/*
* Copyright (C) 2013 The Guava Authors
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package com.google.common.math;
import static com.google.common.base.Preconditions.checkArgument;
import static com.google.common.truth.Truth.assertThat;
import static java.lang.Double.NEGATIVE_INFINITY;
import static java.lang.Double.NaN;
import static java.lang.Double.POSITIVE_INFINITY;
import static org.junit.Assert.fail;
import com.google.common.base.Predicates;
import com.google.common.collect.ImmutableList;
import com.google.common.collect.Iterables;
import com.google.common.collect.Lists;
import com.google.common.primitives.Doubles;
import com.google.common.primitives.Ints;
import java.math.BigInteger;
import java.util.List;
/**
* Inputs, expected outputs, and helper methods for tests of {@link StatsAccumulator},
* {@link Stats}, {@link PairedStatsAccumulator}, and {@link PairedStats}.
*
* @author Pete Gillin
*/
class StatsTesting {
static final double ALLOWED_ERROR = 1e-10;
// Inputs and their statistics:
static final double ONE_VALUE = 12.34;
static final double OTHER_ONE_VALUE = -56.78;
static final ImmutableList<Double> TWO_VALUES = ImmutableList.of(12.34, -56.78);
static final double TWO_VALUES_MEAN = (12.34 - 56.78) / 2;
static final double TWO_VALUES_SUM_OF_SQUARES_OF_DELTAS =
(12.34 - TWO_VALUES_MEAN) * (12.34 - TWO_VALUES_MEAN)
+ (-56.78 - TWO_VALUES_MEAN) * (-56.78 - TWO_VALUES_MEAN);
static final double TWO_VALUES_MAX = 12.34;
static final double TWO_VALUES_MIN = -56.78;
static final ImmutableList<Double> OTHER_TWO_VALUES = ImmutableList.of(123.456, -789.012);
static final double OTHER_TWO_VALUES_MEAN = (123.456 - 789.012) / 2;
static final double TWO_VALUES_SUM_OF_PRODUCTS_OF_DELTAS =
(12.34 - TWO_VALUES_MEAN) * (123.456 - OTHER_TWO_VALUES_MEAN)
+ (-56.78 - TWO_VALUES_MEAN) * (-789.012 - OTHER_TWO_VALUES_MEAN);
/**
* Helper class for testing with non-finite values. {@link #ALL_MANY_VALUES} gives a number
* instances with many combinations of finite and non-finite values. All have
* {@link #MANY_VALUES_COUNT} values. If all the values are finite then the mean is
* {@link #MANY_VALUES_MEAN} and the sum-of-squares-of-deltas is
* {@link #MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS}. The smallest and largest finite values are
* always {@link #MANY_VALUES_MIN} and {@link #MANY_VALUES_MAX}, although setting non-finite
* values will change the true min and max.
*/
static class ManyValues {
private final ImmutableList<Double> values;
ManyValues(double[] values) {
this.values = ImmutableList.copyOf(Doubles.asList(values));
}
ImmutableList<Double> asIterable() {
return values;
}
double[] asArray() {
return Doubles.toArray(values);
}
boolean hasAnyPositiveInfinity() {
return Iterables.any(values, Predicates.equalTo(POSITIVE_INFINITY));
}
boolean hasAnyNegativeInfinity() {
return Iterables.any(values, Predicates.equalTo(NEGATIVE_INFINITY));
}
boolean hasAnyNaN() {
return Iterables.any(values, Predicates.equalTo(NaN));
}
boolean hasAnyNonFinite() {
return hasAnyPositiveInfinity() || hasAnyNegativeInfinity() || hasAnyNaN();
