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* 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.math.optimization.direct;
import org.apache.commons.math.ConvergenceException;
import org.apache.commons.math.FunctionEvaluationException;
import org.apache.commons.math.analysis.MultivariateRealFunction;
import org.apache.commons.math.optimization.GoalType;
import org.apache.commons.math.optimization.OptimizationException;
import org.apache.commons.math.optimization.RealPointValuePair;
import org.apache.commons.math.optimization.SimpleScalarValueChecker;
import org.junit.Assert;
import org.junit.Test;
public class MultiDirectionalTest {
@Test
public void testFunctionEvaluationExceptions() {
MultivariateRealFunction wrong =
new MultivariateRealFunction() {
private static final long serialVersionUID = 4751314470965489371L;
public double value(double[] x) throws FunctionEvaluationException {
if (x[0] < 0) {
throw new FunctionEvaluationException(x, "{0}", "oops");
} else if (x[0] > 1) {
throw new FunctionEvaluationException(new RuntimeException("oops"), x);
} else {
return x[0] * (1 - x[0]);
}
}
};
try {
MultiDirectional optimizer = new MultiDirectional(0.9, 1.9);
optimizer.optimize(wrong, GoalType.MINIMIZE, new double[] { -1.0 });
Assert.fail("an exception should have been thrown");
} catch (FunctionEvaluationException ce) {
// expected behavior
Assert.assertNull(ce.getCause());
} catch (Exception e) {
Assert.fail("wrong exception caught: " + e.getMessage());
}
try {
MultiDirectional optimizer = new MultiDirectional(0.9, 1.9);
optimizer.optimize(wrong, GoalType.MINIMIZE, new double[] { +2.0 });
Assert.fail("an exception should have been thrown");
} catch (FunctionEvaluationException ce) {
// expected behavior
Assert.assertNotNull(ce.getCause());
} catch (Exception e) {
Assert.fail("wrong exception caught: " + e.getMessage());
}
}
@Test
public void testMinimizeMaximize()
throws FunctionEvaluationException, ConvergenceException {
// the following function has 4 local extrema:
final double xM = -3.841947088256863675365;
final double yM = -1.391745200270734924416;
final double xP = 0.2286682237349059125691;
final double yP = -yM;
final double valueXmYm = 0.2373295333134216789769; // local maximum
final double valueXmYp = -valueXmYm; // local minimum
final double valueXpYm = -0.7290400707055187115322; // global minimum
final double valueXpYp = -valueXpYm; // global maximum
MultivariateRealFunction fourExtrema = new MultivariateRealFunction() {
private static final long serialVersionUID = -7039124064449091152L;
public double value(double[] variables) throws FunctionEvaluationException {
final double x = variables[0];
final double y = variables[1];
return ((x == 0) || (y == 0)) ? 0 : (Math.atan(x) * Math.atan(x + 2) * Math.atan(y) * Math.atan(y) / (x * y));
}
};
MultiDirectional optimizer = new MultiDirectional();
optimizer.setConvergenceChecker(new SimpleScalarValueChecker(1.0e-11, 1.0e-30));
optimizer.setMaxIterations(200);
optimizer.setStartConfiguration(new double[] { 0.2, 0.2 });
RealPointValuePair optimum;
// minimization
optimum = optimizer.optimize(fourExtrema, GoalType.MINIMIZE, new double[] { -3.0, 0 });
Assert.assertEquals(xM, optimum.getPoint()[0], 4.0e-6);
Assert.assertEquals(yP, optimum.getPoint()[1], 3.0e-6);
Assert.assertEquals(valueXmYp, optimum.getValue(), 8.0e-13);
Assert.assertTrue(optimizer.getEvaluations() > 120);
Assert.assertTrue(optimizer.getEvaluations() < 150);
optimum = optimizer.optimize(fourExtrema, GoalType.MINIMIZE, new double[] { +1, 0 });
Assert.assertEquals(xP, optimum.getPoint()[0], 2.0e-8);
Assert.assertEquals(yM, optimum.getPoint()[1], 3.0e-6);
Assert.assertEquals(valueXpYm, optimum.getValue(), 2.0e-12);
Assert.assertTrue(optimizer.getEvaluations() > 120);
Assert.assertTrue(optimizer.getEvaluations() < 150);
// maximization
optimum = optimizer.optimize(fourExtrema, GoalType.MAXIMIZE, new double[] { -3.0, 0.0 });
Assert.assertEquals(xM, optimum.getPoint()[0], 7.0e-7);
Assert.assertEquals(yM, optimum.getPoint()[1], 3.0e-7);
Assert.assertEquals(valueXmYm, optimum.getValue(), 2.0e-14);
