Package org.apache.commons.math3.ode

Examples of org.apache.commons.math3.ode.TestProblem1

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

    TestProblem1 pb = new TestProblem1();
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.2;

    FirstOrderIntegrator integ = new GillIntegrator(step);
    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() > 0.0004);
    Assert.assertTrue(handler.getMaximalValueError() > 0.005);
    Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);

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  public void serialization()
    throws IOException, ClassNotFoundException,
           DimensionMismatchException, NumberIsTooSmallException,
           MaxCountExceededException, NoBracketingException {

    TestProblem1 pb = new TestProblem1();
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;
    EulerIntegrator integ = new EulerIntegrator(step);
    integ.addStepHandler(new ContinuousOutputModel());
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);

    ByteArrayOutputStream bos = new ByteArrayOutputStream();
    ObjectOutputStream    oos = new ObjectOutputStream(bos);
    for (StepHandler handler : integ.getStepHandlers()) {
        oos.writeObject(handler);
    }

    ByteArrayInputStream  bis = new ByteArrayInputStream(bos.toByteArray());
    ObjectInputStream     ois = new ObjectInputStream(bis);
    ContinuousOutputModel cm  = (ContinuousOutputModel) ois.readObject();

    Random random = new Random(347588535632l);
    double maxError = 0.0;
    for (int i = 0; i < 1000; ++i) {
      double r = random.nextDouble();
      double time = r * pb.getInitialTime() + (1.0 - r) * pb.getFinalTime();
      cm.setInterpolatedTime(time);
      double[] interpolatedY = cm.getInterpolatedState ();
      double[] theoreticalY  = pb.computeTheoreticalState(time);
      double dx = interpolatedY[0] - theoreticalY[0];
      double dy = interpolatedY[1] - theoreticalY[1];
      double error = dx * dx + dy * dy;
      if (error > maxError) {
        maxError = error;
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  @Test(expected=DimensionMismatchException.class)
  public void testDimensionCheck()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {
      TestProblem1 pb = new TestProblem1();
      DormandPrince54Integrator integrator = new DormandPrince54Integrator(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]);
  }
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  @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 DormandPrince54Integrator(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");

  }
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      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;

      EmbeddedRungeKuttaIntegrator integ =
          new DormandPrince54Integrator(minStep, maxStep,
                                        scalAbsoluteTolerance, scalRelativeTolerance);
      TestProblemHandler handler = new TestProblemHandler(pb, integ);
      integ.setSafety(0.8);
      integ.setMaxGrowth(5.0);
      integ.setMinReduction(0.3);
      integ.addStepHandler(handler);
      integ.integrate(pb,
                      pb.getInitialTime(), pb.getInitialState(),
                      pb.getFinalTime(), new double[pb.getDimension()]);
      Assert.assertEquals(0.8, integ.getSafety(), 1.0e-12);
      Assert.assertEquals(5.0, integ.getMaxGrowth(), 1.0e-12);
      Assert.assertEquals(0.3, integ.getMinReduction(), 1.0e-12);

      // the 0.7 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() < (0.7 * scalAbsoluteTolerance));
      Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);

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

    }
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  @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");

  }
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      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;

    }
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  @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()]);

  }
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  @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.
    }

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  public void serialization()
    throws IOException, ClassNotFoundException,
           DimensionMismatchException, NumberIsTooSmallException,
           MaxCountExceededException, NoBracketingException {

    TestProblem1 pb = new TestProblem1();
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;
    MidpointIntegrator integ = new MidpointIntegrator(step);
    integ.addStepHandler(new ContinuousOutputModel());
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);

    ByteArrayOutputStream bos = new ByteArrayOutputStream();
    ObjectOutputStream    oos = new ObjectOutputStream(bos);
    for (StepHandler handler : integ.getStepHandlers()) {
        oos.writeObject(handler);
    }

    Assert.assertTrue(bos.size () > 135000);
    Assert.assertTrue(bos.size () < 145000);

    ByteArrayInputStream  bis = new ByteArrayInputStream(bos.toByteArray());
    ObjectInputStream     ois = new ObjectInputStream(bis);
    ContinuousOutputModel cm  = (ContinuousOutputModel) ois.readObject();

    Random random = new Random(347588535632l);
    double maxError = 0.0;
    for (int i = 0; i < 1000; ++i) {
      double r = random.nextDouble();
      double time = r * pb.getInitialTime() + (1.0 - r) * pb.getFinalTime();
      cm.setInterpolatedTime(time);
      double[] interpolatedY = cm.getInterpolatedState ();
      double[] theoreticalY  = pb.computeTheoreticalState(time);
      double dx = interpolatedY[0] - theoreticalY[0];
      double dy = interpolatedY[1] - theoreticalY[1];
      double error = dx * dx + dy * dy;
      if (error > maxError) {
        maxError = error;
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Related Classes of org.apache.commons.math3.ode.TestProblem1

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  • org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableVectorFunction
  • org.apache.commons.math3.analysis.function.HarmonicOscillator
  • org.apache.commons.math3.analysis.function.Sin
  • org.apache.commons.math3.analysis.function.Sinc
  • org.apache.commons.math3.analysis.MultivariateFunction
  • org.apache.commons.math3.analysis.QuinticFunction
  • org.apache.commons.math3.analysis.solvers.BrentSolver
  • org.apache.commons.math3.analysis.UnivariateFunction
  • org.apache.commons.math3.complex.Complex
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