/*
* 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.nonlinear.scalar.noderiv;
import org.apache.commons.math4.analysis.MultivariateFunction;
import org.apache.commons.math4.analysis.SumSincFunction;
import org.apache.commons.math4.exception.MathUnsupportedOperationException;
import org.apache.commons.math4.optim.InitialGuess;
import org.apache.commons.math4.optim.MaxEval;
import org.apache.commons.math4.optim.PointValuePair;
import org.apache.commons.math4.optim.SimpleBounds;
import org.apache.commons.math4.optim.nonlinear.scalar.GoalType;
import org.apache.commons.math4.optim.nonlinear.scalar.ObjectiveFunction;
import org.apache.commons.math4.optim.nonlinear.scalar.noderiv.PowellOptimizer;
import org.apache.commons.math4.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
/**
* Test for {@link PowellOptimizer}.
*/
public class PowellOptimizerTest {
@Test(expected=MathUnsupportedOperationException.class)
public void testBoundsUnsupported() {
final MultivariateFunction func = new SumSincFunction(-1);
final PowellOptimizer optim = new PowellOptimizer(1e-8, 1e-5,
1e-4, 1e-4);
optim.optimize(new MaxEval(100),
new ObjectiveFunction(func),
GoalType.MINIMIZE,
new InitialGuess(new double[] { -3, 0 }),
new SimpleBounds(new double[] { -5, -1 },
new double[] { 5, 1 }));
}
@Test
public void testSumSinc() {
final MultivariateFunction func = new SumSincFunction(-1);
int dim = 2;
final double[] minPoint = new double[dim];
for (int i = 0; i < dim; i++) {
minPoint[i] = 0;
}
double[] init = new double[dim];
// Initial is minimum.
for (int i = 0; i < dim; i++) {
init[i] = minPoint[i];
}
doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-9);
// Initial is far from minimum.
for (int i = 0; i < dim; i++) {
init[i] = minPoint[i] + 3;
}
doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-5);
// More stringent line search tolerance enhances the precision
// of the result.
doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-9, 1e-7);
}
@Test
public void testQuadratic() {
final MultivariateFunction func = new MultivariateFunction() {
@Override
public double value(double[] x) {
final double a = x[0] - 1;
final double b = x[1] - 1;
return a * a + b * b + 1;
}
};
int dim = 2;
final double[] minPoint = new double[dim];
for (int i = 0; i < dim; i++) {
minPoint[i] = 1;
}
double[] init = new double[dim];
// Initial is minimum.
for (int i = 0; i < dim; i++) {
init[i] = minPoint[i];
}
doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-8);
// Initial is far from minimum.
for (int i = 0; i < dim; i++) {
init[i] = minPoint[i] - 20;
}
doTest(func, minPoint, init, GoalType.MINIMIZE, 1e-9, 1e-8);
}
@Test
public void testMaximizeQuadratic() {
final MultivariateFunction func = new MultivariateFunction() {
@Override
public double value(double[] x) {
final double a = x[0] - 1;
final double b = x[1] - 1;
return -a * a - b * b + 1;
}
};
int dim = 2;
final double[] maxPoint = new double[dim];
for (int i = 0; i < dim; i++) {
maxPoint[i] = 1;
}
double[] init = new double[dim];
// Initial is minimum.
for (int i = 0; i < dim; i++) {
init[i] = maxPoint[i];
}
doTest(func, maxPoint, init, GoalType.MAXIMIZE, 1e-9, 1e-8);
// Initial is far from minimum.
for (int i = 0; i < dim; i++) {
init[i] = maxPoint[i] - 20;
}
doTest(func, maxPoint, init, GoalType.MAXIMIZE, 1e-9, 1e-8);
}
/**
* Ensure that we do not increase the number of function evaluations when
* the function values are scaled up.
* Note that the tolerances parameters passed to the constructor must
* still hold sensible values because they are used to set the line search
* tolerances.
