/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You 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 org.apache.commons.math3.stat;
import org.apache.commons.math3.TestUtils;
import org.apache.commons.math3.stat.descriptive.DescriptiveStatistics;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.Precision;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.junit.Assert;
import org.junit.Test;
/**
* Test cases for the {@link StatUtils} class.
*/
public final class StatUtilsTest {
private static final double ONE = 1;
private static final float TWO = 2;
private static final int THREE = 3;
private static final double MEAN = 2;
private static final double SUMSQ = 18;
private static final double SUM = 8;
private static final double VAR = 0.666666666666666666667;
private static final double MIN = 1;
private static final double MAX = 3;
private static final double TOLERANCE = 10E-15;
private static final double NAN = Double.NaN;
/** test stats */
@Test
public void testStats() {
double[] values = new double[] { ONE, TWO, TWO, THREE };
Assert.assertEquals("sum", SUM, StatUtils.sum(values), TOLERANCE);
Assert.assertEquals("sumsq", SUMSQ, StatUtils.sumSq(values), TOLERANCE);
Assert.assertEquals("var", VAR, StatUtils.variance(values), TOLERANCE);
Assert.assertEquals("var with mean", VAR, StatUtils.variance(values, MEAN), TOLERANCE);
Assert.assertEquals("mean", MEAN, StatUtils.mean(values), TOLERANCE);
Assert.assertEquals("min", MIN, StatUtils.min(values), TOLERANCE);
Assert.assertEquals("max", MAX, StatUtils.max(values), TOLERANCE);
}
@Test
public void testN0andN1Conditions() {
double[] values = new double[0];
Assert.assertTrue(
"Mean of n = 0 set should be NaN",
Double.isNaN(StatUtils.mean(values)));
Assert.assertTrue(
"Variance of n = 0 set should be NaN",
Double.isNaN(StatUtils.variance(values)));
values = new double[] { ONE };
Assert.assertTrue(
"Mean of n = 1 set should be value of single item n1",
StatUtils.mean(values) == ONE);
Assert.assertTrue(
"Variance of n = 1 set should be zero",
StatUtils.variance(values) == 0);
}
@Test
public void testArrayIndexConditions() {
double[] values = { 1.0, 2.0, 3.0, 4.0 };
Assert.assertEquals(
"Sum not expected",
5.0,
StatUtils.sum(values, 1, 2),
Double.MIN_VALUE);
Assert.assertEquals(
"Sum not expected",
3.0,
StatUtils.sum(values, 0, 2),
Double.MIN_VALUE);
Assert.assertEquals(
"Sum not expected",
7.0,
StatUtils.sum(values, 2, 2),
Double.MIN_VALUE);
try {
StatUtils.sum(values, 2, 3);
Assert.fail("Expected RuntimeException");
} catch (RuntimeException e) {
// expected
}
try {
StatUtils.sum(values, -1, 2);
Assert.fail("Expected RuntimeException");
} catch (RuntimeException e) {
// expected
}
}
@Test
public void testSumSq() {
double[] x = null;
// test null
try {
StatUtils.sumSq(x);
Assert.fail("null is not a valid data array.");
} catch (MathIllegalArgumentException ex) {
// success
}
try {
StatUtils.sumSq(x, 0, 4);
Assert.fail("null is not a valid data array.");
} catch (MathIllegalArgumentException ex) {
// success
}
// test empty
x = new double[] {};
TestUtils.assertEquals(0, StatUtils.sumSq(x), TOLERANCE);
TestUtils.assertEquals(0, StatUtils.sumSq(x, 0, 0), TOLERANCE);
// test one
x = new double[] {TWO};
TestUtils.assertEquals(4, StatUtils.sumSq(x), TOLERANCE);
TestUtils.assertEquals(4, StatUtils.sumSq(x, 0, 1), TOLERANCE);
// test many
x = new double[] {ONE, TWO, TWO, THREE};
TestUtils.assertEquals(18, StatUtils.sumSq(x), TOLERANCE);
TestUtils.assertEquals(8, StatUtils.sumSq(x, 1, 2), TOLERANCE);
}
@Test
public void testProduct() {
double[] x = null;
// test null
try {
StatUtils.product(x);
Assert.fail("null is not a valid data array.");