Assert.assertTrue(optimizer.getEvaluations() > 120);
Assert.assertTrue(optimizer.getEvaluations() < 150);
optimizer.setConvergenceChecker(new SimpleScalarValueChecker(1.0e-15, 1.0e-30));
optimum = optimizer.optimize(fourExtrema, GoalType.MAXIMIZE, new double[] { +1, 0 });
Assert.assertEquals(xP, optimum.getPoint()[0], 2.0e-8);
Assert.assertEquals(yP, optimum.getPoint()[1], 3.0e-6);
Assert.assertEquals(valueXpYp, optimum.getValue(), 2.0e-12);
Assert.assertTrue(optimizer.getEvaluations() > 180);
Assert.assertTrue(optimizer.getEvaluations() < 220);
}
@Test
public void testRosenbrock()
throws FunctionEvaluationException, ConvergenceException {
MultivariateRealFunction rosenbrock =
new MultivariateRealFunction() {
private static final long serialVersionUID = -9044950469615237490L;
public double value(double[] x) throws FunctionEvaluationException {
++count;
double a = x[1] - x[0] * x[0];
double b = 1.0 - x[0];
return 100 * a * a + b * b;
}
};
count = 0;
MultiDirectional optimizer = new MultiDirectional();
optimizer.setConvergenceChecker(new SimpleScalarValueChecker(-1, 1.0e-3));
optimizer.setMaxIterations(100);
optimizer.setStartConfiguration(new double[][] {
{ -1.2, 1.0 }, { 0.9, 1.2 } , { 3.5, -2.3 }
});
RealPointValuePair optimum =
optimizer.optimize(rosenbrock, GoalType.MINIMIZE, new double[] { -1.2, 1.0 });
Assert.assertEquals(count, optimizer.getEvaluations());
Assert.assertTrue(optimizer.getEvaluations() > 50);
Assert.assertTrue(optimizer.getEvaluations() < 100);
Assert.assertTrue(optimum.getValue() > 1.0e-2);
}
@Test
public void testPowell()
throws FunctionEvaluationException, ConvergenceException {
MultivariateRealFunction powell =
new MultivariateRealFunction() {
private static final long serialVersionUID = -832162886102041840L;
public double value(double[] x) throws FunctionEvaluationException {
++count;
double a = x[0] + 10 * x[1];
double b = x[2] - x[3];
double c = x[1] - 2 * x[2];
double d = x[0] - x[3];
return a * a + 5 * b * b + c * c * c * c + 10 * d * d * d * d;
}
};
count = 0;
MultiDirectional optimizer = new MultiDirectional();
optimizer.setConvergenceChecker(new SimpleScalarValueChecker(-1.0, 1.0e-3));
optimizer.setMaxIterations(1000);
RealPointValuePair optimum =
optimizer.optimize(powell, GoalType.MINIMIZE, new double[] { 3.0, -1.0, 0.0, 1.0 });
Assert.assertEquals(count, optimizer.getEvaluations());
Assert.assertTrue(optimizer.getEvaluations() > 800);
Assert.assertTrue(optimizer.getEvaluations() < 900);
Assert.assertTrue(optimum.getValue() > 1.0e-2);
}
@Test
public void testMath283()
throws FunctionEvaluationException, OptimizationException {
// fails because MultiDirectional.iterateSimplex is looping forever
// the while(true) should be replaced with a convergence check
MultiDirectional multiDirectional = new MultiDirectional();
multiDirectional.setMaxIterations(100);
multiDirectional.setMaxEvaluations(1000);
final Gaussian2D function = new Gaussian2D(0.0, 0.0, 1.0);
RealPointValuePair estimate = multiDirectional.optimize(function,
GoalType.MAXIMIZE, function.getMaximumPosition());
final double EPSILON = 1e-5;
final double expectedMaximum = function.getMaximum();
final double actualMaximum = estimate.getValue();
Assert.assertEquals(expectedMaximum, actualMaximum, EPSILON);
final double[] expectedPosition = function.getMaximumPosition();
final double[] actualPosition = estimate.getPoint();
Assert.assertEquals(expectedPosition[0], actualPosition[0], EPSILON );
Assert.assertEquals(expectedPosition[1], actualPosition[1], EPSILON );
}
private static class Gaussian2D implements MultivariateRealFunction {
private final double[] maximumPosition;
private final double std;
public Gaussian2D(double xOpt, double yOpt, double std) {
maximumPosition = new double[] { xOpt, yOpt };
this.std = std;
}
public double getMaximum() {
return value(maximumPosition);
}
public double[] getMaximumPosition() {
return maximumPosition.clone();
}
public double value(double[] point) {
final double x = point[0], y = point[1];
final double twoS2 = 2.0 * std * std;
return 1.0 / (twoS2 * Math.PI) * Math.exp(-(x * x + y * y) / twoS2);
}
}
private int count;
}