the cluster
    final List<T> selectedPoints = selected.getPoints();
    return selectedPoints.remove(random.nextInt(selectedPoints.size()));

}
 

/**
 * JIRA: MATH-691
 */
@Test
public void testOverrideVarianceWithMathClass() throws Exception {
    double[] scores = {1, 2, 3, 4};
    SummaryStatistics stats = new SummaryStatistics();
    stats.setVarianceImpl(new Variance(false)); //use "population variance"
    for(double i : scores) {
      stats.addValue(i);
    }
    Assert.assertEquals((new Variance(false)).evaluate(scores),stats.getVariance(), 0); 
}
 

static double rho(double[][] data) {
    Variance v = new Variance();
    double varX = v.evaluate(data[0]);
    double sigX = Math.sqrt(varX);
    double varY = v.evaluate(data[1]);
    double sigY = Math.sqrt(varY);
    Covariance c = new Covariance(data);
    double sigXY = c.covariance(data[0], data[1]);
    return sigXY/(sigX*sigY);
}
 

@Override
protected Number getExpectedValue(int start, int length)
{
    if (length < 2) {
        return null;
    }

    double[] values = new double[length];
    for (int i = 0; i < length; i++) {
        values[i] = start + i;
    }

    Variance variance = new Variance();
    return variance.evaluate(values);
}
 

/**
 * This implementation can be heavily optimized
 */
public Map<String, Double> getTopNVarianceValues(Set<OWLClass> candidates, int n) {
	double[] icData = refBasedStats.retrieveCandidatesIC(candidates);

	// Compute variance against all cached reference entities
	Map<IRI, Double> iResult = new LinkedHashMap<IRI, Double>();
	List<Double> list = new ArrayList<Double>();
	for (IRI reference : refBasedStats.getReferenceStats().keySet()) {
		double variance = new Variance().evaluate(icData, refBasedStats.getReferenceStats().get(reference).getMean());
		list.add(variance);
		iResult.put(reference, variance);
	}
	// Sort variances ascendantly
	Collections.sort(list);
	
	// Return top-N variances
	
	int iterSize = n < list.size() ? n : list.size();
	Map<String, Double> result = new LinkedHashMap<String, Double>();
	for (int i = 0 ;i < iterSize ; i++) {
		double varValue = list.get(i);
		List<String> refURIs = findRefURIs(varValue, iResult);
		for (String uri : refURIs) {
			result.put(uri, varValue);
		}
	}
	
	return result;
}
 

public double getVarianceValue(Set<OWLClass> candidates, IRI referenceEntity) throws OwlSimVarianceEntityReferenceNotFoundException {
	// Reference entity does not exist - this should probably not happen.
	if (!refBasedStats.getReferenceStats().containsKey(referenceEntity)) {
		throw new OwlSimVarianceEntityReferenceNotFoundException(referenceEntity);
	}
	
	// Create IC list for candidates provided
	double[] icData = refBasedStats.retrieveCandidatesIC(candidates);
	// Return variance against the given reference concept
	return new Variance().evaluate(icData, refBasedStats.getReferenceStats().get(referenceEntity).getMean());
}
 

@Test
public void testSummaryConsistency() {
    final DescriptiveStatistics dstats = new DescriptiveStatistics();
    final SummaryStatistics sstats = new SummaryStatistics();
    final int windowSize = 5;
    dstats.setWindowSize(windowSize);
    final double tol = 1E-12;
    for (int i = 0; i < 20; i++) {
        dstats.addValue(i);
        sstats.clear();
        double[] values = dstats.getValues();
        for (int j = 0; j < values.length; j++) {
            sstats.addValue(values[j]);
        }
        TestUtils.assertEquals(dstats.getMean(), sstats.getMean(), tol);
        TestUtils.assertEquals(new Mean().evaluate(values), dstats.getMean(), tol);
        TestUtils.assertEquals(dstats.getMax(), sstats.getMax(), tol);
        TestUtils.assertEquals(new Max().evaluate(values), dstats.getMax(), tol);
        TestUtils.assertEquals(dstats.getGeometricMean(), sstats.getGeometricMean(), tol);
        TestUtils.assertEquals(new GeometricMean().evaluate(values), dstats.getGeometricMean(), tol);
        TestUtils.assertEquals(dstats.getMin(), sstats.getMin(), tol);
        TestUtils.assertEquals(new Min().evaluate(values), dstats.getMin(), tol);
        TestUtils.assertEquals(dstats.getStandardDeviation(), sstats.getStandardDeviation(), tol);
        TestUtils.assertEquals(dstats.getVariance(), sstats.getVariance(), tol);
        TestUtils.assertEquals(new Variance().evaluate(values), dstats.getVariance(), tol);
        TestUtils.assertEquals(dstats.getSum(), sstats.getSum(), tol);
        TestUtils.assertEquals(new Sum().evaluate(values), dstats.getSum(), tol);
        TestUtils.assertEquals(dstats.getSumsq(), sstats.getSumsq(), tol);
        TestUtils.assertEquals(new SumOfSquares().evaluate(values), dstats.getSumsq(), tol);
        TestUtils.assertEquals(dstats.getPopulationVariance(), sstats.getPopulationVariance(), tol);
        TestUtils.assertEquals(new Variance(false).evaluate(values), dstats.getPopulationVariance(), tol);
    }
}
 

