alvinalexander.com | career | drupal | java | mac | mysql | perl | scala | uml | unix  

Commons Math example source code file (GraggBulirschStoerIntegratorTest.java)

This example Commons Math source code file (GraggBulirschStoerIntegratorTest.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

derivativeexception, derivativeexception, firstorderintegrator, graggbulirschstoerintegrator, graggbulirschstoerintegrator, integratorexception, integratorexception, keplerstephandler, testproblem1, testproblem3, testproblem5, testproblemhandler, testproblemhandler, variablestephandler

The Commons Math GraggBulirschStoerIntegratorTest.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.ode.nonstiff;

import org.apache.commons.math.ode.DerivativeException;
import org.apache.commons.math.ode.FirstOrderIntegrator;
import org.apache.commons.math.ode.IntegratorException;
import org.apache.commons.math.ode.TestProblem1;
import org.apache.commons.math.ode.TestProblem3;
import org.apache.commons.math.ode.TestProblem4;
import org.apache.commons.math.ode.TestProblem5;
import org.apache.commons.math.ode.TestProblemAbstract;
import org.apache.commons.math.ode.TestProblemHandler;
import org.apache.commons.math.ode.events.EventHandler;
import org.apache.commons.math.ode.nonstiff.GraggBulirschStoerIntegrator;
import org.apache.commons.math.ode.sampling.StepHandler;
import org.apache.commons.math.ode.sampling.StepInterpolator;

import junit.framework.*;

public class GraggBulirschStoerIntegratorTest
  extends TestCase {

  public GraggBulirschStoerIntegratorTest(String name) {
    super(name);
  }

  public void testDimensionCheck() {
    try  {
      TestProblem1 pb = new TestProblem1();
      AdaptiveStepsizeIntegrator integrator =
        new GraggBulirschStoerIntegrator(0.0, 1.0, 1.0e-10, 1.0e-10);
      integrator.integrate(pb,
                           0.0, new double[pb.getDimension()+10],
                           1.0, new double[pb.getDimension()+10]);
      fail("an exception should have been thrown");
    } catch(DerivativeException de) {
      fail("wrong exception caught");
    } catch(IntegratorException ie) {
    }
  }

  public void testNullIntervalCheck() {
    try  {
      TestProblem1 pb = new TestProblem1();
      GraggBulirschStoerIntegrator integrator =
        new GraggBulirschStoerIntegrator(0.0, 1.0, 1.0e-10, 1.0e-10);
      integrator.integrate(pb,
                           0.0, new double[pb.getDimension()],
                           0.0, new double[pb.getDimension()]);
      fail("an exception should have been thrown");
    } catch(DerivativeException de) {
      fail("wrong exception caught");
    } catch(IntegratorException ie) {
    }
  }

  public void testMinStep() {

    try {
      TestProblem5 pb  = new TestProblem5();
      double minStep   = 0.1 * Math.abs(pb.getFinalTime() - pb.getInitialTime());
      double maxStep   = Math.abs(pb.getFinalTime() - pb.getInitialTime());
      double[] vecAbsoluteTolerance = { 1.0e-20, 1.0e-21 };
      double[] vecRelativeTolerance = { 1.0e-20, 1.0e-21 };

      FirstOrderIntegrator integ =
        new GraggBulirschStoerIntegrator(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()]);
      fail("an exception should have been thrown");
    } catch(DerivativeException de) {
      fail("wrong exception caught");
    } catch(IntegratorException ie) {
    }

  }

  public void testBackward()
      throws DerivativeException, IntegratorException {

      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 GraggBulirschStoerIntegrator(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()]);

      assertTrue(handler.getLastError() < 9.0e-10);
      assertTrue(handler.getMaximalValueError() < 9.0e-10);
      assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
      assertEquals("Gragg-Bulirsch-Stoer", integ.getName());
  }

  public void testIncreasingTolerance()
    throws DerivativeException, IntegratorException {

    int previousCalls = Integer.MAX_VALUE;
    for (int i = -12; i < -4; ++i) {
      TestProblem1 pb     = new TestProblem1();
      double minStep      = 0;
      double maxStep      = pb.getFinalTime() - pb.getInitialTime();
      double absTolerance = Math.pow(10.0, i);
      double relTolerance = absTolerance;

