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Java example source code file (HighamHall54IntegratorTest.java)

This example Java source code file (HighamHall54IntegratorTest.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

action, dimensionmismatchexception, eventhandler, firstorderintegrator, higham-hall, highamhall54integrator, localexception, maxcountexceededexception, nobracketingexception, numberistoosmallexception, testproblem1, testproblem4, testproblem5, testproblemhandler

The HighamHall54IntegratorTest.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.ode.nonstiff;


import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.exception.NoBracketingException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.TooManyEvaluationsException;
import org.apache.commons.math3.ode.FirstOrderDifferentialEquations;
import org.apache.commons.math3.ode.FirstOrderIntegrator;
import org.apache.commons.math3.ode.TestProblem1;
import org.apache.commons.math3.ode.TestProblem3;
import org.apache.commons.math3.ode.TestProblem4;
import org.apache.commons.math3.ode.TestProblem5;
import org.apache.commons.math3.ode.TestProblemHandler;
import org.apache.commons.math3.ode.events.EventHandler;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;

public class HighamHall54IntegratorTest {

  @Test
  public void testWrongDerivative()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {
      HighamHall54Integrator integrator =
          new HighamHall54Integrator(0.0, 1.0, 1.0e-10, 1.0e-10);
      FirstOrderDifferentialEquations equations =
          new FirstOrderDifferentialEquations() {
            public void computeDerivatives(double t, double[] y, double[] dot) {
            if (t < -0.5) {
                throw new LocalException();
            } else {
                throw new RuntimeException("oops");
           }
          }
          public int getDimension() {
              return 1;
          }
      };

      try  {
        integrator.integrate(equations, -1.0, new double[1], 0.0, new double[1]);
        Assert.fail("an exception should have been thrown");
      } catch(LocalException de) {
        // expected behavior
      }

      try  {
        integrator.integrate(equations, 0.0, new double[1], 1.0, new double[1]);
        Assert.fail("an exception should have been thrown");
      } catch(RuntimeException de) {
        // expected behavior
      }

  }

  @Test(expected=NumberIsTooSmallException.class)
  public void testMinStep()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {

      TestProblem1 pb = new TestProblem1();
      double minStep = 0.1 * (pb.getFinalTime() - pb.getInitialTime());
      double maxStep = pb.getFinalTime() - pb.getInitialTime();
      double[] vecAbsoluteTolerance = { 1.0e-15, 1.0e-16 };
      double[] vecRelativeTolerance = { 1.0e-15, 1.0e-16 };

      FirstOrderIntegrator integ = new HighamHall54Integrator(minStep, maxStep,
                                                              vecAbsoluteTolerance,
                                                              vecRelativeTolerance);
      TestProblemHandler handler = new TestProblemHandler(pb, integ);
      integ.addStepHandler(handler);
      integ.integrate(pb,
                      pb.getInitialTime(), pb.getInitialState(),
                      pb.getFinalTime(), new double[pb.getDimension()]);
      Assert.fail("an exception should have been thrown");

  }

  @Test
  public void testIncreasingTolerance()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {

    int previousCalls = Integer.MAX_VALUE;
    for (int i = -12; i < -2; ++i) {
      TestProblem1 pb = new TestProblem1();
      double minStep = 0;
      double maxStep = pb.getFinalTime() - pb.getInitialTime();
      double scalAbsoluteTolerance = FastMath.pow(10.0, i);
      double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;

      FirstOrderIntegrator integ = new HighamHall54Integrator(minStep, maxStep,
                                                              scalAbsoluteTolerance,
                                                              scalRelativeTolerance);
      TestProblemHandler handler = new TestProblemHandler(pb, integ);
      integ.addStepHandler(handler);
      integ.integrate(pb,
                      pb.getInitialTime(), pb.getInitialState(),
                      pb.getFinalTime(), new double[pb.getDimension()]);

      // the 1.3 factor is only valid for this test
      // and has been obtained from trial and error
      // there is no general relation between local and global errors
      Assert.assertTrue(handler.getMaximalValueError() < (1.3 * scalAbsoluteTolerance));
      Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);

      int calls = pb.getCalls();
      Assert.assertEquals(integ.getEvaluations(), calls);
      Assert.assertTrue(calls <= previousCalls);
      previousCalls = calls;

