home | career | drupal | java | mac | mysql | perl | scala | uml | unix  

Java example source code file (PowellOptimizerTest.java)

This example Java source code file (PowellOptimizerTest.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

deprecated, goaltype, multivariatefunction, multivariateoptimizer, pointvaluepair, powelloptimizer, powelloptimizertest, sumsincfunction, test

The PowellOptimizerTest.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.direct;

import org.apache.commons.math3.analysis.MultivariateFunction;
import org.apache.commons.math3.analysis.SumSincFunction;
import org.apache.commons.math3.optimization.GoalType;
import org.apache.commons.math3.optimization.MultivariateOptimizer;
import org.apache.commons.math3.optimization.PointValuePair;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;

/**
 * Test for {@link PowellOptimizer}.
 */
@Deprecated
public class PowellOptimizerTest {

    @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() {
                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() {
                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() {
                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 MultivariateOptimizer optim = new PowellOptimizer(relTol, 1e-100);

        final PointValuePair funcResult = optim.optimize(maxEval, func, GoalType.MINIMIZE, init);
        final double funcValue = func.value(funcResult.getPoint());
        final int funcEvaluations = optim.getEvaluations();

        final double scale = 1e10;
        final MultivariateFunction funcScaled = new MultivariateFunction() {
                public double value(double[] x) {
                    return scale * func.value(x);
                }
            };

        final PointValuePair funcScaledResult = optim.optimize(maxEval, funcScaled, GoalType.MINIMIZE, 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 MultivariateOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d));

        final PointValuePair result = optim.optimize(1000, func, goal, 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 MultivariateOptimizer optim = new PowellOptimizer(fTol, Math.ulp(1d),
                                                                fLineTol, Math.ulp(1d));

        final PointValuePair result = optim.optimize(1000, func, goal, 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);
        }
    }
}

Other Java examples (source code examples)

Here is a short list of links related to this Java PowellOptimizerTest.java source code file:



my book on functional programming

 

new blog posts

 

Copyright 1998-2021 Alvin Alexander, alvinalexander.com
All Rights Reserved.

A percentage of advertising revenue from
pages under the /java/jwarehouse URI on this website is
paid back to open source projects.