}
@Override
public String toString() {
return values.toString();
}
private static ImmutableList<ManyValues> createAll() {
ImmutableList.Builder<ManyValues> builder = ImmutableList.builder();
double[] values = new double[5];
for (double first : ImmutableList.of(1.1, POSITIVE_INFINITY, NEGATIVE_INFINITY, NaN)) {
values[0] = first;
values[1] = -44.44;
for (double third : ImmutableList.of(33.33, POSITIVE_INFINITY, NEGATIVE_INFINITY, NaN)) {
values[2] = third;
values[3] = 555.555;
for (double fifth : ImmutableList.of(-2.2, POSITIVE_INFINITY, NEGATIVE_INFINITY, NaN)) {
values[4] = fifth;
builder.add(new ManyValues(values));
}
}
}
return builder.build();
}
}
static final ImmutableList<ManyValues> ALL_MANY_VALUES = ManyValues.createAll();
static final ImmutableList<Double> MANY_VALUES =
ImmutableList.of(1.1, -44.44, 33.33, 555.555, -2.2);
static final int MANY_VALUES_COUNT = 5;
static final double MANY_VALUES_MEAN = (1.1 - 44.44 + 33.33 + 555.555 - 2.2) / 5;
static final double MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS =
(1.1 - MANY_VALUES_MEAN) * (1.1 - MANY_VALUES_MEAN)
+ (-44.44 - MANY_VALUES_MEAN) * (-44.44 - MANY_VALUES_MEAN)
+ (33.33 - MANY_VALUES_MEAN) * (33.33 - MANY_VALUES_MEAN)
+ (555.555 - MANY_VALUES_MEAN) * (555.555 - MANY_VALUES_MEAN)
+ (-2.2 - MANY_VALUES_MEAN) * (-2.2 - MANY_VALUES_MEAN);
static final double MANY_VALUES_MAX = 555.555;
static final double MANY_VALUES_MIN = -44.44;
// Doubles which will overflow if summed:
static final double[] LARGE_VALUES = {Double.MAX_VALUE, Double.MAX_VALUE / 2.0};
static final double LARGE_VALUES_MEAN = 0.75 * Double.MAX_VALUE;
static final ImmutableList<Double> OTHER_MANY_VALUES =
ImmutableList.of(1.11, -2.22, 33.3333, -44.4444, 555.555555);
static final int OTHER_MANY_VALUES_COUNT = 5;
static final double OTHER_MANY_VALUES_MEAN = (1.11 - 2.22 + 33.3333 - 44.4444 + 555.555555) / 5;
static final double MANY_VALUES_SUM_OF_PRODUCTS_OF_DELTAS =
(1.1 - MANY_VALUES_MEAN) * (1.11 - OTHER_MANY_VALUES_MEAN)
+ (-44.44 - MANY_VALUES_MEAN) * (-2.22 - OTHER_MANY_VALUES_MEAN)
+ (33.33 - MANY_VALUES_MEAN) * (33.3333 - OTHER_MANY_VALUES_MEAN)
+ (555.555 - MANY_VALUES_MEAN) * (-44.4444 - OTHER_MANY_VALUES_MEAN)
+ (-2.2 - MANY_VALUES_MEAN) * (555.555555 - OTHER_MANY_VALUES_MEAN);
static final ImmutableList<Integer> INTEGER_MANY_VALUES =
ImmutableList.of(11, -22, 3333, -4444, 555555);
static final int INTEGER_MANY_VALUES_COUNT = 5;
static final double INTEGER_MANY_VALUES_MEAN = (11.0 - 22.0 + 3333.0 - 4444.0 + 555555.0) / 5;
static final double INTEGER_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS =
(11.0 - INTEGER_MANY_VALUES_MEAN) * (11.0 - INTEGER_MANY_VALUES_MEAN)
+ (-22.0 - INTEGER_MANY_VALUES_MEAN) * (-22.0 - INTEGER_MANY_VALUES_MEAN)
+ (3333.0 - INTEGER_MANY_VALUES_MEAN) * (3333.0 - INTEGER_MANY_VALUES_MEAN)
+ (-4444.0 - INTEGER_MANY_VALUES_MEAN) * (-4444.0 - INTEGER_MANY_VALUES_MEAN)
+ (555555.0 - INTEGER_MANY_VALUES_MEAN) * (555555.0 - INTEGER_MANY_VALUES_MEAN);
static final double INTEGER_MANY_VALUES_MAX = 555555.0;
static final double INTEGER_MANY_VALUES_MIN = -4444.0;
