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


    @Test
    public void testHighAccuracyExternalDifferentiation()
        throws IntegratorException, DerivativeException {
        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) {
            Brusselator brusselator = new Brusselator(b);
            double[] y = { 1.3, b };
            integ.integrate(brusselator, 0, y, 20.0, y);
            double[] yP = { 1.3, b + hP };
            brusselator.setParameter(0, 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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Examples of org.apache.commons.math.ode.nonstiff.DormandPrince54Integrator


    @Test
    public void testInternalDifferentiation()
        throws IntegratorException, DerivativeException {
        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);
            brusselator.setParameter(0, b);
            double[] z = { 1.3, b };
            double[][] dZdZ0 = new double[2][2];
            double[][] dZdP  = new double[2][1];
            double hY = 1.0e-12;
            FirstOrderIntegratorWithJacobians extInt =
                new FirstOrderIntegratorWithJacobians(integ, brusselator, new double[] { b },
                                                      new double[] { hY, hY }, new double[] { hP });
            extInt.setMaxEvaluations(5000);
            extInt.integrate(0, z, new double[][] { { 0.0 }, { 1.0 } }, 20.0, z, dZdZ0, dZdP);
            Assert.assertEquals(5000, extInt.getMaxEvaluations());
            Assert.assertTrue(extInt.getEvaluations() > 1400);
            Assert.assertTrue(extInt.getEvaluations() < 2000);
            Assert.assertEquals(4 * integ.getEvaluations(), extInt.getEvaluations());
            residualsP0.addValue(dZdP[0][0] - brusselator.dYdP0());
            residualsP1.addValue(dZdP[1][0] - brusselator.dYdP1());
        }
        Assert.assertTrue((residualsP0.getMax() - residualsP0.getMin()) < 0.02);
        Assert.assertTrue(residualsP0.getStandardDeviation() < 0.003);

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


    @Test
    public void testAnalyticalDifferentiation()
        throws IntegratorException, DerivativeException {
        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 });
        SummaryStatistics residualsP0 = new SummaryStatistics();
        SummaryStatistics residualsP1 = new SummaryStatistics();
        for (double b = 2.88; b < 3.08; b += 0.001) {
            Brusselator brusselator = new Brusselator(b);
            brusselator.setParameter(0, b);
            double[] z = { 1.3, b };
            double[][] dZdZ0 = new double[2][2];
            double[][] dZdP  = new double[2][1];
            FirstOrderIntegratorWithJacobians extInt =
                new FirstOrderIntegratorWithJacobians(integ, brusselator);
            extInt.setMaxEvaluations(5000);
            extInt.integrate(0, z, new double[][] { { 0.0 }, { 1.0 } }, 20.0, z, dZdZ0, dZdP);
            Assert.assertEquals(5000, extInt.getMaxEvaluations());
            Assert.assertTrue(extInt.getEvaluations() > 350);
            Assert.assertTrue(extInt.getEvaluations() < 510);
            Assert.assertEquals(integ.getEvaluations(), extInt.getEvaluations());
            residualsP0.addValue(dZdP[0][0] - brusselator.dYdP0());
            residualsP1.addValue(dZdP[1][0] - brusselator.dYdP1());
        }
        Assert.assertTrue((residualsP0.getMax() - residualsP0.getMin()) < 0.014);
        Assert.assertTrue(residualsP0.getStandardDeviation() < 0.003);

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

    }


    @Test
    public void testFinalResult() throws IntegratorException, DerivativeException {
        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[] y = new double[] { 0.0, 1.0 };
        Circle circle = new Circle(y, 1.0, 1.0, 0.1);
        double[][] dydy0 = new double[2][2];
        double[][] dydp  = new double[2][3];
        double t = 18 * FastMath.PI;

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

    }


    @Test
    public void testStepHandlerResult() throws IntegratorException, DerivativeException {
        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[] y = new double[] { 0.0, 1.0 };
        final Circle circle = new Circle(y, 1.0, 1.0, 0.1);
        double[][] dydy0 = new double[2][2];
        double[][] dydp  = new double[2][3];
        double t = 18 * FastMath.PI;

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

    }


    @Test
    public void testEventHandler() throws IntegratorException, DerivativeException {
        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[] y = new double[] { 0.0, 1.0 };
        final Circle circle = new Circle(y, 1.0, 1.0, 0.1);
        double[][] dydy0 = new double[2][2];
        double[][] dydp  = new double[2][3];
        double t = 18 * FastMath.PI;

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

  @Override
  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.math.ode.nonstiff.DormandPrince54Integrator

  }


  public void testDimensionCheck() {
    try  {
      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]);
      fail("an exception should have been thrown");
    } catch(DerivativeException de) {
      fail("wrong exception caught");

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

      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()]);
      fail("an exception should have been thrown");
    } catch(DerivativeException de) {
      fail("wrong exception caught");

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

    double maxStep = FastMath.abs(pb.getFinalTime() - pb.getInitialTime());
    double scalAbsoluteTolerance = 6.0e-4;
    double scalRelativeTolerance = 6.0e-4;


    AdaptiveStepsizeIntegrator integ =
      new DormandPrince54Integrator(minStep, maxStep,
                                    scalAbsoluteTolerance,
                                    scalRelativeTolerance);


    DP54SmallLastHandler handler = new DP54SmallLastHandler(minStep);
    integ.addStepHandler(handler);
    integ.setInitialStepSize(1.7);
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);
    assertTrue(handler.wasLastSeen());
    assertEquals("Dormand-Prince 5(4)", integ.getName());


  }

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