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

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

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        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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        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);
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        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()]);
    }

    private static class KeplerHandler implements StepHandler {
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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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    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.assertEquals(0, handler.getMaximalValueError(), 2.1e-7);
    Assert.assertEquals(0, handler.getMaximalTimeError(), convergence);
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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()]);

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

  @Test
  public void testEventsScheduling() {
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      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);

  }

  private static class SchedulingChecker implements StepHandler, EventHandler {
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                                   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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