// Integers which will overflow if summed (using integer arithmetic):
static final int[] LARGE_INTEGER_VALUES = {Integer.MAX_VALUE, Integer.MAX_VALUE / 2};
static final double LARGE_INTEGER_VALUES_MEAN =
BigInteger.valueOf(Integer.MAX_VALUE)
.multiply(BigInteger.valueOf(3L))
.divide(BigInteger.valueOf(4L))
.doubleValue();
static final double LARGE_INTEGER_VALUES_POPULATION_VARIANCE =
BigInteger.valueOf(Integer.MAX_VALUE)
.multiply(BigInteger.valueOf(Integer.MAX_VALUE))
.divide(BigInteger.valueOf(16L))
.doubleValue();
static final ImmutableList<Long> LONG_MANY_VALUES =
ImmutableList.of(1111L, -2222L, 33333333L, -44444444L, 5555555555L);
static final int LONG_MANY_VALUES_COUNT = 5;
static final double LONG_MANY_VALUES_MEAN =
(1111.0 - 2222.0 + 33333333.0 - 44444444.0 + 5555555555.0) / 5;
static final double LONG_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS =
(1111.0 - LONG_MANY_VALUES_MEAN) * (1111.0 - LONG_MANY_VALUES_MEAN)
+ (-2222.0 - LONG_MANY_VALUES_MEAN) * (-2222.0 - LONG_MANY_VALUES_MEAN)
+ (33333333.0 - LONG_MANY_VALUES_MEAN) * (33333333.0 - LONG_MANY_VALUES_MEAN)
+ (-44444444.0 - LONG_MANY_VALUES_MEAN) * (-44444444.0 - LONG_MANY_VALUES_MEAN)
+ (5555555555.0 - LONG_MANY_VALUES_MEAN) * (5555555555.0 - LONG_MANY_VALUES_MEAN);
static final double LONG_MANY_VALUES_MAX = 5555555555.0;
static final double LONG_MANY_VALUES_MIN = -44444444.0;
// Longs which will overflow if summed (using long arithmetic):
static final long[] LARGE_LONG_VALUES = {Long.MAX_VALUE, Long.MAX_VALUE / 2};
static final double LARGE_LONG_VALUES_MEAN =
BigInteger.valueOf(Long.MAX_VALUE)
.multiply(BigInteger.valueOf(3L))
.divide(BigInteger.valueOf(4L))
.doubleValue();
static final double LARGE_LONG_VALUES_POPULATION_VARIANCE =
BigInteger.valueOf(Long.MAX_VALUE)
.multiply(BigInteger.valueOf(Long.MAX_VALUE))
.divide(BigInteger.valueOf(16L))
.doubleValue();
// Stats instances:
static final Stats EMPTY_STATS_VARARGS = Stats.of();
static final Stats EMPTY_STATS_ITERABLE = Stats.of(ImmutableList.<Double>of());
static final Stats ONE_VALUE_STATS = Stats.of(ONE_VALUE);
static final Stats OTHER_ONE_VALUE_STATS = Stats.of(OTHER_ONE_VALUE);
static final Stats TWO_VALUES_STATS = Stats.of(TWO_VALUES);
static final Stats OTHER_TWO_VALUES_STATS = Stats.of(OTHER_TWO_VALUES);
static final Stats MANY_VALUES_STATS_VARARGS = Stats.of(1.1, -44.44, 33.33, 555.555, -2.2);
static final Stats MANY_VALUES_STATS_ITERABLE = Stats.of(MANY_VALUES);
static final Stats MANY_VALUES_STATS_ITERATOR = Stats.of(MANY_VALUES.iterator());
static final Stats MANY_VALUES_STATS_SNAPSHOT;
static final Stats LARGE_VALUES_STATS = Stats.of(LARGE_VALUES);
static final Stats OTHER_MANY_VALUES_STATS = Stats.of(OTHER_MANY_VALUES);
static final Stats INTEGER_MANY_VALUES_STATS_VARARGS =
Stats.of(Ints.toArray(INTEGER_MANY_VALUES));
static final Stats INTEGER_MANY_VALUES_STATS_ITERABLE = Stats.of(INTEGER_MANY_VALUES);
static final Stats LARGE_INTEGER_VALUES_STATS = Stats.of(LARGE_INTEGER_VALUES);
static final Stats LONG_MANY_VALUES_STATS_ITERATOR = Stats.of(LONG_MANY_VALUES.iterator());
