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

            MaxCountExceededException, NoBracketingException {


        TestProblem1 pb = new TestProblem1();
        double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.2;


        FirstOrderIntegrator integ = new LutherIntegrator(step);
        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() > 0.00002);
        Assert.assertTrue(handler.getMaximalValueError() > 0.001);
        Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);

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            MaxCountExceededException, NoBracketingException {


        TestProblem5 pb = new TestProblem5();
        double step = FastMath.abs(pb.getFinalTime() - pb.getInitialTime()) * 0.001;


        FirstOrderIntegrator integ = new LutherIntegrator(step);
        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() < 3.0e-13);
        Assert.assertTrue(handler.getMaximalValueError() < 5.0e-13);
        Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
        Assert.assertEquals("Luther", integ.getName());
    }

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            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()]);
    }

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    @Test
    public void testStepSize()
            throws DimensionMismatchException, NumberIsTooSmallException,
            MaxCountExceededException, NoBracketingException {
        final double step = 1.23456;
        FirstOrderIntegrator integ = new LutherIntegrator(step);
        integ.addStepHandler(new StepHandler() {
            public void handleStep(StepInterpolator interpolator, boolean isLast) {
                if (! isLast) {
                    Assert.assertEquals(step,
                                        interpolator.getCurrentTime() - interpolator.getPreviousTime(),
                                        1.0e-12);
                }
            }
            public void init(double t0, double[] y0, double t) {
            }
        });
        integ.integrate(new FirstOrderDifferentialEquations() {
            public void computeDerivatives(double t, double[] y, double[] dot) {
                dot[0] = 1.0;
            }
            public int getDimension() {
                return 1;

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    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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    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 VariableHandler());
    double stopTime = integ.integrate(pb,
                                      pb.getInitialTime(), pb.getInitialState(),
                                      pb.getFinalTime(), new double[pb.getDimension()]);
    Assert.assertEquals(pb.getFinalTime(), stopTime, 1.0e-10);
    Assert.assertEquals("Dormand-Prince 8 (5, 3)", integ.getName());
  }

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  @Test
  public void testUnstableDerivative()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {
    final StepProblem stepProblem = new StepProblem(0.0, 1.0, 2.0);
    FirstOrderIntegrator integ =
      new DormandPrince853Integrator(0.1, 10, 1.0e-12, 0.0);
    integ.addEventHandler(stepProblem, 1.0, 1.0e-12, 1000);
    double[] y = { Double.NaN };
    integ.integrate(stepProblem, 0.0, new double[] { 0.0 }, 10.0, y);
    Assert.assertEquals(8.0, y[0], 1.0e-12);
  }

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      };


      SchedulingChecker sinChecker = new SchedulingChecker(0); // events at 0, PI, 2PI ...
      SchedulingChecker cosChecker = new SchedulingChecker(1); // events at PI/2, 3PI/2, 5PI/2 ...


      FirstOrderIntegrator integ =
              new DormandPrince853Integrator(0.001, 1.0, 1.0e-12, 0.0);
      integ.addEventHandler(sinChecker, 0.01, 1.0e-7, 100);
      integ.addStepHandler(sinChecker);
      integ.addEventHandler(cosChecker, 0.01, 1.0e-7, 100);
      integ.addStepHandler(cosChecker);
      double   t0 = 0.5;
      double[] y0 = new double[] { FastMath.sin(t0), FastMath.cos(t0) };
      double   t  = 10.0;
      double[] y  = new double[2];
      integ.integrate(sincos, t0, y0, t, y);


  }

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    @Test
    public void testIncreasingOnly()
        throws DimensionMismatchException, NumberIsTooSmallException,
               MaxCountExceededException, NoBracketingException {
        double e = 1e-15;
        FirstOrderIntegrator integrator;
        integrator = new DormandPrince853Integrator(1.0e-3, 100.0, 1e-7, 1e-7);
        Event allEvents = new Event(true, true);
        integrator.addEventHandler(allEvents, 0.1, e, 1000,
                                   new BracketingNthOrderBrentSolver(1.0e-7, 5));
        Event onlyIncreasing = new Event(false, true);
        integrator.addEventHandler(new EventFilter(onlyIncreasing,
                                                   FilterType.TRIGGER_ONLY_INCREASING_EVENTS),
                                   0.1, e, 100,
                                   new BracketingNthOrderBrentSolver(1.0e-7, 5));
        double t0 = 0.5 * FastMath.PI;
        double tEnd = 5.5 * FastMath.PI;
        double[] y = { 0.0, 1.0 };
        Assert.assertEquals(tEnd,
                            integrator.integrate(new SineCosine(), t0, y, tEnd, y),
                            1.0e-7);


        Assert.assertEquals(5, allEvents.getEventCount());
        Assert.assertEquals(2, onlyIncreasing.getEventCount());

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    @Test
    public void testDecreasingOnly()
        throws DimensionMismatchException, NumberIsTooSmallException,
               MaxCountExceededException, NoBracketingException {
        double e = 1e-15;
        FirstOrderIntegrator integrator;
        integrator = new DormandPrince853Integrator(1.0e-3, 100.0, 1e-7, 1e-7);
        Event allEvents = new Event(true, true);
        integrator.addEventHandler(allEvents, 0.1, e, 1000,
                                   new BracketingNthOrderBrentSolver(1.0e-7, 5));
        Event onlyDecreasing = new Event(true, false);
        integrator.addEventHandler(new EventFilter(onlyDecreasing,
                                                   FilterType.TRIGGER_ONLY_DECREASING_EVENTS),
                                   0.1, e, 1000,
                                   new BracketingNthOrderBrentSolver(1.0e-7, 5));
        double t0 = 0.5 * FastMath.PI;
        double tEnd = 5.5 * FastMath.PI;
        double[] y = { 0.0, 1.0 };
        Assert.assertEquals(tEnd,
                            integrator.integrate(new SineCosine(), t0, y, tEnd, y),
                            1.0e-7);


        Assert.assertEquals(5, allEvents.getEventCount());
        Assert.assertEquals(3, onlyDecreasing.getEventCount());

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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

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