public void testMinStep() {
try {
TestProblem1 pb = new TestProblem1();
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 HighamHall54Integrator(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");
} catch (IntegratorException ie) {
}
}
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 testEventsErrors() {
final TestProblem1 pb = new TestProblem1();
double minStep = 0;
double maxStep = pb.getFinalTime() - pb.getInitialTime();
double scalAbsoluteTolerance = 1.0e-8;
double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;
FirstOrderIntegrator integ =
new HighamHall54Integrator(
minStep, maxStep,
scalAbsoluteTolerance, scalRelativeTolerance);
TestProblemHandler handler = new TestProblemHandler(pb, integ);
integ.addStepHandler(handler);
integ.addEventHandler(
new EventHandler() {
public int eventOccurred(double t, double[] y, boolean increasing) {
return EventHandler.CONTINUE;
}
public double g(double t, double[] y) throws EventException {
double middle = (pb.getInitialTime() + pb.getFinalTime()) / 2;
double offset = t - middle;
if (offset > 0) {
throw new EventException("Evaluation failed for argument = {0}", t);
}
return offset;
}
public void resetState(double t, double[] y) {}
private static final long serialVersionUID = 935652725339916361L;
},
Double.POSITIVE_INFINITY,
1.0e-8 * maxStep,
1000);
try {
integ.integrate(
pb,
pb.getInitialTime(),
pb.getInitialState(),
pb.getFinalTime(),
new double[pb.getDimension()]);
fail("an exception should have been thrown");
} catch (IntegratorException ie) {
// expected behavior
} catch (Exception e) {
fail("wrong exception type caught");
}
}
public void testEventsNoConvergence() {
final TestProblem1 pb = new TestProblem1();
double minStep = 0;
double maxStep = pb.getFinalTime() - pb.getInitialTime();
double scalAbsoluteTolerance = 1.0e-8;
double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;
FirstOrderIntegrator integ =
new HighamHall54Integrator(
minStep, maxStep,
scalAbsoluteTolerance, scalRelativeTolerance);
TestProblemHandler handler = new TestProblemHandler(pb, integ);
integ.addStepHandler(handler);
integ.addEventHandler(
new EventHandler() {
public int eventOccurred(double t, double[] y, boolean increasing) {
return EventHandler.CONTINUE;
}
public double g(double t, double[] y) {
double middle = (pb.getInitialTime() + pb.getFinalTime()) / 2;
double offset = t - middle;
return (offset > 0) ? (offset + 0.5) : (offset - 0.5);
}
public void resetState(double t, double[] y) {}
private static final long serialVersionUID = 935652725339916361L;
},
Double.POSITIVE_INFINITY,
1.0e-8 * maxStep,
3);
try {
integ.integrate(
pb,
pb.getInitialTime(),
pb.getInitialState(),
pb.getFinalTime(),
new double[pb.getDimension()]);
fail("an exception should have been thrown");
} catch (IntegratorException ie) {
assertTrue(ie.getCause() != null);
assertTrue(ie.getCause() instanceof ConvergenceException);
} catch (Exception e) {
fail("wrong exception type caught");
}
}
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;
}
}