    }

  }

  @Test
  public void testBackward()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {

      TestProblem5 pb = new TestProblem5();
      double minStep = 0;
      double maxStep = pb.getFinalTime() - pb.getInitialTime();
      double scalAbsoluteTolerance = 1.0e-8;
      double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;

      FirstOrderIntegrator integ = new HighamHall54Integrator(minStep, maxStep,
                                                              scalAbsoluteTolerance,
                                                              scalRelativeTolerance);
      TestProblemHandler handler = new TestProblemHandler(pb, integ);
      integ.addStepHandler(handler);
      integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
                      pb.getFinalTime(), new double[pb.getDimension()]);

      Assert.assertTrue(handler.getLastError() < 5.0e-7);
      Assert.assertTrue(handler.getMaximalValueError() < 5.0e-7);
      Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
      Assert.assertEquals("Higham-Hall 5(4)", integ.getName());
  }

  @Test
  public void testEvents()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {

    TestProblem4 pb = new TestProblem4();
    double minStep = 0;
    double maxStep = pb.getFinalTime() - pb.getInitialTime();
    double scalAbsoluteTolerance = 1.0e-8;
    double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;

    FirstOrderIntegrator integ = new HighamHall54Integrator(minStep, maxStep,
                                                            scalAbsoluteTolerance,
                                                            scalRelativeTolerance);
    TestProblemHandler handler = new TestProblemHandler(pb, integ);
    integ.addStepHandler(handler);
    EventHandler[] functions = pb.getEventsHandlers();
    double convergence = 1.0e-8 * maxStep;
    for (int l = 0; l < functions.length; ++l) {
      integ.addEventHandler(functions[l],
                                 Double.POSITIVE_INFINITY, convergence, 1000);
    }
    Assert.assertEquals(functions.length, integ.getEventHandlers().size());
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);

    Assert.assertTrue(handler.getMaximalValueError() < 1.0e-7);
    Assert.assertEquals(0, handler.getMaximalTimeError(), convergence);
    Assert.assertEquals(12.0, handler.getLastTime(), convergence);
    integ.clearEventHandlers();
    Assert.assertEquals(0, integ.getEventHandlers().size());

  }

  @Test(expected=LocalException.class)
  public void testEventsErrors()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {

      final TestProblem1 pb = new TestProblem1();
      double minStep = 0;
      double maxStep = pb.getFinalTime() - pb.getInitialTime();
      double scalAbsoluteTolerance = 1.0e-8;
      double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;

      FirstOrderIntegrator integ =
          new HighamHall54Integrator(minStep, maxStep,
                                     scalAbsoluteTolerance, scalRelativeTolerance);
      TestProblemHandler handler = new TestProblemHandler(pb, integ);
      integ.addStepHandler(handler);

      integ.addEventHandler(new EventHandler() {
        public void init(double t0, double[] y0, double t) {
        }
        public Action eventOccurred(double t, double[] y, boolean increasing) {
          return Action.CONTINUE;
        }
        public double g(double t, double[] y) {
          double middle = (pb.getInitialTime() + pb.getFinalTime()) / 2;
          double offset = t - middle;
          if (offset > 0) {
            throw new LocalException();
          }
          return offset;
        }
        public void resetState(double t, double[] y) {
        }
      }, Double.POSITIVE_INFINITY, 1.0e-8 * maxStep, 1000);

      integ.integrate(pb,
                      pb.getInitialTime(), pb.getInitialState(),
                      pb.getFinalTime(), new double[pb.getDimension()]);

  }

  private static class LocalException extends RuntimeException {
    private static final long serialVersionUID = 3041292643919807960L;
  }

  @Test
  public void testEventsNoConvergence()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {

    final TestProblem1 pb = new TestProblem1();
    double minStep = 0;
    double maxStep = pb.getFinalTime() - pb.getInitialTime();
    double scalAbsoluteTolerance = 1.0e-8;
    double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;

