Examples of org.apache.commons.math3.ode.FirstOrderIntegrator

org.apache.commons.math3.ode.FirstOrderIntegrator
This interface represents a first order integrator for differential equations.
The classes which are devoted to solve first order differential equations should implement this interface. The problems which can be handled should implement the {@link FirstOrderDifferentialEquations} interface.
@see FirstOrderDifferentialEquations @see org.apache.commons.math3.ode.sampling.StepHandler @see org.apache.commons.math3.ode.events.EventHandler @since 1.2

  @Test
  public void testUnstableDerivative()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {
    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);
  }

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      yDot[0] = omega * (c[1] - y[1]);
      yDot[1] = omega * (y[0] - c[0]);
    }


    public static void runExample1() {
      FirstOrderIntegrator integrator = new DormandPrince853Integrator(1.0e-8, 100.0, 1.0e-10, 1.0e-10);
      FirstOrderDifferentialEquations ode = new CircleODE(new double[] { 1.0, 1.0 }, 0.1);
      double[] y = new double[] { 0.0, 1.0 }; // initial state
      StepHandler stepHandler = new StepHandler() {
        public void init (double t0, double[] y0, double t) {
        }


        public void handleStep (StepInterpolator interpolator, boolean isLast) {
          double t = interpolator.getCurrentTime();
          double[] y = interpolator.getInterpolatedState();
          System.out.println("->" + t + " " + y[0] + " " + y[1]);
        }
      };
      integrator.addStepHandler(stepHandler);
      integrator.integrate(ode, 0.0, y, 16.0, y); // now y contains final state
                                                  // at time
                                                  // t=16.0
    }

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     * @param reverse whether to reverse the integration direction
     */
    private void doTest(StepNormalizerMode mode, StepNormalizerBounds bounds,
                        double[] expected, boolean reverse) {
        // Forward test.
        FirstOrderIntegrator integ = new GraggBulirschStoerIntegrator(
                                                        1e-8, 1.0, 1e-5, 1e-5);
        integ.addStepHandler(new StepNormalizer(0.5, this, mode, bounds));
        double[] y   = {0.0};
        double start = reverse ? getEnd()   : getStart();
        double end   = reverse ? getStart() : getEnd();
        output       = new ArrayList<Double>();
        integ.integrate(this, start, y, end, y);
        double[] actual = new double[output.size()];
        for(int i = 0; i < actual.length; i++) {
            actual[i] = output.get(i);
        }
        assertArrayEquals(expected, actual, 1e-5);

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      double previousTimeError = Double.NaN;
      for (int i = 4; i < 10; ++i) {


        TestProblemAbstract pb = problems[k].copy();
        double step = (pb.getFinalTime() - pb.getInitialTime()) * FastMath.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) {
            Assert.assertEquals(pb.getFinalTime(), stopTime, 1.0e-10);
        }

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    {


    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()]);


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


  }

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    {


    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()]);


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

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      {


      TestProblem5 pb = new TestProblem5();
      double step = FastMath.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()]);


      Assert.assertTrue(handler.getLastError() < 6.0e-4);
      Assert.assertTrue(handler.getMaximalValueError() < 6.0e-4);
      Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
      Assert.assertEquals("midpoint", integ.getName());
  }

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  @Test
  public void testStepSize()
    {
      final double step = 1.23456;
      FirstOrderIntegrator integ = new MidpointIntegrator(step);
      integ.addStepHandler(new StepHandler() {
          public void handleStep(StepInterpolator interpolator, boolean isLast) {
              if (! isLast) {
                  Assert.assertEquals(step,
                               interpolator.getCurrentTime() - interpolator.getPreviousTime(),
                               1.0e-12);
              }
          }
          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 minStep   = 0.1 * FastMath.abs(pb.getFinalTime() - pb.getInitialTime());
      double maxStep   = FastMath.abs(pb.getFinalTime() - pb.getInitialTime());
      double[] vecAbsoluteTolerance = { 1.0e-20, 1.0e-21 };
      double[] vecRelativeTolerance = { 1.0e-20, 1.0e-21 };


      FirstOrderIntegrator integ =
        new GraggBulirschStoerIntegrator(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()]);


  }

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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 GraggBulirschStoerIntegrator(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()]);


      Assert.assertTrue(handler.getLastError() < 7.5e-9);
      Assert.assertTrue(handler.getMaximalValueError() < 8.1e-9);
      Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
      Assert.assertEquals("Gragg-Bulirsch-Stoer", integ.getName());
  }

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