      FirstOrderIntegrator integ =
        new GraggBulirschStoerIntegrator(minStep, maxStep,
                                         absTolerance, relTolerance);
      TestProblemHandler handler = new TestProblemHandler(pb, integ);
      integ.addStepHandler(handler);
      integ.integrate(pb,
                      pb.getInitialTime(), pb.getInitialState(),
                      pb.getFinalTime(), new double[pb.getDimension()]);

      // the coefficients are only valid for this test
      // and have been obtained from trial and error
      // there is no general relation between local and global errors
      double ratio =  handler.getMaximalValueError() / absTolerance;
      assertTrue(ratio < 2.4);
      assertTrue(ratio > 0.02);
      assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);

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

    }

  }

  public void testIntegratorControls()
  throws DerivativeException, IntegratorException {

    TestProblem3 pb = new TestProblem3(0.999);
    GraggBulirschStoerIntegrator integ =
        new GraggBulirschStoerIntegrator(0, pb.getFinalTime() - pb.getInitialTime(),
                1.0e-8, 1.0e-10);

    double errorWithDefaultSettings = getMaxError(integ, pb);

    // stability control
    integ.setStabilityCheck(true, 2, 1, 0.99);
    assertTrue(errorWithDefaultSettings < getMaxError(integ, pb));
    integ.setStabilityCheck(true, -1, -1, -1);

    integ.setStepsizeControl(0.5, 0.99, 0.1, 2.5);
    assertTrue(errorWithDefaultSettings < getMaxError(integ, pb));
    integ.setStepsizeControl(-1, -1, -1, -1);

    integ.setOrderControl(10, 0.7, 0.95);
    assertTrue(errorWithDefaultSettings < getMaxError(integ, pb));
    integ.setOrderControl(-1, -1, -1);

    integ.setInterpolationControl(true, 3);
    assertTrue(errorWithDefaultSettings < getMaxError(integ, pb));
    integ.setInterpolationControl(true, -1);

  }

  private double getMaxError(FirstOrderIntegrator integrator, TestProblemAbstract pb)
    throws DerivativeException, IntegratorException {
      TestProblemHandler handler = new TestProblemHandler(pb, integrator);
      integrator.addStepHandler(handler);
      integrator.integrate(pb,
                           pb.getInitialTime(), pb.getInitialState(),
                           pb.getFinalTime(), new double[pb.getDimension()]);
      return handler.getMaximalValueError();
  }

  public void testEvents()
    throws DerivativeException, IntegratorException {

    TestProblem4 pb = new TestProblem4();
    double minStep = 0;
    double maxStep = pb.getFinalTime() - pb.getInitialTime();
    double scalAbsoluteTolerance = 1.0e-10;
    double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;

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

    assertTrue(handler.getMaximalValueError() < 5.0e-8);
    assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
    assertEquals(12.0, handler.getLastTime(), 1.0e-8 * maxStep);
    integ.clearEventHandlers();
    assertEquals(0, integ.getEventHandlers().size());

  }

  public void testKepler()
    throws DerivativeException, IntegratorException {

    final TestProblem3 pb = new TestProblem3(0.9);
    double minStep        = 0;
    double maxStep        = pb.getFinalTime() - pb.getInitialTime();
    double absTolerance   = 1.0e-6;
    double relTolerance   = 1.0e-6;

    FirstOrderIntegrator integ =
      new GraggBulirschStoerIntegrator(minStep, maxStep,
                                       absTolerance, relTolerance);
    integ.addStepHandler(new KeplerStepHandler(pb));
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);

    assertEquals(integ.getEvaluations(), pb.getCalls());
    assertTrue(pb.getCalls() < 2150);

