Examples of TestProblem3

org.apache.commons.math.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) = ... 
```
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) = ... 
```

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

  @Test
  public void serialization()
    throws DerivativeException, IntegratorException,
           IOException, ClassNotFoundException {


    TestProblem3 pb = new TestProblem3(0.9);
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003;
    GillIntegrator integ = new GillIntegrator(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);
    }


    assertTrue(bos.size () > 753000);
    assertTrue(bos.size () < 754000);


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

public class ClassicalRungeKuttaStepInterpolatorTest {


  @Test
  public void derivativesConsistency()
  throws DerivativeException, IntegratorException {
    TestProblem3 pb = new TestProblem3();
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;
    ClassicalRungeKuttaIntegrator integ = new ClassicalRungeKuttaIntegrator(step);
    StepInterpolatorTestUtils.checkDerivativesConsistency(integ, pb, 1.0e-10);
  }

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

  @Test
  public void serialization()
    throws DerivativeException, IntegratorException,
           IOException, ClassNotFoundException {


    TestProblem3 pb = new TestProblem3(0.9);
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003;
    ClassicalRungeKuttaIntegrator integ = new ClassicalRungeKuttaIntegrator(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);
    }


    assertTrue(bos.size () > 753000);
    assertTrue(bos.size () < 754000);


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

  }


  public void testKepler()
    throws DerivativeException, IntegratorException {


    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 DormandPrince853Integrator(minStep, maxStep,
                                                                scalAbsoluteTolerance,
                                                                scalRelativeTolerance);
    integ.addStepHandler(new KeplerHandler(pb));
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);


    assertEquals(integ.getEvaluations(), pb.getCalls());
    assertTrue(pb.getCalls() < 3300);


  }

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

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


    final TestProblem3 pb  = new TestProblem3(0.9);
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003;


    FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step);
    integ.addStepHandler(new KeplerHandler(pb));
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);
  }

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

    }


    @Test
    public void testSingleStep() {


        final TestProblem3 pb  = new TestProblem3(0.9);
        double h = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003;


        RungeKuttaIntegrator integ = new LutherIntegrator(Double.NaN);
        double   t = pb.getInitialTime();
        double[] y = pb.getInitialState();
        for (int i = 0; i < 100; ++i) {
            y = integ.singleStep(pb, t, y, t + h);
            t += h;
        }
        double[] yth = pb.computeTheoreticalState(t);
        double dx = y[0] - yth[0];
        double dy = y[1] - yth[1];
        double error = dx * dx + dy * dy;
        Assert.assertEquals(0.0, error, 1.0e-11);
    }

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


    @Test
    public void derivativesConsistency()
            throws DimensionMismatchException, NumberIsTooSmallException,
            MaxCountExceededException, NoBracketingException {
        TestProblem3 pb = new TestProblem3();
        double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;
        LutherIntegrator integ = new LutherIntegrator(step);
        StepInterpolatorTestUtils.checkDerivativesConsistency(integ, pb, 1.0e-10);
    }

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

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


        TestProblem3 pb = new TestProblem3(0.9);
        double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003;
        LutherIntegrator integ = new LutherIntegrator(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() > 1200000);
        Assert.assertTrue(bos.size() < 1250000);


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

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


        final TestProblem3 pb  = new TestProblem3(0.9);
        double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003;


        FirstOrderIntegrator integ = new LutherIntegrator(step);
        integ.addStepHandler(new KeplerHandler(pb));
        integ.integrate(pb,
                        pb.getInitialTime(), pb.getInitialState(),
                        pb.getFinalTime(), new double[pb.getDimension()]);
    }

View Full Code Here

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

  @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 DormandPrince853Integrator(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() < 3300);


  }

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