} catch (MathIllegalArgumentException ex) {
// success
}
try {
StatUtils.product(x, 0, 4);
Assert.fail("null is not a valid data array.");
} catch (MathIllegalArgumentException ex) {
// success
}
// test empty
x = new double[] {};
TestUtils.assertEquals(1, StatUtils.product(x), TOLERANCE);
TestUtils.assertEquals(1, StatUtils.product(x, 0, 0), TOLERANCE);
// test one
x = new double[] {TWO};
TestUtils.assertEquals(TWO, StatUtils.product(x), TOLERANCE);
TestUtils.assertEquals(TWO, StatUtils.product(x, 0, 1), TOLERANCE);
// test many
x = new double[] {ONE, TWO, TWO, THREE};
TestUtils.assertEquals(12, StatUtils.product(x), TOLERANCE);
TestUtils.assertEquals(4, StatUtils.product(x, 1, 2), TOLERANCE);
}
@Test
public void testSumLog() {
double[] x = null;
// test null
try {
StatUtils.sumLog(x);
Assert.fail("null is not a valid data array.");
} catch (MathIllegalArgumentException ex) {
// success
}
try {
StatUtils.sumLog(x, 0, 4);
Assert.fail("null is not a valid data array.");
} catch (MathIllegalArgumentException ex) {
// success
}
// test empty
x = new double[] {};
TestUtils.assertEquals(0, StatUtils.sumLog(x), TOLERANCE);
TestUtils.assertEquals(0, StatUtils.sumLog(x, 0, 0), TOLERANCE);
// test one
x = new double[] {TWO};
TestUtils.assertEquals(FastMath.log(TWO), StatUtils.sumLog(x), TOLERANCE);
TestUtils.assertEquals(FastMath.log(TWO), StatUtils.sumLog(x, 0, 1), TOLERANCE);
// test many
x = new double[] {ONE, TWO, TWO, THREE};
TestUtils.assertEquals(FastMath.log(ONE) + 2.0 * FastMath.log(TWO) + FastMath.log(THREE), StatUtils.sumLog(x), TOLERANCE);
TestUtils.assertEquals(2.0 * FastMath.log(TWO), StatUtils.sumLog(x, 1, 2), TOLERANCE);
}
@Test
public void testMean() {
double[] x = null;
try {
StatUtils.mean(x, 0, 4);
Assert.fail("null is not a valid data array.");
} catch (MathIllegalArgumentException ex) {
// success
}
// test empty
x = new double[] {};
TestUtils.assertEquals(Double.NaN, StatUtils.mean(x, 0, 0), TOLERANCE);
// test one
x = new double[] {TWO};
TestUtils.assertEquals(TWO, StatUtils.mean(x, 0, 1), TOLERANCE);
// test many
x = new double[] {ONE, TWO, TWO, THREE};
TestUtils.assertEquals(2.5, StatUtils.mean(x, 2, 2), TOLERANCE);
}
@Test
public void testVariance() {
double[] x = null;
try {
StatUtils.variance(x, 0, 4);
Assert.fail("null is not a valid data array.");
} catch (MathIllegalArgumentException ex) {
// success
}
// test empty
x = new double[] {};
TestUtils.assertEquals(Double.NaN, StatUtils.variance(x, 0, 0), TOLERANCE);
// test one
x = new double[] {TWO};
TestUtils.assertEquals(0.0, StatUtils.variance(x, 0, 1), TOLERANCE);
// test many
x = new double[] {ONE, TWO, TWO, THREE};
TestUtils.assertEquals(0.5, StatUtils.variance(x, 2, 2), TOLERANCE);
// test precomputed mean
x = new double[] {ONE, TWO, TWO, THREE};
TestUtils.assertEquals(0.5, StatUtils.variance(x,2.5, 2, 2), TOLERANCE);
}
@Test
public void testPopulationVariance() {
double[] x = null;
try {
StatUtils.variance(x, 0, 4);
Assert.fail("null is not a valid data array.");
} catch (MathIllegalArgumentException ex) {
// success
}
// test empty
x = new double[] {};
TestUtils.assertEquals(Double.NaN, StatUtils.populationVariance(x, 0, 0), TOLERANCE);
// test one
x = new double[] {TWO};
TestUtils.assertEquals(0.0, StatUtils.populationVariance(x, 0, 1), TOLERANCE);
// test many
x = new double[] {ONE, TWO, TWO, THREE};
TestUtils.assertEquals(0.25, StatUtils.populationVariance(x, 0, 2), TOLERANCE);
// test precomputed mean
x = new double[] {ONE, TWO, TWO, THREE};
TestUtils.assertEquals(0.25, StatUtils.populationVariance(x, 2.5, 2, 2), TOLERANCE);
}
@Test
public void testMax() {
double[] x = null;
try {
StatUtils.max(x, 0, 4);
