Package org.apache.commons.math3.ode

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

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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 GillIntegrator(0.3);
    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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  @Test
  public void testStepSize()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {
      final double step = 1.23456;
      FirstOrderIntegrator integ = new GillIntegrator(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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      for (int i = 4; i < 8; ++i) {

        TestProblemAbstract pb  = problems[k].copy();
        double step = (pb.getFinalTime() - pb.getInitialTime()) * FastMath.pow(2.0, -i);

        FirstOrderIntegrator integ = new EulerIntegrator(step);
        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-6 * step, 1000);
        }
        double stopTime = integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
                                          pb.getFinalTime(), new double[pb.getDimension()]);
        if (functions.length == 0) {
            Assert.assertEquals(pb.getFinalTime(), stopTime, 1.0e-10);
        }

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             MaxCountExceededException, NoBracketingException {

    TestProblem1 pb  = new TestProblem1();
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;

    FirstOrderIntegrator integ = new EulerIntegrator(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() < 2.0e-4);
   Assert.assertTrue(handler.getMaximalValueError() < 1.0e-3);
   Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
   Assert.assertEquals("Euler", integ.getName());

  }
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             MaxCountExceededException, NoBracketingException {

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

    FirstOrderIntegrator integ = new EulerIntegrator(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() > 0.01);
    Assert.assertTrue(handler.getMaximalValueError() > 0.2);
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             MaxCountExceededException, NoBracketingException {

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

      FirstOrderIntegrator integ = new EulerIntegrator(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() < 0.45);
      Assert.assertTrue(handler.getMaximalValueError() < 0.45);
      Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
      Assert.assertEquals("Euler", integ.getName());
  }
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    double minStep = 0;
    double maxStep = pb.getFinalTime() - pb.getInitialTime();
    double[] vecAbsoluteTolerance = { 1.0e-8, 1.0e-8, 1.0e-10, 1.0e-10 };
    double[] vecRelativeTolerance = { 1.0e-10, 1.0e-10, 1.0e-8, 1.0e-8 };

    FirstOrderIntegrator integ = new HighamHall54Integrator(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.assertEquals(0.0, handler.getMaximalValueError(), 1.5e-4);
    Assert.assertEquals("Higham-Hall 5(4)", integ.getName());
  }
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      double minStep   = 0.1 * FastMath.abs(pb.getFinalTime() - pb.getInitialTime());
      double maxStep   = FastMath.abs(pb.getFinalTime() - pb.getInitialTime());
      double[] vecAbsoluteTolerance = { 1.0e-20, 1.0e-21 };
      double[] vecRelativeTolerance = { 1.0e-20, 1.0e-21 };

      FirstOrderIntegrator integ =
        new GraggBulirschStoerIntegrator(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()]);

  }
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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 GraggBulirschStoerIntegrator(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() < 7.5e-9);
      Assert.assertTrue(handler.getMaximalValueError() < 8.1e-9);
      Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
      Assert.assertEquals("Gragg-Bulirsch-Stoer", integ.getName());
  }
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      double minStep      = 0;
      double maxStep      = pb.getFinalTime() - pb.getInitialTime();
      double absTolerance = FastMath.pow(10.0, i);
      double relTolerance = absTolerance;

      FirstOrderIntegrator integ =
        new GraggBulirschStoerIntegrator(minStep, maxStep,
                                         absTolerance, relTolerance);
      TestProblemHandler handler = new TestProblemHandler(pb, integ);
      integ.addStepHandler(handler);
      integ.integrate(pb,
                      pb.getInitialTime(), pb.getInitialState(),
                      pb.getFinalTime(), new double[pb.getDimension()]);

      // the coefficients are only valid for this test
      // and have been obtained from trial and error
      // there is no general relation between local and global errors
      double ratio =  handler.getMaximalValueError() / absTolerance;
      Assert.assertTrue(ratio < 2.4);
      Assert.assertTrue(ratio > 0.02);
      Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);

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

    }
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Related Classes of org.apache.commons.math3.ode.FirstOrderIntegrator

  • 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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