    FirstOrderIntegrator integ =
        new HighamHall54Integrator(minStep, maxStep,
                                   scalAbsoluteTolerance, scalRelativeTolerance);
    TestProblemHandler handler = new TestProblemHandler(pb, integ);
    integ.addStepHandler(handler);

    integ.addEventHandler(new EventHandler() {
      public void init(double t0, double[] y0, double t) {
      }
      public Action eventOccurred(double t, double[] y, boolean increasing) {
        return Action.CONTINUE;
      }
      public double g(double t, double[] y) {
        double middle = (pb.getInitialTime() + pb.getFinalTime()) / 2;
        double offset = t - middle;
        return (offset > 0) ? (offset + 0.5) : (offset - 0.5);
      }
      public void resetState(double t, double[] y) {
      }
    }, Double.POSITIVE_INFINITY, 1.0e-8 * maxStep, 3);

    try {
      integ.integrate(pb,
                      pb.getInitialTime(), pb.getInitialState(),
                      pb.getFinalTime(), new double[pb.getDimension()]);
      Assert.fail("an exception should have been thrown");
    } catch (TooManyEvaluationsException tmee) {
        // Expected.
    }

}

  @Test
  public void testSanityChecks()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {
      final TestProblem3 pb  = new TestProblem3(0.9);
      double minStep = 0;
      double maxStep = pb.getFinalTime() - pb.getInitialTime();

      try {
        FirstOrderIntegrator integ =
            new HighamHall54Integrator(minStep, maxStep, new double[4], new double[4]);
        integ.integrate(pb, pb.getInitialTime(), new double[6],
                        pb.getFinalTime(), new double[pb.getDimension()]);
        Assert.fail("an exception should have been thrown");
      } catch (DimensionMismatchException ie) {
        // expected behavior
      }

      try {
        FirstOrderIntegrator integ =
            new HighamHall54Integrator(minStep, maxStep, new double[4], new double[4]);
        integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
                        pb.getFinalTime(), new double[6]);
        Assert.fail("an exception should have been thrown");
      } catch (DimensionMismatchException ie) {
        // expected behavior
      }

      try {
        FirstOrderIntegrator integ =
            new HighamHall54Integrator(minStep, maxStep, new double[2], new double[4]);
        integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
                        pb.getFinalTime(), new double[pb.getDimension()]);
        Assert.fail("an exception should have been thrown");
      } catch (DimensionMismatchException ie) {
        // expected behavior
      }

      try {
        FirstOrderIntegrator integ =
            new HighamHall54Integrator(minStep, maxStep, new double[4], new double[2]);
        integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
                        pb.getFinalTime(), new double[pb.getDimension()]);
        Assert.fail("an exception should have been thrown");
      } catch (DimensionMismatchException ie) {
        // expected behavior
      }

      try {
        FirstOrderIntegrator integ =
            new HighamHall54Integrator(minStep, maxStep, new double[4], new double[4]);
        integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
                        pb.getInitialTime(), new double[pb.getDimension()]);
        Assert.fail("an exception should have been thrown");
      } catch (NumberIsTooSmallException ie) {
        // expected behavior
      }

  }

  @Test
  public void testKepler()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {

    final TestProblem3 pb  = new TestProblem3(0.9);
    double minStep = 0;
    double maxStep = pb.getFinalTime() - pb.getInitialTime();
    double[] vecAbsoluteTolerance = { 1.0e-8, 1.0e-8, 1.0e-10, 1.0e-10 };
    double[] vecRelativeTolerance = { 1.0e-10, 1.0e-10, 1.0e-8, 1.0e-8 };

    FirstOrderIntegrator integ = new HighamHall54Integrator(minStep, maxStep,
                                                            vecAbsoluteTolerance,
                                                            vecRelativeTolerance);
    TestProblemHandler handler = new TestProblemHandler(pb, integ);
    integ.addStepHandler(handler);
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);
    Assert.assertEquals(0.0, handler.getMaximalValueError(), 1.5e-4);
    Assert.assertEquals("Higham-Hall 5(4)", integ.getName());
  }

}

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