Assert.fail("null is not a valid data array.");
} catch (MathIllegalArgumentException ex) {
// success
}
// test empty
x = new double[] {};
TestUtils.assertEquals(Double.NaN, StatUtils.max(x, 0, 0), TOLERANCE);
// test one
x = new double[] {TWO};
TestUtils.assertEquals(TWO, StatUtils.max(x, 0, 1), TOLERANCE);
// test many
x = new double[] {ONE, TWO, TWO, THREE};
TestUtils.assertEquals(THREE, StatUtils.max(x, 1, 3), TOLERANCE);
// test first nan is ignored
x = new double[] {NAN, TWO, THREE};
TestUtils.assertEquals(THREE, StatUtils.max(x), TOLERANCE);
// test middle nan is ignored
x = new double[] {ONE, NAN, THREE};
TestUtils.assertEquals(THREE, StatUtils.max(x), TOLERANCE);
// test last nan is ignored
x = new double[] {ONE, TWO, NAN};
TestUtils.assertEquals(TWO, StatUtils.max(x), TOLERANCE);
// test all nan returns nan
x = new double[] {NAN, NAN, NAN};
TestUtils.assertEquals(NAN, StatUtils.max(x), TOLERANCE);
}
@Test
public void testMin() {
double[] x = null;
try {
StatUtils.min(x, 0, 4);
Assert.fail("null is not a valid data array.");
} catch (MathIllegalArgumentException ex) {
// success
}
// test empty
x = new double[] {};
TestUtils.assertEquals(Double.NaN, StatUtils.min(x, 0, 0), TOLERANCE);
// test one
x = new double[] {TWO};
TestUtils.assertEquals(TWO, StatUtils.min(x, 0, 1), TOLERANCE);
// test many
x = new double[] {ONE, TWO, TWO, THREE};
TestUtils.assertEquals(TWO, StatUtils.min(x, 1, 3), TOLERANCE);
// test first nan is ignored
x = new double[] {NAN, TWO, THREE};
TestUtils.assertEquals(TWO, StatUtils.min(x), TOLERANCE);
// test middle nan is ignored
x = new double[] {ONE, NAN, THREE};
TestUtils.assertEquals(ONE, StatUtils.min(x), TOLERANCE);
// test last nan is ignored
x = new double[] {ONE, TWO, NAN};
TestUtils.assertEquals(ONE, StatUtils.min(x), TOLERANCE);
// test all nan returns nan
x = new double[] {NAN, NAN, NAN};
TestUtils.assertEquals(NAN, StatUtils.min(x), TOLERANCE);
}
@Test
public void testPercentile() {
double[] x = null;
// test null
try {
StatUtils.percentile(x, .25);
Assert.fail("null is not a valid data array.");
} catch (MathIllegalArgumentException ex) {
// success
}
try {
StatUtils.percentile(x, 0, 4, 0.25);
Assert.fail("null is not a valid data array.");
} catch (MathIllegalArgumentException ex) {
// success
}
// test empty
x = new double[] {};
TestUtils.assertEquals(Double.NaN, StatUtils.percentile(x, 25), TOLERANCE);
TestUtils.assertEquals(Double.NaN, StatUtils.percentile(x, 0, 0, 25), TOLERANCE);
// test one
x = new double[] {TWO};
TestUtils.assertEquals(TWO, StatUtils.percentile(x, 25), TOLERANCE);
TestUtils.assertEquals(TWO, StatUtils.percentile(x, 0, 1, 25), TOLERANCE);
// test many
x = new double[] {ONE, TWO, TWO, THREE};
TestUtils.assertEquals(2.5, StatUtils.percentile(x, 70), TOLERANCE);
TestUtils.assertEquals(2.5, StatUtils.percentile(x, 1, 3, 62.5), TOLERANCE);
}
@Test
public void testDifferenceStats() {
double sample1[] = {1d, 2d, 3d, 4d};
double sample2[] = {1d, 3d, 4d, 2d};
double diff[] = {0d, -1d, -1d, 2d};
double small[] = {1d, 4d};
double meanDifference = StatUtils.meanDifference(sample1, sample2);
Assert.assertEquals(StatUtils.sumDifference(sample1, sample2), StatUtils.sum(diff), TOLERANCE);
Assert.assertEquals(meanDifference, StatUtils.mean(diff), TOLERANCE);
Assert.assertEquals(StatUtils.varianceDifference(sample1, sample2, meanDifference),
StatUtils.variance(diff), TOLERANCE);
try {
StatUtils.meanDifference(sample1, small);
Assert.fail("Expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// expected
}
try {
StatUtils.varianceDifference(sample1, small, meanDifference);
Assert.fail("Expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// expected