static final Stats LONG_MANY_VALUES_STATS_SNAPSHOT;
static final Stats LARGE_LONG_VALUES_STATS = Stats.of(LARGE_LONG_VALUES);
static {
StatsAccumulator accumulator = new StatsAccumulator();
accumulator.addAll(MANY_VALUES);
MANY_VALUES_STATS_SNAPSHOT = accumulator.snapshot();
accumulator.add(999.999); // should do nothing to the snapshot
}
static {
StatsAccumulator accumulator = new StatsAccumulator();
accumulator.addAll(LONG_MANY_VALUES);
LONG_MANY_VALUES_STATS_SNAPSHOT = accumulator.snapshot();
}
static final ImmutableList<Stats> ALL_STATS =
ImmutableList.of(
EMPTY_STATS_VARARGS,
EMPTY_STATS_ITERABLE,
ONE_VALUE_STATS,
OTHER_ONE_VALUE_STATS,
TWO_VALUES_STATS,
OTHER_TWO_VALUES_STATS,
MANY_VALUES_STATS_VARARGS,
MANY_VALUES_STATS_ITERABLE,
MANY_VALUES_STATS_ITERATOR,
MANY_VALUES_STATS_SNAPSHOT,
LARGE_VALUES_STATS,
OTHER_MANY_VALUES_STATS,
INTEGER_MANY_VALUES_STATS_VARARGS,
INTEGER_MANY_VALUES_STATS_ITERABLE,
LARGE_INTEGER_VALUES_STATS,
LONG_MANY_VALUES_STATS_ITERATOR,
LONG_MANY_VALUES_STATS_SNAPSHOT,
LARGE_LONG_VALUES_STATS);
// PairedStats instances:
static final PairedStats EMPTY_PAIRED_STATS =
createPairedStatsOf(ImmutableList.<Double>of(), ImmutableList.<Double>of());
static final PairedStats ONE_VALUE_PAIRED_STATS =
createPairedStatsOf(ImmutableList.of(ONE_VALUE), ImmutableList.of(OTHER_ONE_VALUE));
static final PairedStats TWO_VALUES_PAIRED_STATS =
createPairedStatsOf(TWO_VALUES, OTHER_TWO_VALUES);
static final PairedStats MANY_VALUES_PAIRED_STATS;
static final PairedStats DUPLICATE_MANY_VALUES_PAIRED_STATS =
createPairedStatsOf(MANY_VALUES, OTHER_MANY_VALUES);
static final PairedStats HORIZONTAL_VALUES_PAIRED_STATS;
static final PairedStats VERTICAL_VALUES_PAIRED_STATS;
static final PairedStats CONSTANT_VALUES_PAIRED_STATS;
static {
PairedStatsAccumulator accumulator =
createFilledPairedStatsAccumulator(MANY_VALUES, OTHER_MANY_VALUES);
MANY_VALUES_PAIRED_STATS = accumulator.snapshot();
accumulator.add(99.99, 9999.9999); // should do nothing to the snapshot
}
static {
PairedStatsAccumulator accumulator = new PairedStatsAccumulator();
for (double x : MANY_VALUES) {
accumulator.add(x, OTHER_ONE_VALUE);
}
HORIZONTAL_VALUES_PAIRED_STATS = accumulator.snapshot();
}
static {
PairedStatsAccumulator accumulator = new PairedStatsAccumulator();
for (double y : OTHER_MANY_VALUES) {
accumulator.add(ONE_VALUE, y);
}
VERTICAL_VALUES_PAIRED_STATS = accumulator.snapshot();
}
static {
PairedStatsAccumulator accumulator = new PairedStatsAccumulator();
for (int i = 0; i < MANY_VALUES_COUNT; ++i) {
accumulator.add(ONE_VALUE, OTHER_ONE_VALUE);
}
CONSTANT_VALUES_PAIRED_STATS = accumulator.snapshot();
}
static final ImmutableList<PairedStats> ALL_PAIRED_STATS =
ImmutableList.of(
EMPTY_PAIRED_STATS,
ONE_VALUE_PAIRED_STATS,
TWO_VALUES_PAIRED_STATS,
MANY_VALUES_PAIRED_STATS,
DUPLICATE_MANY_VALUES_PAIRED_STATS,
HORIZONTAL_VALUES_PAIRED_STATS,
VERTICAL_VALUES_PAIRED_STATS,
CONSTANT_VALUES_PAIRED_STATS);
// Helper methods:
static void assertStatsApproxEqual(Stats expectedStats, Stats actualStats) {
assertThat(actualStats.count()).isEqualTo(expectedStats.count());
