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https://issues.apache.org/jira/browse/MATH-605?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13055577#comment-13055577
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Luc Maisonobe commented on MATH-605:
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Your approach is _really_ interesting.
You are right, the current handling of events still has many hacks. Ignoring
events at start time was a way to solve issue MATH-421. There was also another
problem resulting from a wrong choice in bracketed root depicted in issue
MATH-322. As we can now ask the solver to select exactly the solution we want,
we can probably have more robust and simpler handling.
There are some caveats, though, so we need to check a few corner cases.
First, we cannot ensure yet user will select a solmver that handles bracketing
as we want. It would be nice to have a BracketingSolver and force events
handler to use that. However, there is no such interface. There is a solvers
hierarchy, and there is a BracketedSolution interface (by the way, I think this
name is not appropriate, a solver is not a solution). I would suggest we adjust
our hierarchy slightly and force user to use a solver from the bracketing part
of the hierarchy only.
Second, we should let the integrator (or better the internal event state
handler) select the side by itself. It should select the right side for forward
integration, but it should select the left side for backward integration.
Looking at your example, I'm a little puzzled by the switching function.
Switching functions are not required to be globally smooth, but they should not
have discontinuities around the switch event. Here, the event is _defined_ by
discontinuities between +1 and -1. In addition, between discontinuities, the
function is constant, so the solver has no clue to find a solution quickly, it
simply recursively reduces the interval, leading to a lot of calls to g. For
such cases, it is better to design a slightly different g function, ensuring it
has the zero at the proper places, is continuous around the roots, and does not
change sign between the roots (i.e. it will alternate signs between successive
roots).
Here is one way to do this in your case, which should work either when
eventOccurred returns STOP and is reused later, or returns CONTINUE and is
reused in the same integration:
{code}
private int sign = 1;
public double g(double t, double[] y) throws EventException {
return (y[idx] < 0.5) ? (sign * y[idx]) : (sign * (1.0 - y[idx]));
}
public int eventOccurred(double t, double[] y, boolean increasing) throws
EventException {
sign = -sign;
return STOP;
}
{code}
However, with this implementation of the g function, the hack in the test case
does not work anymore.
I have tried to simply suppress the small ignore zone at the start of the
integration, but it wasn't sufficient. I think we'll have to dig deeper in the
code.
So as a partial conclusion, I think we should do as you propose and use smart
selection of side in bracketing solver, force use of such solvers, and remove
the ignore zone at the start of the integration.
We should make sure that it works for all existing unit tests (some of them are
regression tests for previous bugs), that it works for your discontinuous
function (despite such functions are not recommended), and that it works for
the patched function above.
Thanks a lot for this report and the solution, it is really the way to go!
> Missing state events due to events between t0 and t0+e being ignored
> --------------------------------------------------------------------
>
> Key: MATH-605
> URL: https://issues.apache.org/jira/browse/MATH-605
> Project: Commons Math
> Issue Type: Improvement
> Affects Versions: 3.0
> Reporter: Dennis Hendriks
> Attachments: OverlappingEventsTest.java
>
>
> The Commons Math page on ODEs
> (http://commons.apache.org/math/userguide/ode.html) states in section 13.3
> (Discrete Events Handling), that: "Note that g function signs changes at the
> very beginning of the integration (from t0 to t0 + ε where ε is the events
> detection convergence threshold) are explicitely ignored. This prevents
> having the integration stuck at its initial point when a new integration is
> restarted just at the same point a previous one had been stopped by an event."
> However, due the following issues:
> - MATH-586: Allow using a custom root-finding algorithm to detect state
> events
> - MATH-599: Re-implementation of Secant-based root finding algorithms
> we can now use for instance the PegasusSolver to detect state events. Using
> the AllowedSolutions.RIGHT_SIDE we can guarantee that we have passed the
> event. As such, skipping (future) events between t0 and t0+e is not desired.
> I attached a Java class to show this issue. It has 2 continuous variables,
> each starts at 0.0. The first has derivative 1.0, the second 2.0. Whenever
> they become larger than 1.0, they are reset. We thus expect resets for event
> 1 at 1.0, 2.0, 3.0, etc. We expect resets for event 2 at 0.5, 1.0, 1.5, etc.
> The events overlap (at 1.0, 2.0, etc). Due to numerical differences, the
> events however are not detected at the exact same times. After we processed
> the first, the 'skip everything between t0 and t0+e' may result in skipping
> events, as can be observed from the failing unit test. The second test has a
> hack to get around this problem: it is manually checked whether the guard
> changes, by evaluating t0 and t0+e. If an event is detected, a step of e is
> done, and integration is restarted from t0+e. This solves the issue, and the
> unit tests succeeds (we get the events at the expected times, and we don't
> miss any events).
> From what I understand, event detection is complicated, as discussed in
> MATH-484. I propose to make the skipping of events betweeen t0 and t0+e
> optional, as that is no longer needed in the cases I described above, and in
> fact causes severe problems that can only be solved by hacks. For other
> (non-bracketed solution) algorithms, it may still be necessary to skip such
> roots. Maybe an option could be introduced to control this behavior?
> So, if an event is detected at time t, integration may continue from t0=t,
> and if there is a sign change for t0 and t0+e, then the step handler should
> be called for t0+e, and the step handler should be called for t0+e as well,
> with isLast=true. I'm not sure what the value of e should be. It could be the
> absolute accuracy of the root-finding algorithm. if there are multiple ones,
> maybe the maximum of all of them. Maybe even the minimal integration step
> should be taken into account, taking the maximum of that an dall the absolute
> accuracies of the root-finding algorithms?
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