  }

  public void testVariableSteps()
    throws DerivativeException, IntegratorException {

    final TestProblem3 pb = new TestProblem3(0.9);
    double minStep        = 0;
    double maxStep        = pb.getFinalTime() - pb.getInitialTime();
    double absTolerance   = 1.0e-8;
    double relTolerance   = 1.0e-8;
    FirstOrderIntegrator integ =
      new GraggBulirschStoerIntegrator(minStep, maxStep,
                                       absTolerance, relTolerance);
    integ.addStepHandler(new VariableStepHandler());
    double stopTime = integ.integrate(pb,
                                      pb.getInitialTime(), pb.getInitialState(),
                                      pb.getFinalTime(), new double[pb.getDimension()]);
    assertEquals(pb.getFinalTime(), stopTime, 1.0e-10);
    assertEquals("Gragg-Bulirsch-Stoer", integ.getName());
  }

  public void testUnstableDerivative()
    throws DerivativeException, IntegratorException {
    final StepProblem stepProblem = new StepProblem(0.0, 1.0, 2.0);
    FirstOrderIntegrator integ =
      new GraggBulirschStoerIntegrator(0.1, 10, 1.0e-12, 0.0);
    integ.addEventHandler(stepProblem, 1.0, 1.0e-12, 1000);
    double[] y = { Double.NaN };
    integ.integrate(stepProblem, 0.0, new double[] { 0.0 }, 10.0, y);
    assertEquals(8.0, y[0], 1.0e-12);
  }

  private static class KeplerStepHandler implements StepHandler {
    public KeplerStepHandler(TestProblem3 pb) {
      this.pb = pb;
      reset();
    }
    public boolean requiresDenseOutput() {
      return true;
    }
    public void reset() {
      nbSteps = 0;
      maxError = 0;
    }
    public void handleStep(StepInterpolator interpolator,
                           boolean isLast)
    throws DerivativeException {

      ++nbSteps;
      for (int a = 1; a < 100; ++a) {

        double prev   = interpolator.getPreviousTime();
        double curr   = interpolator.getCurrentTime();
        double interp = ((100 - a) * prev + a * curr) / 100;
        interpolator.setInterpolatedTime(interp);

        double[] interpolatedY = interpolator.getInterpolatedState ();
        double[] theoreticalY  = pb.computeTheoreticalState(interpolator.getInterpolatedTime());
        double dx = interpolatedY[0] - theoreticalY[0];
        double dy = interpolatedY[1] - theoreticalY[1];
        double error = dx * dx + dy * dy;
        if (error > maxError) {
          maxError = error;
        }
      }
      if (isLast) {
        assertTrue(maxError < 2.7e-6);
        assertTrue(nbSteps < 80);
      }
    }
    private int nbSteps;
    private double maxError;
    private TestProblem3 pb;
  }

  public static class VariableStepHandler implements StepHandler {
    public VariableStepHandler() {
      reset();
    }
    public boolean requiresDenseOutput() {
      return false;
    }
    public void reset() {
      firstTime = true;
      minStep = 0;
      maxStep = 0;
    }
    public void handleStep(StepInterpolator interpolator,
                           boolean isLast) {

      double step = Math.abs(interpolator.getCurrentTime()
                             - interpolator.getPreviousTime());
      if (firstTime) {
        minStep   = Math.abs(step);
        maxStep   = minStep;
        firstTime = false;
      } else {
        if (step < minStep) {
          minStep = step;
        }
        if (step > maxStep) {
          maxStep = step;
        }
      }

      if (isLast) {
        assertTrue(minStep < 8.2e-3);
        assertTrue(maxStep > 1.7);
      }
    }
    private boolean firstTime;
    private double  minStep;
    private double  maxStep;
  }

}

Other Commons Math examples (source code examples)

Here is a short list of links related to this Commons Math GraggBulirschStoerIntegratorTest.java source code file:

... this post is sponsored by my books ...

#1 New Release!

FP Best Seller

 

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.