/*
* 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.math4.stat.descriptive.moment;
import org.apache.commons.math4.TestUtils;
import org.apache.commons.math4.exception.NullArgumentException;
import org.apache.commons.math4.stat.StatUtils;
import org.apache.commons.math4.stat.descriptive.moment.SemiVariance;
import org.junit.Assert;
import org.junit.Test;
public class SemiVarianceTest {
@Test
public void testInsufficientData() {
double[] nothing = null;
SemiVariance sv = new SemiVariance();
try {
sv.evaluate(nothing);
Assert.fail("null is not a valid data array.");
} catch (NullArgumentException nae) {
}
try {
sv.setVarianceDirection(SemiVariance.UPSIDE_VARIANCE);
sv.evaluate(nothing);
Assert.fail("null is not a valid data array.");
} catch (NullArgumentException nae) {
}
nothing = new double[] {};
Assert.assertTrue(Double.isNaN(sv.evaluate(nothing)));
}
@Test
public void testSingleDown() {
SemiVariance sv = new SemiVariance();
double[] values = { 50.0d };
double singletest = sv.evaluate(values);
Assert.assertEquals(0.0d, singletest, 0);
}
@Test
public void testSingleUp() {
SemiVariance sv = new SemiVariance(SemiVariance.UPSIDE_VARIANCE);
double[] values = { 50.0d };
double singletest = sv.evaluate(values);
Assert.assertEquals(0.0d, singletest, 0);
}
@Test
public void testSample() {
final double[] values = { -2.0d, 2.0d, 4.0d, -2.0d, 22.0d, 11.0d, 3.0d, 14.0d, 5.0d };
final int length = values.length;
final double mean = StatUtils.mean(values); // 6.333...
final SemiVariance sv = new SemiVariance(); // Default bias correction is true
final double downsideSemiVariance = sv.evaluate(values); // Downside is the default
Assert.assertEquals(TestUtils.sumSquareDev(new double[] {-2d, 2d, 4d, -2d, 3d, 5d}, mean) / (length - 1),
downsideSemiVariance, 1E-14);
sv.setVarianceDirection(SemiVariance.UPSIDE_VARIANCE);
final double upsideSemiVariance = sv.evaluate(values);
Assert.assertEquals(TestUtils.sumSquareDev(new double[] {22d, 11d, 14d}, mean) / (length - 1),
upsideSemiVariance, 1E-14);
// Verify that upper + lower semivariance against the mean sum to variance
Assert.assertEquals(StatUtils.variance(values), downsideSemiVariance + upsideSemiVariance, 10e-12);
}
@Test
public void testPopulation() {
double[] values = { -2.0d, 2.0d, 4.0d, -2.0d, 22.0d, 11.0d, 3.0d, 14.0d, 5.0d };
SemiVariance sv = new SemiVariance(false);
double singletest = sv.evaluate(values);
Assert.assertEquals(19.556d, singletest, 0.01d);
sv.setVarianceDirection(SemiVariance.UPSIDE_VARIANCE);
singletest = sv.evaluate(values);
Assert.assertEquals(36.222d, singletest, 0.01d);
}
@Test
public void testNonMeanCutoffs() {
double[] values = { -2.0d, 2.0d, 4.0d, -2.0d, 22.0d, 11.0d, 3.0d, 14.0d, 5.0d };
SemiVariance sv = new SemiVariance(false); // Turn off bias correction - use df = length
double singletest = sv.evaluate(values, 1.0d, SemiVariance.DOWNSIDE_VARIANCE, false, 0, values.length);
Assert.assertEquals(TestUtils.sumSquareDev(new double[] { -2d, -2d }, 1.0d) / values.length,
singletest, 0.01d);
singletest = sv.evaluate(values, 3.0d, SemiVariance.UPSIDE_VARIANCE, false, 0, values.length);
Assert.assertEquals(TestUtils.sumSquareDev(new double[] { 4d, 22d, 11d, 14d, 5d }, 3.0d) / values.length, singletest,
0.01d);
}
/**
* Check that the lower + upper semivariance against the mean sum to the
* variance.
*/
@Test
public void testVarianceDecompMeanCutoff() {
double[] values = { -2.0d, 2.0d, 4.0d, -2.0d, 22.0d, 11.0d, 3.0d, 14.0d, 5.0d };
double variance = StatUtils.variance(values);
SemiVariance sv = new SemiVariance(true); // Bias corrected
sv.setVarianceDirection(SemiVariance.DOWNSIDE_VARIANCE);
final double lower = sv.evaluate(values);
sv.setVarianceDirection(SemiVariance.UPSIDE_VARIANCE);
final double upper = sv.evaluate(values);
Assert.assertEquals(variance, lower + upper, 10e-12);
}
/**
* Check that upper and lower semivariances against a cutoff sum to the sum
* of squared deviations of the full set of values against the cutoff
* divided by df = length - 1 (assuming bias-corrected).
*/
@Test
public void testVarianceDecompNonMeanCutoff() {
double[] values = { -2.0d, 2.0d, 4.0d, -2.0d, 22.0d, 11.0d, 3.0d, 14.0d, 5.0d };
double target = 0;
double totalSumOfSquares = TestUtils.sumSquareDev(values, target);
SemiVariance sv = new SemiVariance(true); // Bias corrected
sv.setVarianceDirection(SemiVariance.DOWNSIDE_VARIANCE);
double lower = sv.evaluate(values, target);
sv.setVarianceDirection(SemiVariance.UPSIDE_VARIANCE);
double upper = sv.evaluate(values, target);
Assert.assertEquals(totalSumOfSquares / (values.length - 1), lower + upper, 10e-12);
}
@Test
public void testNoVariance() {
final double[] values = {100d, 100d, 100d, 100d};
SemiVariance sv = new SemiVariance();
Assert.assertEquals(0, sv.evaluate(values), 10E-12);
Assert.assertEquals(0, sv.evaluate(values, 100d), 10E-12);
Assert.assertEquals(0, sv.evaluate(values, 100d, SemiVariance.UPSIDE_VARIANCE, false, 0, values.length), 10E-12);
}
}