Examples of ClassicalRungeKuttaIntegrator

org.apache.commons.math.ode.ClassicalRungeKuttaIntegrator
This class implements the classical fourth order Runge-Kutta integrator for Ordinary Differential Equations (it is the most often used Runge-Kutta method).
This method is an explicit Runge-Kutta method, its Butcher-array is the following one :
```
 0  |  0    0    0    0 1/2 | 1/2   0    0    0 1/2 |  0   1/2   0    0 1  |  0    0    1    0 |-------------------- | 1/6  1/3  1/3  1/6 
```
@see EulerIntegrator @see GillIntegrator @see MidpointIntegrator @see ThreeEighthesIntegrator @version $Revision: 620312 $ $Date: 2008-02-10 12:28:59 -0700 (Sun, 10 Feb 2008) $ @since 1.2
org.apache.commons.math.ode.nonstiff.ClassicalRungeKuttaIntegrator
This class implements the classical fourth order Runge-Kutta integrator for Ordinary Differential Equations (it is the most often used Runge-Kutta method).
This method is an explicit Runge-Kutta method, its Butcher-array is the following one :
```
 0  |  0    0    0    0 1/2 | 1/2   0    0    0 1/2 |  0   1/2   0    0 1  |  0    0    1    0 |-------------------- | 1/6  1/3  1/3  1/6 
```
@see EulerIntegrator @see GillIntegrator @see MidpointIntegrator @see ThreeEighthesIntegrator @version $Revision: 810196 $ $Date: 2009-09-01 21:47:46 +0200 (mar. 01 sept. 2009) $ @since 1.2
org.apache.commons.math3.ode.nonstiff.ClassicalRungeKuttaIntegrator
This class implements the classical fourth order Runge-Kutta integrator for Ordinary Differential Equations (it is the most often used Runge-Kutta method).
This method is an explicit Runge-Kutta method, its Butcher-array is the following one :
```
 0  |  0    0    0    0 1/2 | 1/2   0    0    0 1/2 |  0   1/2   0    0 1  |  0    0    1    0 |-------------------- | 1/6  1/3  1/3  1/6 
```
@see EulerIntegrator @see GillIntegrator @see MidpointIntegrator @see ThreeEighthesIntegrator @see LutherIntegrator @since 1.2

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

    throws DerivativeException, IntegratorException,
           IOException, ClassNotFoundException {


    TestProblem3 pb = new TestProblem3(0.9);
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003;
    ClassicalRungeKuttaIntegrator integ = new ClassicalRungeKuttaIntegrator(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 () > 700000);
    assertTrue(bos.size () < 701000);


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

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

  }


  public void testSanityChecks() {
    try  {
      TestProblem1 pb = new TestProblem1();
      new ClassicalRungeKuttaIntegrator(0.01).integrate(pb,
                                                        0.0, new double[pb.getDimension()+10],
                                                        1.0, new double[pb.getDimension()]);
        fail("an exception should have been thrown");
    } catch(DerivativeException de) {
      fail("wrong exception caught");
    } catch(IntegratorException ie) {
    }
    try  {
        TestProblem1 pb = new TestProblem1();
        new ClassicalRungeKuttaIntegrator(0.01).integrate(pb,
                                                          0.0, new double[pb.getDimension()],
                                                          1.0, new double[pb.getDimension()+10]);
          fail("an exception should have been thrown");
      } catch(DerivativeException de) {
        fail("wrong exception caught");
      } catch(IntegratorException ie) {
      }
    try  {
      TestProblem1 pb = new TestProblem1();
      new ClassicalRungeKuttaIntegrator(0.01).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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Examples of org.apache.commons.math.ode.ClassicalRungeKuttaIntegrator


        TestProblemAbstract pb = (TestProblemAbstract) problems[k].clone();
        double step = (pb.getFinalTime() - pb.getInitialTime())
          * Math.pow(2.0, -i);


        FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(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) {
          assertTrue(error < Math.abs(previousError));

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

    throws DerivativeException, IntegratorException {


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


    FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(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-13);
    assertTrue(handler.getMaximalValueError() < 4.0e-12);
    assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
    assertEquals("classical Runge-Kutta", integ.getName());
  }

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

    throws DerivativeException, IntegratorException {


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


    FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(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() > 0.0004);
    assertTrue(handler.getMaximalValueError() > 0.005);
    assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);

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

    throws DerivativeException, IntegratorException {


    final TestProblem3 pb  = new TestProblem3(0.9);
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003;


    FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step);
    integ.setStepHandler(new KeplerHandler(pb));
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);
  }

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

                                            double step)
  throws DerivativeException, IntegratorException {
    double[] y0 = new double[2];
    y0[0] = Math.sin(omega * t0);
    y0[1] = omega * Math.cos(omega * t0);
    ClassicalRungeKuttaIntegrator i = new ClassicalRungeKuttaIntegrator(step);
    double[] y = new double[2];
    i.integrate(new FirstOrderConverter(new Equations(1, omega)), t0, y0, t, y);
    return y[0];
  }

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

                                            double step)
  throws DerivativeException, IntegratorException {
    double[] y0 = new double[2];
    y0[0] = Math.sin(omega * t0);
    y0[1] = omega * Math.cos(omega * t0);
    ClassicalRungeKuttaIntegrator i = new ClassicalRungeKuttaIntegrator(step);
    double[] y = new double[2];
    i.integrate(new FirstOrderConverter(new Equations(1, omega)), t0, y0, t, y);
    return y[0];
  }

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

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


      ClassicalRungeKuttaIntegrator integrator = new ClassicalRungeKuttaIntegrator(60.0);


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


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

  }


  public void testSanityChecks() {
    try  {
      TestProblem1 pb = new TestProblem1();
      new ClassicalRungeKuttaIntegrator(0.01).integrate(pb,
                                                        0.0, new double[pb.getDimension()+10],
                                                        1.0, new double[pb.getDimension()]);
        fail("an exception should have been thrown");
    } catch(DerivativeException de) {
      fail("wrong exception caught");
    } catch(IntegratorException ie) {
    }
    try  {
        TestProblem1 pb = new TestProblem1();
        new ClassicalRungeKuttaIntegrator(0.01).integrate(pb,
                                                          0.0, new double[pb.getDimension()],
                                                          1.0, new double[pb.getDimension()+10]);
          fail("an exception should have been thrown");
      } catch(DerivativeException de) {
        fail("wrong exception caught");
      } catch(IntegratorException ie) {
      }
    try  {
      TestProblem1 pb = new TestProblem1();
      new ClassicalRungeKuttaIntegrator(0.01).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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