Examples of DormandPrince54Integrator

org.apache.commons.math.ode.DormandPrince54Integrator
This class implements the 5(4) Dormand-Prince integrator for Ordinary Differential Equations.
This integrator is an embedded Runge-Kutta integrator of order 5(4) used in local extrapolation mode (i.e. the solution is computed using the high order formula) with stepsize control (and automatic step initialization) and continuous output. This method uses 7 functions evaluations per step. However, since this is an fsal, the last evaluation of one step is the same as the first evaluation of the next step and hence can be avoided. So the cost is really 6 functions evaluations per step.

This method has been published (whithout the continuous output that was added by Shampine in 1986) in the following article :
```
 A family of embedded Runge-Kutta formulae J. R. Dormand and P. J. Prince Journal of Computational and Applied Mathematics volume 6, no 1, 1980, pp. 19-26 
```
@version $Revision: 620312 $ $Date: 2008-02-10 12:28:59 -0700 (Sun, 10 Feb 2008) $ @since 1.2
org.apache.commons.math.ode.nonstiff.DormandPrince54Integrator
This class implements the 5(4) Dormand-Prince integrator for Ordinary Differential Equations.
This integrator is an embedded Runge-Kutta integrator of order 5(4) used in local extrapolation mode (i.e. the solution is computed using the high order formula) with stepsize control (and automatic step initialization) and continuous output. This method uses 7 functions evaluations per step. However, since this is an fsal, the last evaluation of one step is the same as the first evaluation of the next step and hence can be avoided. So the cost is really 6 functions evaluations per step.

This method has been published (whithout the continuous output that was added by Shampine in 1986) in the following article :
```
 A family of embedded Runge-Kutta formulae J. R. Dormand and P. J. Prince Journal of Computational and Applied Mathematics volume 6, no 1, 1980, pp. 19-26 
```
@version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $ @since 1.2
org.apache.commons.math3.ode.nonstiff.DormandPrince54Integrator
This class implements the 5(4) Dormand-Prince integrator for Ordinary Differential Equations.
This integrator is an embedded Runge-Kutta integrator of order 5(4) used in local extrapolation mode (i.e. the solution is computed using the high order formula) with stepsize control (and automatic step initialization) and continuous output. This method uses 7 functions evaluations per step. However, since this is an fsal, the last evaluation of one step is the same as the first evaluation of the next step and hence can be avoided. So the cost is really 6 functions evaluations per step.

This method has been published (whithout the continuous output that was added by Shampine in 1986) in the following article :
```
 A family of embedded Runge-Kutta formulae J. R. Dormand and P. J. Prince Journal of Computational and Applied Mathematics volume 6, no 1, 1980, pp. 19-26 
```
@since 1.2

Examples of org.apache.commons.math.ode.nonstiff.DormandPrince54Integrator

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


      FirstOrderIntegrator integ = new DormandPrince54Integrator(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() < 2.0e-7);
      assertTrue(handler.getMaximalValueError() < 2.0e-7);
      assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
      assertEquals("Dormand-Prince 5(4)", integ.getName());
  }

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Examples of org.apache.commons.math.ode.nonstiff.DormandPrince54Integrator

      double maxStep = pb.getFinalTime() - pb.getInitialTime();
      double scalAbsoluteTolerance = Math.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()]);
      assertEquals(0.8, integ.getSafety(), 1.0e-12);
      assertEquals(5.0, integ.getMaxGrowth(), 1.0e-12);
      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
      assertTrue(handler.getMaximalValueError() < (0.7 * scalAbsoluteTolerance));
      assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);


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


    }

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Examples of org.apache.commons.math.ode.nonstiff.DormandPrince54Integrator

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


    FirstOrderIntegrator integ = new DormandPrince54Integrator(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-6);
    assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
    assertEquals(12.0, handler.getLastTime(), 1.0e-8 * maxStep);
    integ.clearEventHandlers();
    assertEquals(0, integ.getEventHandlers().size());


  }

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Examples of org.apache.commons.math.ode.nonstiff.DormandPrince54Integrator

    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()]);


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


  }

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Examples of org.apache.commons.math.ode.nonstiff.DormandPrince54Integrator