if (expectedStats.count() == 0) {
try {
actualStats.mean();
fail("Expected IllegalStateException");
} catch (IllegalStateException expected) {
}
try {
actualStats.populationVariance();
fail("Expected IllegalStateException");
} catch (IllegalStateException expected) {
}
try {
actualStats.min();
fail("Expected IllegalStateException");
} catch (IllegalStateException expected) {
}
try {
actualStats.max();
fail("Expected IllegalStateException");
} catch (IllegalStateException expected) {
}
} else if (expectedStats.count() == 1) {
assertThat(actualStats.mean()).isWithin(ALLOWED_ERROR).of(expectedStats.mean());
assertThat(actualStats.populationVariance()).isWithin(0.0).of(0.0);
assertThat(actualStats.min()).isWithin(ALLOWED_ERROR).of(expectedStats.min());
assertThat(actualStats.max()).isWithin(ALLOWED_ERROR).of(expectedStats.max());
} else {
assertThat(actualStats.mean()).isWithin(ALLOWED_ERROR).of(expectedStats.mean());
assertThat(actualStats.populationVariance())
.isWithin(ALLOWED_ERROR)
.of(expectedStats.populationVariance());
assertThat(actualStats.min()).isWithin(ALLOWED_ERROR).of(expectedStats.min());
assertThat(actualStats.max()).isWithin(ALLOWED_ERROR).of(expectedStats.max());
}
}
/**
* Asserts that {@code transformation} is diagonal (i.e. neither horizontal or vertical) and
* passes through both {@code (x1, y1)} and {@code (x1 + xDelta, y1 + yDelta)}. Includes
* assertions about all the public instance methods of {@link LinearTransformation} (on both
* {@code transformation} and its inverse). Since the transformation is expected to be diagonal,
* neither {@code xDelta} nor {@code yDelta} may be zero.
*/
static void assertDiagonalLinearTransformation(
LinearTransformation transformation, double x1, double y1, double xDelta, double yDelta) {
checkArgument(xDelta != 0.0);
checkArgument(yDelta != 0.0);
assertThat(transformation.isHorizontal()).isFalse();
assertThat(transformation.isVertical()).isFalse();
assertThat(transformation.inverse().isHorizontal()).isFalse();
assertThat(transformation.inverse().isVertical()).isFalse();
assertThat(transformation.transform(x1)).isWithin(ALLOWED_ERROR).of(y1);
assertThat(transformation.transform(x1 + xDelta)).isWithin(ALLOWED_ERROR).of(y1 + yDelta);
assertThat(transformation.inverse().transform(y1)).isWithin(ALLOWED_ERROR).of(x1);
assertThat(transformation.inverse().transform(y1 + yDelta))
.isWithin(ALLOWED_ERROR)
.of(x1 + xDelta);
assertThat(transformation.slope()).isWithin(ALLOWED_ERROR).of(yDelta / xDelta);
assertThat(transformation.inverse().slope()).isWithin(ALLOWED_ERROR).of(xDelta / yDelta);
assertThat(transformation.inverse()).isSameAs(transformation.inverse());
assertThat(transformation.inverse().inverse()).isSameAs(transformation);
}
/**
* Asserts that {@code transformation} is horizontal with the given value of {@code y}. Includes
* assertions about all the public instance methods of {@link LinearTransformation}, including an
* assertion that {@link LinearTransformation#transform} and {@link LinearTransformation#slope}
* on its inverse throws as expected.