}
try {
double[] single = {1.0};
StatUtils.varianceDifference(single, single, meanDifference);
Assert.fail("Expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// expected
}
}
@Test
public void testGeometricMean() {
double[] test = null;
try {
StatUtils.geometricMean(test);
Assert.fail("Expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// expected
}
test = new double[] {2, 4, 6, 8};
Assert.assertEquals(FastMath.exp(0.25d * StatUtils.sumLog(test)),
StatUtils.geometricMean(test), Double.MIN_VALUE);
Assert.assertEquals(FastMath.exp(0.5 * StatUtils.sumLog(test, 0, 2)),
StatUtils.geometricMean(test, 0, 2), Double.MIN_VALUE);
}
/**
* Run the test with the values 50 and 100 and assume standardized values
*/
@Test
public void testNormalize1() {
double sample[] = { 50, 100 };
double expectedSample[] = { -25 / FastMath.sqrt(1250), 25 / FastMath.sqrt(1250) };
double[] out = StatUtils.normalize(sample);
for (int i = 0; i < out.length; i++) {
Assert.assertTrue(Precision.equals(out[i], expectedSample[i], 1));
}
}
/**
* Run with 77 random values, assuming that the outcome has a mean of 0 and a standard deviation of 1 with a
* precision of 1E-10.
*/
@Test
public void testNormalize2() {
// create an sample with 77 values
int length = 77;
double sample[] = new double[length];
for (int i = 0; i < length; i++) {
sample[i] = FastMath.random();
}
// normalize this sample
double standardizedSample[] = StatUtils.normalize(sample);
DescriptiveStatistics stats = new DescriptiveStatistics();
// Add the data from the array
for (int i = 0; i < length; i++) {
stats.addValue(standardizedSample[i]);
}
// the calculations do have a limited precision
double distance = 1E-10;
// check the mean an standard deviation
Assert.assertEquals(0.0, stats.getMean(), distance);
Assert.assertEquals(1.0, stats.getStandardDeviation(), distance);
}
@Test
public void testMode() {
final double[] singleMode = {0, 1, 0, 2, 7, 11, 12};
final double[] modeSingle = StatUtils.mode(singleMode);
Assert.assertEquals(0, modeSingle[0], Double.MIN_VALUE);
Assert.assertEquals(1, modeSingle.length);
final double[] twoMode = {0, 1, 2, 0, 2, 3, 7, 11};
final double[] modeDouble = StatUtils.mode(twoMode);
Assert.assertEquals(0, modeDouble[0], Double.MIN_VALUE);
Assert.assertEquals(2, modeDouble[1], Double.MIN_VALUE);
Assert.assertEquals(2, modeDouble.length);
final double[] nanInfested = {0, 0, 0, Double.NaN, Double.NaN, Double.NaN, Double.NaN, 2, 2, 2, 3, 5};
final double[] modeNan = StatUtils.mode(nanInfested);
Assert.assertEquals(0, modeNan[0], Double.MIN_VALUE);
Assert.assertEquals(2, modeNan[1], Double.MIN_VALUE);
Assert.assertEquals(2, modeNan.length);
final double[] infInfested = {0, 0, Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY,
Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY, 2, 2, 3, 5};
final double[] modeInf = StatUtils.mode(infInfested);
Assert.assertEquals(Double.NEGATIVE_INFINITY, modeInf[0], Double.MIN_VALUE);
Assert.assertEquals(0, modeInf[1], Double.MIN_VALUE);
Assert.assertEquals(2, modeInf[2], Double.MIN_VALUE);
Assert.assertEquals(Double.POSITIVE_INFINITY, modeInf[3], Double.MIN_VALUE);
Assert.assertEquals(4, modeInf.length);
final double[] noData = {};
final double[] modeNodata = StatUtils.mode(noData);
Assert.assertEquals(0, modeNodata.length);
final double[] nansOnly = {Double.NaN, Double.NaN};
final double[] modeNansOnly = StatUtils.mode(nansOnly);
Assert.assertEquals(0, modeNansOnly.length);
final double[] nullArray = null;
try {
StatUtils.mode(nullArray);
Assert.fail("Expecting MathIllegalArgumentException");
} catch (MathIllegalArgumentException ex) {
// Expected
}
}
}