Examples of MidpointIntegrator

org.apache.commons.math.ode.MidpointIntegrator
This class implements a second order Runge-Kutta integrator for Ordinary Differential Equations.
This method is an explicit Runge-Kutta method, its Butcher-array is the following one :
```
 0  |  0    0 1/2 | 1/2   0 |---------- |  0    1 
```
@see EulerIntegrator @see ClassicalRungeKuttaIntegrator @see GillIntegrator @version $Revision: 620312 $ $Date: 2008-02-10 12:28:59 -0700 (Sun, 10 Feb 2008) $ @since 1.2
org.apache.commons.math.ode.nonstiff.MidpointIntegrator
This class implements a second order Runge-Kutta integrator for Ordinary Differential Equations.
This method is an explicit Runge-Kutta method, its Butcher-array is the following one :
```
 0  |  0    0 1/2 | 1/2   0 |---------- |  0    1 
```
@see EulerIntegrator @see ClassicalRungeKuttaIntegrator @see GillIntegrator @version $Revision: 810196 $ $Date: 2009-09-01 21:47:46 +0200 (mar. 01 sept. 2009) $ @since 1.2

Examples of org.apache.commons.math.ode.MidpointIntegrator

  }


  public void testDimensionCheck() {
    try  {
      TestProblem1 pb = new TestProblem1();
      new MidpointIntegrator(0.01).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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Examples of org.apache.commons.math.ode.MidpointIntegrator

      for (int i = 4; i < 10; ++i) {


        TestProblemAbstract pb = (TestProblemAbstract) problems[k].clone();
        double step = (pb.getFinalTime() - pb.getInitialTime())
          * Math.pow(2.0, -i);
        FirstOrderIntegrator integ = new MidpointIntegrator(step);
        TestProblemHandler handler = new TestProblemHandler(pb, integ);
        integ.setStepHandler(handler);
        SwitchingFunction[] functions = pb.getSwitchingFunctions();
        for (int l = 0; l < functions.length; ++l) {
          integ.addSwitchingFunction(functions[l],
                                     Double.POSITIVE_INFINITY, 1.0e-6 * step, 1000);
        }
        integ.integrate(pb,
                        pb.getInitialTime(), pb.getInitialState(),
                        pb.getFinalTime(), new double[pb.getDimension()]);


        double error = handler.getMaximalValueError();
        if (i > 4) {

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Examples of org.apache.commons.math.ode.MidpointIntegrator

    throws DerivativeException, IntegratorException {


    TestProblem1 pb  = new TestProblem1();
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;


    FirstOrderIntegrator integ = new MidpointIntegrator(step);
    TestProblemHandler handler = new TestProblemHandler(pb, integ);
    integ.setStepHandler(handler);
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);


    assertTrue(handler.getLastError() < 2.0e-7);
    assertTrue(handler.getMaximalValueError() < 1.0e-6);
    assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
    assertEquals("midpoint", integ.getName());


  }

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Examples of org.apache.commons.math.ode.MidpointIntegrator

    throws DerivativeException, IntegratorException {


    TestProblem1 pb  = new TestProblem1();
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.2;


    FirstOrderIntegrator integ = new MidpointIntegrator(step);
    TestProblemHandler handler = new TestProblemHandler(pb, integ);
    integ.setStepHandler(handler);
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);


    assertTrue(handler.getLastError() > 0.01);
    assertTrue(handler.getMaximalValueError() > 0.05);

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Examples of org.apache.commons.math.ode.MidpointIntegrator

    throws DerivativeException, IntegratorException,
           IOException, ClassNotFoundException {


    TestProblem1 pb = new TestProblem1();
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;
    MidpointIntegrator integ = new MidpointIntegrator(step);
    integ.setStepHandler(new ContinuousOutputModel());
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);


    ByteArrayOutputStream bos = new ByteArrayOutputStream();
    ObjectOutputStream    oos = new ObjectOutputStream(bos);
    oos.writeObject(integ.getStepHandler());


    assertTrue(bos.size () > 98000);
    assertTrue(bos.size () < 99000);


    ByteArrayInputStream  bis = new ByteArrayInputStream(bos.toByteArray());

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

  }


  public void testDimensionCheck() {
    try  {
      TestProblem1 pb = new TestProblem1();
      new MidpointIntegrator(0.01).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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Examples of org.apache.commons.math.ode.nonstiff.MidpointIntegrator

      for (int i = 4; i < 10; ++i) {


        TestProblemAbstract pb = problems[k].copy();
        double step = (pb.getFinalTime() - pb.getInitialTime())
          * Math.pow(2.0, -i);
        FirstOrderIntegrator integ = new MidpointIntegrator(step);
        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-6 * step, 1000);
        }
        double stopTime = integ.integrate(pb,
                                          pb.getInitialTime(), pb.getInitialState(),
                                          pb.getFinalTime(), new double[pb.getDimension()]);
        if (functions.length == 0) {
            assertEquals(pb.getFinalTime(), stopTime, 1.0e-10);
        }

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

    throws DerivativeException, IntegratorException {


    TestProblem1 pb  = new TestProblem1();
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;


    FirstOrderIntegrator integ = new MidpointIntegrator(step);
    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() < 2.0e-7);
    assertTrue(handler.getMaximalValueError() < 1.0e-6);
    assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
    assertEquals("midpoint", integ.getName());


  }

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

    throws DerivativeException, IntegratorException {


    TestProblem1 pb  = new TestProblem1();
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.2;


    FirstOrderIntegrator integ = new MidpointIntegrator(step);
    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() > 0.01);
    assertTrue(handler.getMaximalValueError() > 0.05);

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

      throws DerivativeException, IntegratorException {


      TestProblem5 pb = new TestProblem5();
      double step = Math.abs(pb.getFinalTime() - pb.getInitialTime()) * 0.001;


      FirstOrderIntegrator integ = new MidpointIntegrator(step);
      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() < 6.0e-4);
      assertTrue(handler.getMaximalValueError() < 6.0e-4);
      assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
      assertEquals("midpoint", integ.getName());
  }

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