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

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

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

org.apache.commons.math.ode.nonstiff.DormandPrince853Integrator
This class implements the 8(5,3) Dormand-Prince integrator for Ordinary Differential Equations.
This integrator is an embedded Runge-Kutta integrator of order 8(5,3) used in local extrapolation mode (i.e. the solution is computed using the high order formula) with stepsize control (and automatic step initialization) and continuous output. This method uses 12 functions evaluations per step for integration and 4 evaluations for interpolation. However, since the first interpolation evaluation is the same as the first integration evaluation of the next step, we have included it in the integrator rather than in the interpolator and specified the method was an fsal. Hence, despite we have 13 stages here, the cost is really 12 evaluations per step even if no interpolation is done, and the overcost of interpolation is only 3 evaluations.

This method is based on an 8(6) method by Dormand and Prince (i.e. order 8 for the integration and order 6 for error estimation) modified by Hairer and Wanner to use a 5th order error estimator with 3rd order correction. This modification was introduced because the original method failed in some cases (wrong steps can be accepted when step size is too large, for example in the Brusselator problem) and also had severe difficulties when applied to problems with discontinuities. This modification is explained in the second edition of the first volume (Nonstiff Problems) of the reference book by Hairer, Norsett and Wanner: Solving Ordinary Differential Equations (Springer-Verlag, ISBN 3-540-56670-8).
@version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $ @since 1.2

                  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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Related Classes of org.apache.commons.math.ode.nonstiff.DormandPrince853Integrator

org.apache.commons.math.ode.ContinuousOutputModelTest

org.apache.commons.math.ode.MultistepIntegrator

org.apache.commons.math.ode.nonstiff.DormandPrince853IntegratorTest

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