Package org.apache.commons.math.ode.nonstiff

Examples of org.apache.commons.math.ode.nonstiff.DormandPrince853Integrator.integrate()

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      // integrate backward from π to 0;
      ContinuousOutputModel cm1 = new ContinuousOutputModel();
      FirstOrderIntegrator integ1 =
          new DormandPrince853Integrator(0, 1.0, 1.0e-8, 1.0e-8);
      integ1.addStepHandler(cm1);
      integ1.integrate(problem, Math.PI, new double[] { -1.0, 0.0 },
                       0, new double[2]);

      // integrate backward from 2π to π
      ContinuousOutputModel cm2 = new ContinuousOutputModel();
      FirstOrderIntegrator integ2 =
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      // integrate backward from 2π to π
      ContinuousOutputModel cm2 = new ContinuousOutputModel();
      FirstOrderIntegrator integ2 =
          new DormandPrince853Integrator(0, 0.1, 1.0e-12, 1.0e-12);
      integ2.addStepHandler(cm2);
      integ2.integrate(problem, 2.0 * Math.PI, new double[] { 1.0, 0.0 },
                       Math.PI, new double[2]);

      // merge the two half circles
      ContinuousOutputModel cm = new ContinuousOutputModel();
      cm.append(cm2);
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  public void testDimensionCheck() {
    try  {
      TestProblem1 pb = new TestProblem1();
      DormandPrince853Integrator integrator = new DormandPrince853Integrator(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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  public void testNullIntervalCheck() {
    try  {
      TestProblem1 pb = new TestProblem1();
      DormandPrince853Integrator integrator = new DormandPrince853Integrator(0.0, 1.0,
                                                                             1.0e-10, 1.0e-10);
      integrator.integrate(pb,
                           0.0, new double[pb.getDimension()],
                           0.0, new double[pb.getDimension()]);
      fail("an exception should have been thrown");
    } catch(DerivativeException de) {
      fail("wrong exception caught");
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      FirstOrderIntegrator integ = new DormandPrince853Integrator(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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      FirstOrderIntegrator integ = new DormandPrince853Integrator(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()]);

      // the 1.3 factor is only valid for this test
      // and has been obtained from trial and error
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      FirstOrderIntegrator integ = new DormandPrince853Integrator(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() < 8.0e-8);
      assertTrue(handler.getMaximalValueError() < 2.0e-7);
      assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
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    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-8);
    assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
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    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()]);

    assertEquals(integ.getEvaluations(), pb.getCalls());
    assertTrue(pb.getCalls() < 3300);
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    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()]);
    assertEquals(pb.getFinalTime(), stopTime, 1.0e-10);
    assertEquals("Dormand-Prince 8 (5, 3)", integ.getName());
  }
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