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* 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.
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package org.apache.commons.math3.optimization.univariate;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.TooManyEvaluationsException;
import org.apache.commons.math3.analysis.QuinticFunction;
import org.apache.commons.math3.analysis.SinFunction;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.optimization.GoalType;
import org.apache.commons.math3.stat.descriptive.DescriptiveStatistics;
import org.junit.Assert;
import org.junit.Test;
/**
* @version $Id$
*/
public final class BrentOptimizerTest {
@Test
public void testSinMin() {
UnivariateFunction f = new SinFunction();
UnivariateOptimizer optimizer = new BrentOptimizer(1e-10, 1e-14);
Assert.assertEquals(3 * Math.PI / 2, optimizer.optimize(200, f, GoalType.MINIMIZE, 4, 5).getPoint(),1e-8);
Assert.assertTrue(optimizer.getEvaluations() <= 50);
Assert.assertEquals(200, optimizer.getMaxEvaluations());
Assert.assertEquals(3 * Math.PI / 2, optimizer.optimize(200, f, GoalType.MINIMIZE, 1, 5).getPoint(), 1e-8);
Assert.assertTrue(optimizer.getEvaluations() <= 100);
Assert.assertTrue(optimizer.getEvaluations() >= 15);
try {
optimizer.optimize(10, f, GoalType.MINIMIZE, 4, 5);
Assert.fail("an exception should have been thrown");
} catch (TooManyEvaluationsException fee) {
// expected
}
}
@Test
public void testBoundaries() {
final double lower = -1.0;
final double upper = +1.0;
UnivariateFunction f = new UnivariateFunction() {
public double value(double x) {
if (x < lower) {
throw new NumberIsTooSmallException(x, lower, true);
} else if (x > upper) {
throw new NumberIsTooLargeException(x, upper, true);
} else {
return x;
}
}
};
UnivariateOptimizer optimizer = new BrentOptimizer(1e-10, 1e-14);
Assert.assertEquals(lower,
optimizer.optimize(100, f, GoalType.MINIMIZE, lower, upper).getPoint(),
1.0e-8);
Assert.assertEquals(upper,
optimizer.optimize(100, f, GoalType.MAXIMIZE, lower, upper).getPoint(),
1.0e-8);
}
@Test
public void testQuinticMin() {
// The function has local minima at -0.27195613 and 0.82221643.
UnivariateFunction f = new QuinticFunction();
UnivariateOptimizer optimizer = new BrentOptimizer(1e-10, 1e-14);
Assert.assertEquals(-0.27195613, optimizer.optimize(200, f, GoalType.MINIMIZE, -0.3, -0.2).getPoint(), 1.0e-8);
Assert.assertEquals( 0.82221643, optimizer.optimize(200, f, GoalType.MINIMIZE, 0.3, 0.9).getPoint(), 1.0e-8);
Assert.assertTrue(optimizer.getEvaluations() <= 50);
// search in a large interval
Assert.assertEquals(-0.27195613, optimizer.optimize(200, f, GoalType.MINIMIZE, -1.0, 0.2).getPoint(), 1.0e-8);
Assert.assertTrue(optimizer.getEvaluations() <= 50);
}
@Test
public void testQuinticMinStatistics() {
// The function has local minima at -0.27195613 and 0.82221643.
UnivariateFunction f = new QuinticFunction();
UnivariateOptimizer optimizer = new BrentOptimizer(1e-11, 1e-14);
final DescriptiveStatistics[] stat = new DescriptiveStatistics[2];
for (int i = 0; i < stat.length; i++) {
stat[i] = new DescriptiveStatistics();
}
final double min = -0.75;
final double max = 0.25;
final int nSamples = 200;
final double delta = (max - min) / nSamples;
for (int i = 0; i < nSamples; i++) {
final double start = min + i * delta;
stat[0].addValue(optimizer.optimize(40, f, GoalType.MINIMIZE, min, max, start).getPoint());
stat[1].addValue(optimizer.getEvaluations());
}
final double meanOptValue = stat[0].getMean();
final double medianEval = stat[1].getPercentile(50);
Assert.assertTrue(meanOptValue > -0.2719561281);
Assert.assertTrue(meanOptValue < -0.2719561280);
Assert.assertEquals(23, (int) medianEval);
}
@Test
public void testQuinticMax() {
// The quintic function has zeros at 0, +-0.5 and +-1.
// The function has a local maximum at 0.27195613.
UnivariateFunction f = new QuinticFunction();
UnivariateOptimizer optimizer = new BrentOptimizer(1e-12, 1e-14);
Assert.assertEquals(0.27195613, optimizer.optimize(100, f, GoalType.MAXIMIZE, 0.2, 0.3).getPoint(), 1e-8);
try {
optimizer.optimize(5, f, GoalType.MAXIMIZE, 0.2, 0.3);
Assert.fail("an exception should have been thrown");
} catch (TooManyEvaluationsException miee) {
// expected
}
}
@Test
public void testMinEndpoints() {
UnivariateFunction f = new SinFunction();
UnivariateOptimizer optimizer = new BrentOptimizer(1e-8, 1e-14);
// endpoint is minimum
double result = optimizer.optimize(50, f, GoalType.MINIMIZE, 3 * Math.PI / 2, 5).getPoint();
Assert.assertEquals(3 * Math.PI / 2, result, 1e-6);
result = optimizer.optimize(50, f, GoalType.MINIMIZE, 4, 3 * Math.PI / 2).getPoint();
Assert.assertEquals(3 * Math.PI / 2, result, 1e-6);
}
}