@Override
protected Number getExpectedValue(int start, int length)
{
    if (length == 0) {
        return null;
    }

    double[] values = new double[length];
    for (int i = 0; i < length; i++) {
        values[i] = start + i;
    }

    Variance variance = new Variance(false);
    return variance.evaluate(values);
}
 

@Test
public void testSummaryConsistency() {
    final DescriptiveStatistics dstats = new DescriptiveStatistics();
    final SummaryStatistics sstats = new SummaryStatistics();
    final int windowSize = 5;
    dstats.setWindowSize(windowSize);
    final double tol = 1E-12;
    for (int i = 0; i < 20; i++) {
        dstats.addValue(i);
        sstats.clear();
        double[] values = dstats.getValues();
        for (int j = 0; j < values.length; j++) {
            sstats.addValue(values[j]);
        }
        TestUtils.assertEquals(dstats.getMean(), sstats.getMean(), tol);
        TestUtils.assertEquals(new Mean().evaluate(values), dstats.getMean(), tol);
        TestUtils.assertEquals(dstats.getMax(), sstats.getMax(), tol);
        TestUtils.assertEquals(new Max().evaluate(values), dstats.getMax(), tol);
        TestUtils.assertEquals(dstats.getGeometricMean(), sstats.getGeometricMean(), tol);
        TestUtils.assertEquals(new GeometricMean().evaluate(values), dstats.getGeometricMean(), tol);
        TestUtils.assertEquals(dstats.getMin(), sstats.getMin(), tol);
        TestUtils.assertEquals(new Min().evaluate(values), dstats.getMin(), tol);
        TestUtils.assertEquals(dstats.getStandardDeviation(), sstats.getStandardDeviation(), tol);
        TestUtils.assertEquals(dstats.getVariance(), sstats.getVariance(), tol);
        TestUtils.assertEquals(new Variance().evaluate(values), dstats.getVariance(), tol);
        TestUtils.assertEquals(dstats.getSum(), sstats.getSum(), tol);
        TestUtils.assertEquals(new Sum().evaluate(values), dstats.getSum(), tol);
        TestUtils.assertEquals(dstats.getSumsq(), sstats.getSumsq(), tol);
        TestUtils.assertEquals(new SumOfSquares().evaluate(values), dstats.getSumsq(), tol);
        TestUtils.assertEquals(dstats.getPopulationVariance(), sstats.getPopulationVariance(), tol);
        TestUtils.assertEquals(new Variance(false).evaluate(values), dstats.getPopulationVariance(), tol);
    }
}
 

/**
 * JIRA: MATH-691
 */
@Test
public void testOverrideVarianceWithMathClass() {
    double[] scores = {1, 2, 3, 4};
    SummaryStatistics stats = new SummaryStatistics();
    stats.setVarianceImpl(new Variance(false)); //use "population variance"
    for(double i : scores) {
      stats.addValue(i);
    }
    Assert.assertEquals((new Variance(false)).evaluate(scores),stats.getVariance(), 0); 
}
 

