Commons Math example source code file (MultiDirectionalTest.java)

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

Java - Commons Math tags/keywords

convergenceexception, epsilon, exception, functionevaluationexception, functionevaluationexception, gaussian2d, multidirectional, multidirectional, multidirectionaltest, multivariaterealfunction, multivariaterealfunction, realpointvaluepair, test, test

The Commons Math MultiDirectionalTest.java 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.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;

}