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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.
*/
package org.apache.commons.math4.optim.univariate;
import org.apache.commons.math4.analysis.FunctionUtils;
import org.apache.commons.math4.analysis.QuinticFunction;
import org.apache.commons.math4.analysis.UnivariateFunction;
import org.apache.commons.math4.analysis.function.Sin;
import org.apache.commons.math4.analysis.function.StepFunction;
import org.apache.commons.math4.exception.NumberIsTooLargeException;
import org.apache.commons.math4.exception.NumberIsTooSmallException;
import org.apache.commons.math4.exception.TooManyEvaluationsException;
import org.apache.commons.math4.optim.ConvergenceChecker;
import org.apache.commons.math4.optim.MaxEval;
import org.apache.commons.math4.optim.nonlinear.scalar.GoalType;
import org.apache.commons.math4.optim.univariate.BrentOptimizer;
import org.apache.commons.math4.optim.univariate.SearchInterval;
import org.apache.commons.math4.optim.univariate.SimpleUnivariateValueChecker;
import org.apache.commons.math4.optim.univariate.UnivariateObjectiveFunction;
import org.apache.commons.math4.optim.univariate.UnivariateOptimizer;
import org.apache.commons.math4.optim.univariate.UnivariatePointValuePair;
import org.apache.commons.math4.stat.descriptive.DescriptiveStatistics;
import org.apache.commons.math4.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
/**
*/
public final class BrentOptimizerTest {
@Test
public void testSinMin() {
UnivariateFunction f = new Sin();
UnivariateOptimizer optimizer = new BrentOptimizer(1e-10, 1e-14);
Assert.assertEquals(3 * Math.PI / 2, optimizer.optimize(new MaxEval(200),
new UnivariateObjectiveFunction(f),
GoalType.MINIMIZE,
new SearchInterval(4, 5)).getPoint(), 1e-8);
Assert.assertTrue(optimizer.getEvaluations() <= 50);
Assert.assertEquals(200, optimizer.getMaxEvaluations());
Assert.assertEquals(3 * Math.PI / 2, optimizer.optimize(new MaxEval(200),
new UnivariateObjectiveFunction(f),
GoalType.MINIMIZE,
new SearchInterval(1, 5)).getPoint(), 1e-8);
Assert.assertTrue(optimizer.getEvaluations() <= 100);
Assert.assertTrue(optimizer.getEvaluations() >= 15);
try {
optimizer.optimize(new MaxEval(10),
new UnivariateObjectiveFunction(f),
GoalType.MINIMIZE,
new SearchInterval(4, 5));
Assert.fail("an exception should have been thrown");
} catch (TooManyEvaluationsException fee) {
// expected
}
}
@Test
public void testSinMinWithValueChecker() {
final UnivariateFunction f = new Sin();
final ConvergenceChecker<UnivariatePointValuePair> checker = new SimpleUnivariateValueChecker(1e-5, 1e-14);
// The default stopping criterion of Brent's algorithm should not
// pass, but the search will stop at the given relative tolerance
// for the function value.
final UnivariateOptimizer optimizer = new BrentOptimizer(1e-10, 1e-14, checker);
final UnivariatePointValuePair result = optimizer.optimize(new MaxEval(200),
new UnivariateObjectiveFunction(f),
GoalType.MINIMIZE,
new SearchInterval(4, 5));
Assert.assertEquals(3 * Math.PI / 2, result.getPoint(), 1e-3);
}
@Test
public void testBoundaries() {
final double lower = -1.0;
final double upper = +1.0;
UnivariateFunction f = new UnivariateFunction() {
@Override
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(new MaxEval(100),
new UnivariateObjectiveFunction(f),
GoalType.MINIMIZE,
new SearchInterval(lower, upper)).getPoint(),
1.0e-8);
Assert.assertEquals(upper,
optimizer.optimize(new MaxEval(100),
new UnivariateObjectiveFunction(f),
GoalType.MAXIMIZE,
new SearchInterval(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(new MaxEval(200),
new UnivariateObjectiveFunction(f),
GoalType.MINIMIZE,
new SearchInterval(-0.3, -0.2)).getPoint(), 1.0e-8);
Assert.assertEquals( 0.82221643, optimizer.optimize(new MaxEval(200),
new UnivariateObjectiveFunction(f),
GoalType.MINIMIZE,
new SearchInterval(0.3, 0.9)).getPoint(), 1.0e-8);
Assert.assertTrue(optimizer.getEvaluations() <= 50);
// search in a large interval
Assert.assertEquals(-0.27195613, optimizer.optimize(new MaxEval(200),
new UnivariateObjectiveFunction(f),
GoalType.MINIMIZE,
new SearchInterval(-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(new MaxEval(40),
new UnivariateObjectiveFunction(f),
GoalType.MINIMIZE,
new SearchInterval(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);
// MATH-1121: Ensure that the iteration counter is incremented.
