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Java example source code file (BrentOptimizerTest.java)

This example Java source code file (BrentOptimizerTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

best, brentoptimizer, brentoptimizertest, convergencechecker, descriptivestatistics, numberistoolargeexception, quinticfunction, sin, stepfunction, test, toomanyevaluationsexception, univariatefunction, univariateoptimizer, univariatepointvaluepair

The BrentOptimizerTest.java Java example source code

/*
 * 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.math3.optimization.univariate;


import org.apache.commons.math3.analysis.QuinticFunction;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.function.Sin;
import org.apache.commons.math3.analysis.function.StepFunction;
import org.apache.commons.math3.analysis.FunctionUtils;
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.optimization.ConvergenceChecker;
import org.apache.commons.math3.optimization.GoalType;
import org.apache.commons.math3.stat.descriptive.DescriptiveStatistics;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;

/**
 */
@Deprecated
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(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 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(200, f, GoalType.MINIMIZE, 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() {
            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 Sin();
        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);
    }

    @Test
    public void testMath832() {
        final UnivariateFunction f = new UnivariateFunction() {
                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(1483,
                                                 f,
                                                 GoalType.MINIMIZE,
                                                 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(200, f, GoalType.MINIMIZE,
                                 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(200, f, GoalType.MINIMIZE,
                                 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));
    }
}

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