    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()]);
    assertEquals(pb.getFinalTime(), stopTime, 1.0e-10);
  }

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Examples of org.apache.commons.math3.ode.nonstiff.DormandPrince54Integrator

  @Before
  public void setUp() {
    pb = new TestProblem3(0.9);
    double minStep = 0;
    double maxStep = pb.getFinalTime() - pb.getInitialTime();
    integ = new DormandPrince54Integrator(minStep, maxStep, 1.0e-8, 1.0e-8);
  }

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Examples of org.apache.commons.math3.ode.nonstiff.DormandPrince54Integrator

  @Before
  public void setUp() {
    pb = new TestProblem3(0.9);
    double minStep = 0;
    double maxStep = pb.getFinalTime() - pb.getInitialTime();
    integ = new DormandPrince54Integrator(minStep, maxStep, 10.e-8, 1.0e-8);
    lastSeen = false;
  }

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Examples of org.apache.commons.math3.ode.nonstiff.DormandPrince54Integrator

  @Before
  public void setUp() {
    pb = new TestProblem3(0.9);
    double minStep = 0;
    double maxStep = pb.getFinalTime() - pb.getInitialTime();
    integ = new DormandPrince54Integrator(minStep, maxStep, 1.0e-8, 1.0e-8);
  }

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Examples of org.apache.commons.math3.ode.nonstiff.DormandPrince54Integrator

        // essentially noise.
        // This test is taken from Hairer, Norsett and Wanner book
        // Solving Ordinary Differential Equations I (Nonstiff problems),
        // the curves dy/dp = g(b) are in figure 6.5
        FirstOrderIntegrator integ =
            new DormandPrince54Integrator(1.0e-8, 100.0, new double[] { 1.0e-4, 1.0e-4 }, new double[] { 1.0e-4, 1.0e-4 });
        double hP = 1.0e-12;
        SummaryStatistics residualsP0 = new SummaryStatistics();
        SummaryStatistics residualsP1 = new SummaryStatistics();
        for (double b = 2.88; b < 3.08; b += 0.001) {
            Brusselator brusselator = new Brusselator(b);
            double[] y = { 1.3, b };
            integ.integrate(brusselator, 0, y, 20.0, y);
            double[] yP = { 1.3, b + hP };
            integ.integrate(brusselator, 0, yP, 20.0, yP);
            residualsP0.addValue((yP[0] - y[0]) / hP - brusselator.dYdP0());
            residualsP1.addValue((yP[1] - y[1]) / hP - brusselator.dYdP1());
        }
        Assert.assertTrue((residualsP0.getMax() - residualsP0.getMin()) > 500);
        Assert.assertTrue(residualsP0.getStandardDeviation() > 30);

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Examples of org.apache.commons.math3.ode.nonstiff.DormandPrince54Integrator

    @Test
    public void testHighAccuracyExternalDifferentiation()
        throws NumberIsTooSmallException, DimensionMismatchException,
               MaxCountExceededException, NoBracketingException, UnknownParameterException {
        FirstOrderIntegrator integ =
            new DormandPrince54Integrator(1.0e-8, 100.0, new double[] { 1.0e-10, 1.0e-10 }, new double[] { 1.0e-10, 1.0e-10 });
        double hP = 1.0e-12;
        SummaryStatistics residualsP0 = new SummaryStatistics();
        SummaryStatistics residualsP1 = new SummaryStatistics();
        for (double b = 2.88; b < 3.08; b += 0.001) {
            ParamBrusselator brusselator = new ParamBrusselator(b);
            double[] y = { 1.3, b };
            integ.integrate(brusselator, 0, y, 20.0, y);
            double[] yP = { 1.3, b + hP };
            brusselator.setParameter("b", b + hP);
            integ.integrate(brusselator, 0, yP, 20.0, yP);
            residualsP0.addValue((yP[0] - y[0]) / hP - brusselator.dYdP0());
            residualsP1.addValue((yP[1] - y[1]) / hP - brusselator.dYdP1());
        }
        Assert.assertTrue((residualsP0.getMax() - residualsP0.getMin()) > 0.02);
        Assert.assertTrue((residualsP0.getMax() - residualsP0.getMin()) < 0.03);

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