Assert.assertTrue(optimizer.getIterations() > 0);
}
@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(new MaxEval(100),
new UnivariateObjectiveFunction(f),
GoalType.MAXIMIZE,
new SearchInterval(0.2, 0.3)).getPoint(), 1e-8);
try {
optimizer.optimize(new MaxEval(5),
new UnivariateObjectiveFunction(f),
GoalType.MAXIMIZE,
new SearchInterval(0.2, 0.3));
Assert.fail("an exception should have been thrown");
} catch (TooManyEvaluationsException miee) {
// expected
}
}
@Test
public void testMinEndpoints() {
UnivariateFunction f = new Sin();
UnivariateOptimizer optimizer = new BrentOptimizer(1e-8, 1e-14);
// endpoint is minimum
double result = optimizer.optimize(new MaxEval(50),
new UnivariateObjectiveFunction(f),
GoalType.MINIMIZE,
new SearchInterval(3 * Math.PI / 2, 5)).getPoint();
Assert.assertEquals(3 * Math.PI / 2, result, 1e-6);
result = optimizer.optimize(new MaxEval(50),
new UnivariateObjectiveFunction(f),
GoalType.MINIMIZE,
new SearchInterval(4, 3 * Math.PI / 2)).getPoint();
Assert.assertEquals(3 * Math.PI / 2, result, 1e-6);
}
@Test
public void testMath832() {
final UnivariateFunction f = new UnivariateFunction() {
@Override
public double value(double x) {
final double sqrtX = FastMath.sqrt(x);
final double a = 1e2 * sqrtX;
final double b = 1e6 / x;
final double c = 1e4 / sqrtX;
return a + b + c;
}
};
UnivariateOptimizer optimizer = new BrentOptimizer(1e-10, 1e-8);
final double result = optimizer.optimize(new MaxEval(1483),
new UnivariateObjectiveFunction(f),
GoalType.MINIMIZE,
new SearchInterval(Double.MIN_VALUE,
Double.MAX_VALUE)).getPoint();
Assert.assertEquals(804.9355825, result, 1e-6);
}
/**
* Contrived example showing that prior to the resolution of MATH-855
* (second revision), the algorithm would not return the best point if
* it happened to be the initial guess.
*/
@Test
public void testKeepInitIfBest() {
final double minSin = 3 * Math.PI / 2;
final double offset = 1e-8;
final double delta = 1e-7;
final UnivariateFunction f1 = new Sin();
final UnivariateFunction f2 = new StepFunction(new double[] { minSin, minSin + offset, minSin + 2 * offset},
new double[] { 0, -1, 0 });
final UnivariateFunction f = FunctionUtils.add(f1, f2);
// A slightly less stringent tolerance would make the test pass
// even with the previous implementation.
final double relTol = 1e-8;
final UnivariateOptimizer optimizer = new BrentOptimizer(relTol, 1e-100);
final double init = minSin + 1.5 * offset;
final UnivariatePointValuePair result
= optimizer.optimize(new MaxEval(200),
new UnivariateObjectiveFunction(f),
GoalType.MINIMIZE,
new SearchInterval(minSin - 6.789 * delta,
minSin + 9.876 * delta,
init));
final double sol = result.getPoint();
final double expected = init;
// System.out.println("numEval=" + numEval);
// System.out.println("min=" + init + " f=" + f.value(init));
// System.out.println("sol=" + sol + " f=" + f.value(sol));
// System.out.println("exp=" + expected + " f=" + f.value(expected));
Assert.assertTrue("Best point not reported", f.value(sol) <= f.value(expected));
}
/**
* Contrived example showing that prior to the resolution of MATH-855,
* the algorithm, by always returning the last evaluated point, would
* sometimes not report the best point it had found.
*/
@Test
public void testMath855() {
final double minSin = 3 * Math.PI / 2;
final double offset = 1e-8;
final double delta = 1e-7;
final UnivariateFunction f1 = new Sin();
final UnivariateFunction f2 = new StepFunction(new double[] { minSin, minSin + offset, minSin + 5 * offset },
new double[] { 0, -1, 0 });
final UnivariateFunction f = FunctionUtils.add(f1, f2);
final UnivariateOptimizer optimizer = new BrentOptimizer(1e-8, 1e-100);
final UnivariatePointValuePair result
= optimizer.optimize(new MaxEval(200),
new UnivariateObjectiveFunction(f),
GoalType.MINIMIZE,
new SearchInterval(minSin - 6.789 * delta,
minSin + 9.876 * delta));
final double sol = result.getPoint();
final double expected = 4.712389027602411;
// System.out.println("min=" + (minSin + offset) + " f=" + f.value(minSin + offset));
// System.out.println("sol=" + sol + " f=" + f.value(sol));
// System.out.println("exp=" + expected + " f=" + f.value(expected));
Assert.assertTrue("Best point not reported", f.value(sol) <= f.value(expected));
}
}