@Test
public void testSummaryConsistency() {
    final DescriptiveStatistics dstats = new DescriptiveStatistics();
    final SummaryStatistics sstats = new SummaryStatistics();
    final int windowSize = 5;
    dstats.setWindowSize(windowSize);
    final double tol = 1E-12;
    for (int i = 0; i < 20; i++) {
        dstats.addValue(i);
        sstats.clear();
        double[] values = dstats.getValues();
        for (int j = 0; j < values.length; j++) {
            sstats.addValue(values[j]);
        }
        TestUtils.assertEquals(dstats.getMean(), sstats.getMean(), tol);
        TestUtils.assertEquals(new Mean().evaluate(values), dstats.getMean(), tol);
        TestUtils.assertEquals(dstats.getMax(), sstats.getMax(), tol);
        TestUtils.assertEquals(new Max().evaluate(values), dstats.getMax(), tol);
        TestUtils.assertEquals(dstats.getGeometricMean(), sstats.getGeometricMean(), tol);
        TestUtils.assertEquals(new GeometricMean().evaluate(values), dstats.getGeometricMean(), tol);
        TestUtils.assertEquals(dstats.getMin(), sstats.getMin(), tol);
        TestUtils.assertEquals(new Min().evaluate(values), dstats.getMin(), tol);
        TestUtils.assertEquals(dstats.getStandardDeviation(), sstats.getStandardDeviation(), tol);
        TestUtils.assertEquals(dstats.getVariance(), sstats.getVariance(), tol);
        TestUtils.assertEquals(new Variance().evaluate(values), dstats.getVariance(), tol);
        TestUtils.assertEquals(dstats.getSum(), sstats.getSum(), tol);
        TestUtils.assertEquals(new Sum().evaluate(values), dstats.getSum(), tol);
        TestUtils.assertEquals(dstats.getSumsq(), sstats.getSumsq(), tol);
        TestUtils.assertEquals(new SumOfSquares().evaluate(values), dstats.getSumsq(), tol);
        TestUtils.assertEquals(dstats.getPopulationVariance(), sstats.getPopulationVariance(), tol);
        TestUtils.assertEquals(new Variance(false).evaluate(values), dstats.getPopulationVariance(), tol);
    }
}
 

@Test
public void testSummaryConsistency() {
    final DescriptiveStatistics dstats = new DescriptiveStatistics();
    final SummaryStatistics sstats = new SummaryStatistics();
    final int windowSize = 5;
    dstats.setWindowSize(windowSize);
    final double tol = 1E-12;
    for (int i = 0; i < 20; i++) {
        dstats.addValue(i);
        sstats.clear();
        double[] values = dstats.getValues();
        for (int j = 0; j < values.length; j++) {
            sstats.addValue(values[j]);
        }
        TestUtils.assertEquals(dstats.getMean(), sstats.getMean(), tol);
        TestUtils.assertEquals(new Mean().evaluate(values), dstats.getMean(), tol);
        TestUtils.assertEquals(dstats.getMax(), sstats.getMax(), tol);
        TestUtils.assertEquals(new Max().evaluate(values), dstats.getMax(), tol);
        TestUtils.assertEquals(dstats.getGeometricMean(), sstats.getGeometricMean(), tol);
        TestUtils.assertEquals(new GeometricMean().evaluate(values), dstats.getGeometricMean(), tol);
        TestUtils.assertEquals(dstats.getMin(), sstats.getMin(), tol);
        TestUtils.assertEquals(new Min().evaluate(values), dstats.getMin(), tol);
        TestUtils.assertEquals(dstats.getStandardDeviation(), sstats.getStandardDeviation(), tol);
        TestUtils.assertEquals(dstats.getVariance(), sstats.getVariance(), tol);
        TestUtils.assertEquals(new Variance().evaluate(values), dstats.getVariance(), tol);
        TestUtils.assertEquals(dstats.getSum(), sstats.getSum(), tol);
        TestUtils.assertEquals(new Sum().evaluate(values), dstats.getSum(), tol);
        TestUtils.assertEquals(dstats.getSumsq(), sstats.getSumsq(), tol);
        TestUtils.assertEquals(new SumOfSquares().evaluate(values), dstats.getSumsq(), tol);
        TestUtils.assertEquals(dstats.getPopulationVariance(), sstats.getPopulationVariance(), tol);
        TestUtils.assertEquals(new Variance(false).evaluate(values), dstats.getPopulationVariance(), tol);
    }
}
 

/**
 * Get a random point from the {@link Cluster} with the largest distance variance.
 *
 * @param clusters the {@link Cluster}s to search
 * @return a random point from the selected cluster
 * @throws ConvergenceException if clusters are all empty
 */
private T getPointFromLargestVarianceCluster(final Collection<CentroidCluster<T>> clusters)
        throws ConvergenceException {

    double maxVariance = Double.NEGATIVE_INFINITY;
    Cluster<T> selected = null;
    for (final CentroidCluster<T> cluster : clusters) {
        if (!cluster.getPoints().isEmpty()) {

            // compute the distance variance of the current cluster
            final Clusterable center = cluster.getCenter();
            final Variance stat = new Variance();
            for (final T point : cluster.getPoints()) {
                stat.increment(distance(point, center));
            }
            final double variance = stat.getResult();

