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* this work for additional information regarding copyright ownership.
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* (the "License"); you may not use this file except in compliance with
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* http://www.apache.org/licenses/LICENSE-2.0
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* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
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package org.apache.commons.math.optimization.direct;
import static org.junit.Assert.assertEquals;
import static org.junit.Assert.assertNotNull;
import static org.junit.Assert.assertNull;
import static org.junit.Assert.assertTrue;
import static org.junit.Assert.fail;
import org.apache.commons.math.ConvergenceException;
import org.apache.commons.math.FunctionEvaluationException;
import org.apache.commons.math.MathException;
import org.apache.commons.math.MaxEvaluationsExceededException;
import org.apache.commons.math.MaxIterationsExceededException;
import org.apache.commons.math.analysis.MultivariateRealFunction;
import org.apache.commons.math.analysis.MultivariateVectorialFunction;
import org.apache.commons.math.exception.util.LocalizedFormats;
import org.apache.commons.math.linear.Array2DRowRealMatrix;
import org.apache.commons.math.linear.RealMatrix;
import org.apache.commons.math.optimization.GoalType;
import org.apache.commons.math.optimization.LeastSquaresConverter;
import org.apache.commons.math.optimization.OptimizationException;
import org.apache.commons.math.optimization.RealPointValuePair;
import org.apache.commons.math.optimization.SimpleRealPointChecker;
import org.apache.commons.math.optimization.SimpleScalarValueChecker;
import org.apache.commons.math.util.FastMath;
import org.junit.Test;
public class NelderMeadTest {
@Test
public void testFunctionEvaluationException() throws OptimizationException, FunctionEvaluationException, IllegalArgumentException {
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, LocalizedFormats.SIMPLE_MESSAGE, "oops");
} else if (x[0] > 1) {
throw new FunctionEvaluationException(new RuntimeException("oops"), x);
} else {
return x[0] * (1 - x[0]);
}
}
};
try {
NelderMead optimizer = new NelderMead(0.9, 1.9, 0.4, 0.6);
optimizer.optimize(wrong, GoalType.MINIMIZE, new double[] { -1.0 });
fail("an exception should have been thrown");
} catch (FunctionEvaluationException ce) {
// expected behavior
assertNull(ce.getCause());
}
try {
NelderMead optimizer = new NelderMead(0.9, 1.9, 0.4, 0.6);
optimizer.optimize(wrong, GoalType.MINIMIZE, new double[] { +2.0 });
fail("an exception should have been thrown");
} catch (FunctionEvaluationException ce) {
// expected behavior
assertNotNull(ce.getCause());
}
}
@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 : (FastMath.atan(x) * FastMath.atan(x + 2) * FastMath.atan(y) * FastMath.atan(y) / (x * y));
}
};
NelderMead optimizer = new NelderMead();
optimizer.setConvergenceChecker(new SimpleScalarValueChecker(1.0e-10, 1.0e-30));
optimizer.setMaxIterations(100);
optimizer.setStartConfiguration(new double[] { 0.2, 0.2 });
RealPointValuePair optimum;
// minimization
optimum = optimizer.optimize(fourExtrema, GoalType.MINIMIZE, new double[] { -3.0, 0 });
assertEquals(xM, optimum.getPoint()[0], 2.0e-7);
assertEquals(yP, optimum.getPoint()[1], 2.0e-5);
assertEquals(valueXmYp, optimum.getValue(), 6.0e-12);
assertTrue(optimizer.getEvaluations() > 60);
assertTrue(optimizer.getEvaluations() < 90);
optimum = optimizer.optimize(fourExtrema, GoalType.MINIMIZE, new double[] { +1, 0 });
assertEquals(xP, optimum.getPoint()[0], 5.0e-6);
assertEquals(yM, optimum.getPoint()[1], 6.0e-6);
assertEquals(valueXpYm, optimum.getValue(), 1.0e-11);
assertTrue(optimizer.getEvaluations() > 60);
assertTrue(optimizer.getEvaluations() < 90);
// maximization
optimum = optimizer.optimize(fourExtrema, GoalType.MAXIMIZE, new double[] { -3.0, 0.0 });
assertEquals(xM, optimum.getPoint()[0], 1.0e-5);
assertEquals(yM, optimum.getPoint()[1], 3.0e-6);
assertEquals(valueXmYm, optimum.getValue(), 3.0e-12);
assertTrue(optimizer.getEvaluations() > 60);
assertTrue(optimizer.getEvaluations() < 90);
optimum = optimizer.optimize(fourExtrema, GoalType.MAXIMIZE, new double[] { +1, 0 });
assertEquals(xP, optimum.getPoint()[0], 4.0e-6);
assertEquals(yP, optimum.getPoint()[1], 5.0e-6);
assertEquals(valueXpYp, optimum.getValue(), 7.0e-12);
assertTrue(optimizer.getEvaluations() > 60);
assertTrue(optimizer.getEvaluations() < 90);
}
@Test
public void testRosenbrock()
throws FunctionEvaluationException, ConvergenceException {
Rosenbrock rosenbrock = new Rosenbrock();
NelderMead optimizer = new NelderMead();
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 });
assertEquals(rosenbrock.getCount(), optimizer.getEvaluations());
assertTrue(optimizer.getEvaluations() > 40);
assertTrue(optimizer.getEvaluations() < 50);
