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

org.apache.commons.math3.ode.FirstOrderIntegrator
This interface represents a first order integrator for differential equations.
The classes which are devoted to solve first order differential equations should implement this interface. The problems which can be handled should implement the {@link FirstOrderDifferentialEquations} interface.
@see FirstOrderDifferentialEquations @see org.apache.commons.math3.ode.sampling.StepHandler @see org.apache.commons.math3.ode.events.EventHandler @since 1.2

      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()]);


  }

View Full Code Here

    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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      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
      }

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     */
    public void test(int eventType)
        throws DimensionMismatchException, NumberIsTooSmallException,
               MaxCountExceededException, NoBracketingException {
        double e = 1e-15;
        FirstOrderIntegrator integrator = new DormandPrince853Integrator(e, 100.0, 1e-7, 1e-7);
        BaseSecantSolver rootSolver = new PegasusSolver(e, e);
        EventHandler evt1 = new Event(0, eventType);
        EventHandler evt2 = new Event(1, eventType);
        integrator.addEventHandler(evt1, 0.1, e, 999, rootSolver);
        integrator.addEventHandler(evt2, 0.1, e, 999, rootSolver);
        double t = 0.0;
        double tEnd = 10.0;
        double[] y = {0.0, 0.0};
        List<Double> events1 = new ArrayList<Double>();
        List<Double> events2 = new ArrayList<Double>();
        while (t < tEnd) {
            t = integrator.integrate(this, t, y, tEnd, y);
            //System.out.println("t=" + t + ",\t\ty=[" + y[0] + "," + y[1] + "]");


            if (y[0] >= 1.0) {
                y[0] = 0.0;
                events1.add(t);

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    public double test(int integratorType)
        throws DimensionMismatchException, NumberIsTooSmallException,
               MaxCountExceededException, NoBracketingException {
        double e = 1e-15;
        FirstOrderIntegrator integrator;
        integrator = (integratorType == 1)
                     ? new DormandPrince853Integrator(e, 100.0, 1e-7, 1e-7)
                     : new GraggBulirschStoerIntegrator(e, 100.0, 1e-7, 1e-7);
        PegasusSolver rootSolver = new PegasusSolver(e, e);
        integrator.addEventHandler(new Event(), 0.1, e, 1000, rootSolver);
        double t0 = 6.0;
        double tEnd = 10.0;
        double[] y = {2.0, 2.0, 2.0, 4.0, 2.0, 7.0, 15.0};
        return integrator.integrate(new Ode(), t0, y, tEnd, y);
    }

View Full Code Here

      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");


  }

View Full Code Here

      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()]);


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

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    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();
    double convergence = 1.0e-8 * maxStep;
    for (int l = 0; l < functions.length; ++l) {
      integ.addEventHandler(functions[l],
                                 Double.POSITIVE_INFINITY, convergence, 1000);
    }
    Assert.assertEquals(functions.length, integ.getEventHandlers().size());
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);


    Assert.assertTrue(handler.getMaximalValueError() < 5.0e-6);
    Assert.assertEquals(0, handler.getMaximalTimeError(), convergence);
    Assert.assertEquals(12.0, handler.getLastTime(), convergence);
    integ.clearEventHandlers();
    Assert.assertEquals(0, integ.getEventHandlers().size());


  }

View Full Code Here

    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

    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);
  }

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