*/
static void assertHorizontalLinearTransformation(LinearTransformation transformation, double y) {
assertThat(transformation.isHorizontal()).isTrue();
assertThat(transformation.isVertical()).isFalse();
assertThat(transformation.inverse().isHorizontal()).isFalse();
assertThat(transformation.inverse().isVertical()).isTrue();
assertThat(transformation.transform(-1.0)).isWithin(ALLOWED_ERROR).of(y);
assertThat(transformation.transform(1.0)).isWithin(ALLOWED_ERROR).of(y);
try {
transformation.inverse().transform(0.0);
fail("Expected IllegalStateException");
} catch (IllegalStateException expected) {
}
assertThat(transformation.slope()).isWithin(ALLOWED_ERROR).of(0.0);
try {
transformation.inverse().slope();
fail("Expected IllegalStateException");
} catch (IllegalStateException expected) {
}
assertThat(transformation.inverse()).isSameAs(transformation.inverse());
assertThat(transformation.inverse().inverse()).isSameAs(transformation);
}
/**
* Asserts that {@code transformation} is vertical with the given value of {@code x}. Includes
* assertions about all the public instance methods of {@link LinearTransformation}, including
* assertions that {@link LinearTransformation#slope} and {@link LinearTransformation#transform}
* throw as expected.
*/
static void assertVerticalLinearTransformation(LinearTransformation transformation, double x) {
assertThat(transformation.isHorizontal()).isFalse();
assertThat(transformation.isVertical()).isTrue();
assertThat(transformation.inverse().isHorizontal()).isTrue();
assertThat(transformation.inverse().isVertical()).isFalse();
try {
transformation.transform(0.0);
fail("Expected IllegalStateException");
} catch (IllegalStateException expected) {
}
assertThat(transformation.inverse().transform(-1.0)).isWithin(ALLOWED_ERROR).of(x);
assertThat(transformation.inverse().transform(1.0)).isWithin(ALLOWED_ERROR).of(x);
try {
transformation.slope();
fail("Expected IllegalStateException");
} catch (IllegalStateException expected) {
}
assertThat(transformation.inverse().slope()).isWithin(ALLOWED_ERROR).of(0.0);
assertThat(transformation.inverse()).isSameAs(transformation.inverse());
assertThat(transformation.inverse().inverse()).isSameAs(transformation);
}
/**
* Asserts that {@code transformation} behaves as expected for
* {@link LinearTransformation#forNaN}.
*/
static void assertLinearTransformationNaN(LinearTransformation transformation) {
assertThat(transformation.isHorizontal()).isFalse();
assertThat(transformation.isVertical()).isFalse();
assertThat(transformation.slope()).isNaN();
assertThat(transformation.transform(0.0)).isNaN();
assertThat(transformation.inverse()).isSameAs(transformation);
}
/**
* Creates a {@link PairedStats} from with the given lists of {@code x} and {@code y} values,
* which must be of the same size.
*/
static PairedStats createPairedStatsOf(List<Double> xValues, List<Double> yValues) {
return createFilledPairedStatsAccumulator(xValues, yValues).snapshot();
}
/**
* Creates a {@link PairedStatsAccumulator} filled with the given lists of {@code x} and {@code y}
* values, which must be of the same size.
*/
static PairedStatsAccumulator createFilledPairedStatsAccumulator(
List<Double> xValues, List<Double> yValues) {
checkArgument(xValues.size() == yValues.size());
PairedStatsAccumulator accumulator = new PairedStatsAccumulator();
for (int index = 0; index < xValues.size(); index++) {
accumulator.add(xValues.get(index), yValues.get(index));
}
return accumulator;
}
/**
* Creates a {@link PairedStatsAccumulator} filled with the given lists of {@code x} and {@code y}
* values, which must be of the same size, added in groups of {@code partitionSize} using
* {@link PairedStatsAccumulator#addAll(PairedStats)}.
*/
static PairedStatsAccumulator createPartitionedFilledPairedStatsAccumulator(
List<Double> xValues, List<Double> yValues, int partitionSize) {
checkArgument(xValues.size() == yValues.size());
checkArgument(partitionSize > 0);
PairedStatsAccumulator accumulator = new PairedStatsAccumulator();
List<List<Double>> xPartitions = Lists.partition(xValues, partitionSize);
List<List<Double>> yPartitions = Lists.partition(yValues, partitionSize);
for (int index = 0; index < xPartitions.size(); index++) {
accumulator.addAll(createPairedStatsOf(xPartitions.get(index), yPartitions.get(index)));
}
return accumulator;
}
private StatsTesting() {}
}