assertTrue(optimum.getValue() < 8.0e-4);
}
@Test
public void testPowell()
throws FunctionEvaluationException, ConvergenceException {
Powell powell = new Powell();
NelderMead optimizer = new NelderMead();
optimizer.setConvergenceChecker(new SimpleScalarValueChecker(-1.0, 1.0e-3));
optimizer.setMaxIterations(200);
RealPointValuePair optimum =
optimizer.optimize(powell, GoalType.MINIMIZE, new double[] { 3.0, -1.0, 0.0, 1.0 });
assertEquals(powell.getCount(), optimizer.getEvaluations());
assertTrue(optimizer.getEvaluations() > 110);
assertTrue(optimizer.getEvaluations() < 130);
assertTrue(optimum.getValue() < 2.0e-3);
}
@Test
public void testLeastSquares1()
throws FunctionEvaluationException, ConvergenceException {
final RealMatrix factors =
new Array2DRowRealMatrix(new double[][] {
{ 1.0, 0.0 },
{ 0.0, 1.0 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorialFunction() {
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2.0, -3.0 });
NelderMead optimizer = new NelderMead();
optimizer.setConvergenceChecker(new SimpleScalarValueChecker(-1.0, 1.0e-6));
optimizer.setMaxIterations(200);
RealPointValuePair optimum =
optimizer.optimize(ls, GoalType.MINIMIZE, new double[] { 10.0, 10.0 });
assertEquals( 2.0, optimum.getPointRef()[0], 3.0e-5);
assertEquals(-3.0, optimum.getPointRef()[1], 4.0e-4);
assertTrue(optimizer.getEvaluations() > 60);
assertTrue(optimizer.getEvaluations() < 80);
assertTrue(optimum.getValue() < 1.0e-6);
}
@Test
public void testLeastSquares2()
throws FunctionEvaluationException, ConvergenceException {
final RealMatrix factors =
new Array2DRowRealMatrix(new double[][] {
{ 1.0, 0.0 },
{ 0.0, 1.0 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorialFunction() {
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2.0, -3.0 }, new double[] { 10.0, 0.1 });
NelderMead optimizer = new NelderMead();
optimizer.setConvergenceChecker(new SimpleScalarValueChecker(-1.0, 1.0e-6));
optimizer.setMaxIterations(200);
RealPointValuePair optimum =
optimizer.optimize(ls, GoalType.MINIMIZE, new double[] { 10.0, 10.0 });
assertEquals( 2.0, optimum.getPointRef()[0], 5.0e-5);
assertEquals(-3.0, optimum.getPointRef()[1], 8.0e-4);
assertTrue(optimizer.getEvaluations() > 60);
assertTrue(optimizer.getEvaluations() < 80);
assertTrue(optimum.getValue() < 1.0e-6);
}
@Test
public void testLeastSquares3()
throws FunctionEvaluationException, ConvergenceException {
final RealMatrix factors =
new Array2DRowRealMatrix(new double[][] {
{ 1.0, 0.0 },
{ 0.0, 1.0 }
}, false);
LeastSquaresConverter ls = new LeastSquaresConverter(new MultivariateVectorialFunction() {
public double[] value(double[] variables) {
return factors.operate(variables);
}
}, new double[] { 2.0, -3.0 }, new Array2DRowRealMatrix(new double [][] {
{ 1.0, 1.2 }, { 1.2, 2.0 }
}));
NelderMead optimizer = new NelderMead();
optimizer.setConvergenceChecker(new SimpleScalarValueChecker(-1.0, 1.0e-6));
optimizer.setMaxIterations(200);
RealPointValuePair optimum =
optimizer.optimize(ls, GoalType.MINIMIZE, new double[] { 10.0, 10.0 });
assertEquals( 2.0, optimum.getPointRef()[0], 2.0e-3);
assertEquals(-3.0, optimum.getPointRef()[1], 8.0e-4);
assertTrue(optimizer.getEvaluations() > 60);
assertTrue(optimizer.getEvaluations() < 80);
assertTrue(optimum.getValue() < 1.0e-6);
}
@Test(expected = MaxIterationsExceededException.class)
public void testMaxIterations() throws MathException {
try {
Powell powell = new Powell();
NelderMead optimizer = new NelderMead();
optimizer.setConvergenceChecker(new SimpleScalarValueChecker(-1.0, 1.0e-3));
optimizer.setMaxIterations(20);
optimizer.optimize(powell, GoalType.MINIMIZE, new double[] { 3.0, -1.0, 0.0, 1.0 });
} catch (OptimizationException oe) {
if (oe.getCause() instanceof ConvergenceException) {
throw (ConvergenceException) oe.getCause();
}
throw oe;
}
}
@Test(expected = MaxEvaluationsExceededException.class)
public void testMaxEvaluations() throws MathException {
try {
Powell powell = new Powell();
NelderMead optimizer = new NelderMead();
optimizer.setConvergenceChecker(new SimpleRealPointChecker(-1.0, 1.0e-3));
optimizer.setMaxEvaluations(20);
optimizer.optimize(powell, GoalType.MINIMIZE, new double[] { 3.0, -1.0, 0.0, 1.0 });
} catch (FunctionEvaluationException fee) {
if (fee.getCause() instanceof ConvergenceException) {
throw (ConvergenceException) fee.getCause();
}
throw fee;
}
}
private static class Rosenbrock implements MultivariateRealFunction {
private int count;
public Rosenbrock() {
count = 0;
}
public double value(double[] x) {
++count;
double a = x[1] - x[0] * x[0];
double b = 1.0 - x[0];
return 100 * a * a + b * b;
}
public int getCount() {
return count;
}
}
private static class Powell implements MultivariateRealFunction {
private int count;
public Powell() {
count = 0;
}
public double value(double[] x) {
++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;
}
public int getCount() {
return count;
}
}
}