            // select the cluster with the largest variance
            if (variance > maxVariance) {
                maxVariance = variance;
                selected = cluster;
            }

        }
    }

    // did we find at least one non-empty cluster ?
    if (selected == null) {
        throw new ConvergenceException(LocalizedFormats.EMPTY_CLUSTER_IN_K_MEANS);
    }

    // extract a random point from the cluster
    final List<T> selectedPoints = selected.getPoints();
    return selectedPoints.remove(random.nextInt(selectedPoints.size()));

}
 

/**
 * Get a random point from the {@link Cluster} with the largest distance variance.
 *
 * @param clusters the {@link Cluster}s to search
 * @return a random point from the selected cluster
 * @throws ConvergenceException if clusters are all empty
 */
private T getPointFromLargestVarianceCluster(final Collection<Cluster<T>> clusters)
throws ConvergenceException {

    double maxVariance = Double.NEGATIVE_INFINITY;
    Cluster<T> selected = null;
    for (final Cluster<T> cluster : clusters) {
        if (!cluster.getPoints().isEmpty()) {

            // compute the distance variance of the current cluster
            final T center = cluster.getCenter();
            final Variance stat = new Variance();
            for (final T point : cluster.getPoints()) {
                stat.increment(point.distanceFrom(center));
            }
            final double variance = stat.getResult();

            // select the cluster with the largest variance
            if (variance > maxVariance) {
                maxVariance = variance;
                selected = cluster;
            }

        }
    }

    // did we find at least one non-empty cluster ?
    if (selected == null) {
        throw new ConvergenceException(LocalizedFormats.EMPTY_CLUSTER_IN_K_MEANS);
    }

    // extract a random point from the cluster
    final List<T> selectedPoints = selected.getPoints();
    return selectedPoints.remove(random.nextInt(selectedPoints.size()));

}
 

/**
 * JIRA: MATH-691
 */
@Test
public void testOverrideVarianceWithMathClass() {
    double[] scores = {1, 2, 3, 4};
    SummaryStatistics stats = new SummaryStatistics();
    stats.setVarianceImpl(new Variance(false)); //use "population variance"
    for(double i : scores) {
      stats.addValue(i);
    }
    Assert.assertEquals((new Variance(false)).evaluate(scores),stats.getVariance(), 0); 
}
 

/**
 * Get a random point from the {@link Cluster} with the largest distance variance.
 *
 * @param clusters the {@link Cluster}s to search
 * @return a random point from the selected cluster
 * @throws ConvergenceException if clusters are all empty
 */
private T getPointFromLargestVarianceCluster(final Collection<Cluster<T>> clusters)
throws ConvergenceException {

    double maxVariance = Double.NEGATIVE_INFINITY;
    Cluster<T> selected = null;
    for (final Cluster<T> cluster : clusters) {
        if (!cluster.getPoints().isEmpty()) {

            // compute the distance variance of the current cluster
            final T center = cluster.getCenter();
            final Variance stat = new Variance();
            for (final T point : cluster.getPoints()) {
                stat.increment(point.distanceFrom(center));
            }
            final double variance = stat.getResult();

            // select the cluster with the largest variance
            if (variance > maxVariance) {
                maxVariance = variance;
                selected = cluster;
            }

        }
    }

    // did we find at least one non-empty cluster ?
    if (selected == null) {
        throw new ConvergenceException(LocalizedFormats.EMPTY_CLUSTER_IN_K_MEANS);
    }

    // extract a random point from the cluster
    final List<T> selectedPoints = selected.getPoints();
    return selectedPoints.remove(random.nextInt(selectedPoints.size()));

}
 

/**
 * Compute a covariance matrix from a matrix whose columns represent
 * covariates.
 * @param matrix input matrix (must have at least two columns and two rows)
 * @param biasCorrected determines whether or not covariance estimates are bias-corrected
 * @return covariance matrix
 */
protected RealMatrix computeCovarianceMatrix(RealMatrix matrix, boolean biasCorrected) {
    int dimension = matrix.getColumnDimension();
    Variance variance = new Variance(biasCorrected);
    RealMatrix outMatrix = new BlockRealMatrix(dimension, dimension);
    for (int i = 0; i < dimension; i++) {
        for (int j = 0; j < i; j++) {
          double cov = covariance(matrix.getColumn(i), matrix.getColumn(j), biasCorrected);
          outMatrix.setEntry(i, j, cov);
          outMatrix.setEntry(j, i, cov);
        }
        outMatrix.setEntry(i, i, variance.evaluate(matrix.getColumn(i)));
    }
    return outMatrix;
}