*/
@Test
public void testRelativeToleranceOnScaledValues() {
final MultivariateFunction func = new MultivariateFunction() {
@Override
public double value(double[] x) {
final double a = x[0] - 1;
final double b = x[1] - 1;
return a * a * FastMath.sqrt(FastMath.abs(a)) + b * b + 1;
}
};
int dim = 2;
final double[] minPoint = new double[dim];
for (int i = 0; i < dim; i++) {
minPoint[i] = 1;
}
double[] init = new double[dim];
// Initial is far from minimum.
for (int i = 0; i < dim; i++) {
init[i] = minPoint[i] - 20;
}
final double relTol = 1e-10;
final int maxEval = 1000;
// Very small absolute tolerance to rely solely on the relative
// tolerance as a stopping criterion
final PowellOptimizer optim = new PowellOptimizer(relTol, 1e-100);
final PointValuePair funcResult = optim.optimize(new MaxEval(maxEval),
new ObjectiveFunction(func),
GoalType.MINIMIZE,
new InitialGuess(init));
final double funcValue = func.value(funcResult.getPoint());
final int funcEvaluations = optim.getEvaluations();
final double scale = 1e10;
final MultivariateFunction funcScaled = new MultivariateFunction() {
@Override
public double value(double[] x) {
return scale * func.value(x);
}
};
final PointValuePair funcScaledResult = optim.optimize(new MaxEval(maxEval),
new ObjectiveFunction(funcScaled),
GoalType.MINIMIZE,
new InitialGuess(init));
final double funcScaledValue = funcScaled.value(funcScaledResult.getPoint());
final int funcScaledEvaluations = optim.getEvaluations();
// Check that both minima provide the same objective funciton values,
// within the relative function tolerance.
Assert.assertEquals(1, funcScaledValue / (scale * funcValue), relTol);
// Check that the numbers of evaluations are the same.
Assert.assertEquals(funcEvaluations, funcScaledEvaluations);
}
/**
* @param func Function to optimize.
* @param optimum Expected optimum.
* @param init Starting point.
* @param goal Minimization or maximization.
* @param fTol Tolerance (relative error on the objective function) for
* "Powell" algorithm.
* @param pointTol Tolerance for checking that the optimum is correct.
*/
private void doTest(MultivariateFunction func,
double[] optimum,
double[] init,
GoalType goal,
double fTol,
double pointTol) {
final PowellOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d));
final PointValuePair result = optim.optimize(new MaxEval(1000),
new ObjectiveFunction(func),
goal,
new InitialGuess(init));
final double[] point = result.getPoint();
for (int i = 0, dim = optimum.length; i < dim; i++) {
Assert.assertEquals("found[" + i + "]=" + point[i] + " value=" + result.getValue(),
optimum[i], point[i], pointTol);
}
}
/**
* @param func Function to optimize.
* @param optimum Expected optimum.
* @param init Starting point.
* @param goal Minimization or maximization.
* @param fTol Tolerance (relative error on the objective function) for
* "Powell" algorithm.
* @param fLineTol Tolerance (relative error on the objective function)
* for the internal line search algorithm.
* @param pointTol Tolerance for checking that the optimum is correct.
*/
private void doTest(MultivariateFunction func,
double[] optimum,
double[] init,
GoalType goal,
double fTol,
double fLineTol,
double pointTol) {
final PowellOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d),
fLineTol, Math.ulp(1d));
final PointValuePair result = optim.optimize(new MaxEval(1000),
new ObjectiveFunction(func),
goal,
new InitialGuess(init));
final double[] point = result.getPoint();
for (int i = 0, dim = optimum.length; i < dim; i++) {
Assert.assertEquals("found[" + i + "]=" + point[i] + " value=" + result.getValue(),
optimum[i], point[i], pointTol);
}
Assert.assertTrue(optim.getIterations() > 0);
}
}