public void testIncreasingTolerance() throws DerivativeException, IntegratorException {

    int previousCalls = Integer.MAX_VALUE;
    for (int i = -12; i < -2; ++i) {
      TestProblem1 pb = new TestProblem1();
      double minStep = 0;
      double maxStep = pb.getFinalTime() - pb.getInitialTime();
      double scalAbsoluteTolerance = Math.pow(10.0, i);
      double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;

      FirstOrderIntegrator integ =
          new HighamHall54Integrator(
              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;
    }
  }
  public void testIncreasingTolerance() throws DerivativeException, IntegratorException {

    int previousCalls = Integer.MAX_VALUE;
    for (int i = -12; i < -4; ++i) {
      TestProblem1 pb = new TestProblem1();
      double minStep = 0;
      double maxStep = pb.getFinalTime() - pb.getInitialTime();
      double absTolerance = Math.pow(10.0, i);
      double relTolerance = absTolerance;

      FirstOrderIntegrator integ =
          new GraggBulirschStoerIntegrator(
              minStep, maxStep,
              absTolerance, relTolerance);
      TestProblemHandler handler = new TestProblemHandler(pb, integ);
      integ.addStepHandler(handler);
      integ.integrate(
          pb,
          pb.getInitialTime(),
          pb.getInitialState(),
          pb.getFinalTime(),
          new double[pb.getDimension()]);

      // the coefficients are only valid for this test
      // and have been obtained from trial and error
      // there is no general relation between local and global errors
      double ratio = handler.getMaximalValueError() / absTolerance;
      assertTrue(ratio < 2.4);
      assertTrue(ratio > 0.02);
      assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);

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