Examples of org.apache.commons.math3.ode.TestProblem3

org.apache.commons.math3.ode.TestProblem3
This class is used in the junit tests for the ODE integrators.
This specific problem is the following differential equation :
```
 y1'' = -y1/r^3  y1 (0) = 1-e  y1' (0) = 0 y2'' = -y2/r^3  y2 (0) = 0    y2' (0) =sqrt((1+e)/(1-e)) r = sqrt (y1^2 + y2^2), e = 0.9 
```
This is a two-body problem in the plane which can be solved by Kepler's equation
```
 y1 (t) = ... 
```

  @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 scalAbsoluteTolerance = 1.0e-8;
    double scalRelativeTolerance = scalAbsoluteTolerance;


    FirstOrderIntegrator integ = new DormandPrince54Integrator(minStep, maxStep,
                                                               scalAbsoluteTolerance,
                                                               scalRelativeTolerance);
    integ.addStepHandler(new KeplerHandler(pb));
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);


    Assert.assertEquals(integ.getEvaluations(), pb.getCalls());
    Assert.assertTrue(pb.getCalls() < 2800);


  }

View Full Code Here

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


    final TestProblem3 pb  = new TestProblem3(0.9);
    double minStep = 0;
    double maxStep = pb.getFinalTime() - pb.getInitialTime();
    double scalAbsoluteTolerance = 1.0e-8;
    double scalRelativeTolerance = scalAbsoluteTolerance;


    FirstOrderIntegrator integ = new DormandPrince54Integrator(minStep, maxStep,
                                                               scalAbsoluteTolerance,
                                                               scalRelativeTolerance);
    integ.addStepHandler(new VariableHandler());
    double stopTime = integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
                                      pb.getFinalTime(), new double[pb.getDimension()]);
    Assert.assertEquals(pb.getFinalTime(), stopTime, 1.0e-10);
  }

View Full Code Here


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


    GraggBulirschStoerIntegrator integ =
      new GraggBulirschStoerIntegrator(minStep, maxStep,

View Full Code Here


  @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
      }

View Full Code Here

  @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());
  }

View Full Code Here


  @Test
  public void derivativesConsistency()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {
    TestProblem3 pb = new TestProblem3(0.1);
    double minStep = 0;
    double maxStep = pb.getFinalTime() - pb.getInitialTime();
    double scalAbsoluteTolerance = 1.0e-8;
    double scalRelativeTolerance = scalAbsoluteTolerance;
    DormandPrince853Integrator integ = new DormandPrince853Integrator(minStep, maxStep,
                                                                      scalAbsoluteTolerance,
                                                                      scalRelativeTolerance);

View Full Code Here

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


    TestProblem3 pb = new TestProblem3(0.9);
    double minStep = 0;
    double maxStep = pb.getFinalTime() - pb.getInitialTime();
    double scalAbsoluteTolerance = 1.0e-8;
    double scalRelativeTolerance = scalAbsoluteTolerance;
    DormandPrince853Integrator integ = new DormandPrince853Integrator(minStep, maxStep,
                                                                      scalAbsoluteTolerance,
                                                                      scalRelativeTolerance);
    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 () > 90000);
    Assert.assertTrue(bos.size () < 100000);


    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;

View Full Code Here


  @Test
  public void checklone()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {
    TestProblem3 pb = new TestProblem3(0.9);
    double minStep = 0;
    double maxStep = pb.getFinalTime() - pb.getInitialTime();
    double scalAbsoluteTolerance = 1.0e-8;
    double scalRelativeTolerance = scalAbsoluteTolerance;
    DormandPrince853Integrator integ = new DormandPrince853Integrator(minStep, maxStep,
                                                                      scalAbsoluteTolerance,
                                                                      scalRelativeTolerance);
    integ.addStepHandler(new StepHandler() {
        public void handleStep(StepInterpolator interpolator, boolean isLast)
            throws MaxCountExceededException {
            StepInterpolator cloned = interpolator.copy();
            double tA = cloned.getPreviousTime();
            double tB = cloned.getCurrentTime();
            double halfStep = FastMath.abs(tB - tA) / 2;
            Assert.assertEquals(interpolator.getPreviousTime(), tA, 1.0e-12);
            Assert.assertEquals(interpolator.getCurrentTime(), tB, 1.0e-12);
            for (int i = 0; i < 10; ++i) {
                double t = (i * tB + (9 - i) * tA) / 9;
                interpolator.setInterpolatedTime(t);
                Assert.assertTrue(FastMath.abs(cloned.getInterpolatedTime() - t) > (halfStep / 10));
                cloned.setInterpolatedTime(t);
                Assert.assertEquals(t, cloned.getInterpolatedTime(), 1.0e-12);
                double[] referenceState = interpolator.getInterpolatedState();
                double[] cloneState     = cloned.getInterpolatedState();
                for (int j = 0; j < referenceState.length; ++j) {
                    Assert.assertEquals(referenceState[j], cloneState[j], 1.0e-12);
                }
            }
        }
        public void init(double t0, double[] y0, double t) {
        }
    });
    integ.integrate(pb,
            pb.getInitialTime(), pb.getInitialState(),
            pb.getFinalTime(), new double[pb.getDimension()]);


  }

View Full Code Here

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


    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

View Full Code Here

  @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 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()]);


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


  }

View Full Code Here

0 1 2 3 4 5 6 7 8 9

TOP

Related Classes of org.apache.commons.math3.ode.TestProblem3

org.apache.commons.math3.analysis.differentiation.DerivativeStructure

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

All source code are property of their respective owners. Java is a trademark of Sun Microsystems, Inc and owned by ORACLE Inc. Contact coftware#gmail.com.