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

Examples of org.apache.commons.math.ode.nonstiff.DormandPrince853Integrator


                  yDot[i] = k[i] * y[i];
              }
          }
      };

      DormandPrince853Integrator integrator = new DormandPrince853Integrator(0.0, 100.0,
                                                                             1.0e-10, 1.0e-10);

      double[] y0   = new double[k.length];
      for (int i = 0; i < y0.length; ++i) {
          y0[i] = i + 1;
      }
      double[] y    = new double[k.length];

      integrator.setInitialStepSize(60.0);
      double finalT = integrator.integrate(ode, t0, y0, tEvent, y);
      Assert.assertEquals(tEvent, finalT, 5.0e-6);
      for (int i = 0; i < y.length; ++i) {
          Assert.assertEquals(y0[i] * Math.exp(k[i] * (finalT - t0)), y[i], 1.0e-9);
      }

      integrator.setInitialStepSize(60.0);
      integrator.addEventHandler(new EventHandler() {

          public void resetState(double t, double[] y) {
          }

          public double g(double t, double[] y) {
              return t - tEvent;
          }

          public int eventOccurred(double t, double[] y, boolean increasing) {
              Assert.assertEquals(tEvent, t, 5.0e-6);
              return CONTINUE;
          }
      }, Double.POSITIVE_INFINITY, 1.0e-20, 100);
      finalT = integrator.integrate(ode, t0, y0, tEvent + 120, y);
      Assert.assertEquals(tEvent + 120, finalT, 5.0e-6);
      for (int i = 0; i < y.length; ++i) {
          Assert.assertEquals(y0[i] * Math.exp(k[i] * (finalT - t0)), y[i], 1.0e-9);
      }

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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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      double minStep = 0.1 * (pb.getFinalTime() - pb.getInitialTime());
      double maxStep = pb.getFinalTime() - pb.getInitialTime();
      double[] vecAbsoluteTolerance = { 1.0e-15, 1.0e-16 };
      double[] vecRelativeTolerance = { 1.0e-15, 1.0e-16 };

      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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      double minStep = 0;
      double maxStep = pb.getFinalTime() - pb.getInitialTime();
      double scalAbsoluteTolerance = Math.pow(10.0, i);
      double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;

      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
      // there is no general relation between local and global errors
      assertTrue(handler.getMaximalValueError() < (1.3 * scalAbsoluteTolerance));
      assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);

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

    }

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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 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() < 8.1e-8);
      assertTrue(handler.getMaximalValueError() < 1.1e-7);
      assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
      assertEquals("Dormand-Prince 8 (5, 3)", integ.getName());
  }
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    double minStep = 0;
    double maxStep = pb.getFinalTime() - pb.getInitialTime();
    double scalAbsoluteTolerance = 1.0e-9;
    double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;

    FirstOrderIntegrator integ = new DormandPrince853Integrator(minStep, maxStep,
                                                                scalAbsoluteTolerance,
                                                                scalRelativeTolerance);
    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-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);
    assertEquals(12.0, handler.getLastTime(), 1.0e-8 * maxStep);
    integ.clearEventHandlers();
    assertEquals(0, integ.getEventHandlers().size());

  }
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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()]);

    assertEquals(integ.getEvaluations(), pb.getCalls());
    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()]);
    assertEquals(pb.getFinalTime(), stopTime, 1.0e-10);
    assertEquals("Dormand-Prince 8 (5, 3)", integ.getName());
  }
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    double minStep = 0.1 * (pb1.getFinalTime() - pb1.getInitialTime());
    double maxStep = pb1.getFinalTime() - pb1.getInitialTime();
    double scalAbsoluteTolerance = 1.0e-4;
    double scalRelativeTolerance = 1.0e-4;

    FirstOrderIntegrator integ = new DormandPrince853Integrator(minStep, maxStep,
                                                                scalAbsoluteTolerance,
                                                                scalRelativeTolerance);
    integ.addStepHandler(DummyStepHandler.getInstance());
    integ.integrate(pb1,
                    pb1.getInitialTime(), pb1.getInitialState(),
                    pb1.getFinalTime(), new double[pb1.getDimension()]);
    int callsWithoutDenseOutput = pb1.getCalls();
    assertEquals(integ.getEvaluations(), callsWithoutDenseOutput);

    integ.addStepHandler(new InterpolatingStepHandler());
    integ.integrate(pb2,
                    pb2.getInitialTime(), pb2.getInitialState(),
                    pb2.getFinalTime(), new double[pb2.getDimension()]);
    int callsWithDenseOutput = pb2.getCalls();
    assertEquals(integ.getEvaluations(), callsWithDenseOutput);

    assertTrue(callsWithDenseOutput > callsWithoutDenseOutput);

  }
View Full Code Here

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