Package org.apache.commons.math3.analysis.integration

Examples of org.apache.commons.math3.analysis.integration.IterativeLegendreGaussIntegrator.integrate()

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             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);
  }

  private static class KeplerStepHandler implements StepHandler {
    public KeplerStepHandler(TestProblem3 pb) {
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              }
          }
          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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        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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    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);
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    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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    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);
  }

  private static class KeplerHandler implements StepHandler {
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      }

      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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    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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      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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      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);
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