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From Dennis Hendriks <D.Hendr...@tue.nl>
Subject Re: [Math] How to force integration past the state event?
Date Fri, 10 Jun 2011 08:20:40 GMT
Hi Luc,

Thanks for your quick reply. It would be a possible solution.

I decided to familiarize myself with the internals of the code that is 
used, in order to better understand what code is responsible for the root 
finding. I found the org.apache.commons.math.analysis.solvers package, at 
http://commons.apache.org/math/api-2.2/org/apache/commons/math/analysis/solvers/package-summary.html.

In particular, the UnivariateRealSolver interface seems to be the interface 
for all root-finding algorithms.

I also found the EventState class 
(http://svn.apache.org/viewvc/commons/proper/math/tags/MATH_2_2/src/main/java/org/apache/commons/math/ode/events/EventState.java?view=markup)

which at line 242 creates an instance of the BrentSolver to use as 
root-finding algorithm. It seems that the BrentSolver root-finding 
algorithm is hard-coded, and no other root-finding algorithm can be used to 
find state events...

I was wondering if there is any possibility to use another root-finding 
algorithm for state event detection during ODE solver integration. That 
would allow me to create my own UnivariateRealSolver implementation that 
does guarantee that the point returned never undershoots the state event. I 
believe that would be the preferred solution to my initial problem.

Best regards,
Dennis




luc.maisonobe@free.fr wrote:
> ----- "Dennis Hendriks" <D.Hendriks@tue.nl> a écrit :
> 
>> Hi all,
> 
> Hi Dennis,
> 
>> I have the following (simplified) ODE problem:
>>
>>    V(0) = 10.000000645817822
>>    V' = -sqrt(V)
>>
>> and the following state event:
>>
>>    V <= 2.0
>>
>> Using:
>>
>>    t = 6.6845103160078425
>>    GraggBulirschStoerIntegrator(1e-10, 100.0, 1e-10, 1e-10)
>>    integrator.addEventHandler(event, 100.0, 1e-10, 999)
>>
>> I obtain the last time point as:
>>
>>    t = 10.180638128882343
>>    V = 2.000000830098894
>>    V' = -1.414213855857346
>>
>> For this last time point, V <= 2.0 does not hold. In my previous 
> 
> What you experience here is that convergence is reached on the side of the root you don't
want.
> From a pure event root finder point of view, there is no guarantee about the
> side at which the solver will stop. You can reduce the convergence threshold, of course,
> but it will only make the undershoot smaller, it will not always prevent it.
> 
>> experiences with DDASRT (DAE solver written in Fortran, see 
>> http://www.netlib.org/ode/ddasrt.f), it was actually guaranteed that 
>> integration would go PAST the state event.
>>
>> So, my question is: Is there any way to force integration PAST the
>> state 
>> event, to make sure that afterwards the V <= 2.0 condition actually
>> holds? 
>> In other words, is it possible to make sure it stops PAST the state
>> event, 
>> instead of sometimes PAST it and sometimes BEFORE it?
> 
> I would suggest to use a StepHandler in addition to the EventHandler, and to
> retrieve the final result from the step handler instead of the ODE itself.
> This means, instead of:
> 
>   integrator.addEventHandler(...);
>   double tEnd = integrator.integrate(...);
> 
> you would use:
> 
>   integrator.addEventHandler(...);
>   integrator.addStepHandler(mySpecialStepHandler);
>   integrator.integrate(...);
>   double tEnd = mySpecialStepHandler.getTend();
>   double[] yEnd = mySpecialStepHandler.getY();
> 
> with myStepHandler being a local class of your own with an implementation like:
> 
>   public class MyStepHandler implements StepHandler {
> 
>     double tEnd;
>     double[] y;
> 
>     public boolean requiresDenseOutput() {
>       return true;
>     }
> 
>     public void reset() {
>     }
> 
>     public void handleStep(StepInterpolator interpolator, boolean isLast) {
>       if (isLast) {
>          tEnd = interpolator.getCurrentTime();
>          while (true) {
>            interpolator.setInterpolatedTime(tEnd);
>            yEnd = interpolator.getInterpolatedState();
>            if (yEnd[0] <= 2) {
>              return;
>            }
> 
>            // we are on the wrong side, slightly shift end time
>            double[] yEndDot = interpolator.getInterpolatedDerivatives();
>            tEnd += (yEnd[0] - 2) / yEndDot[0];
> 
>          }
>       }
>     }
> 
>     public double getTend() {
>       return tEnd;
>     }
> 
>     public double[] getYend() {
>       return yEnd;
>     }
> 
>   }
> 
> The trick here is that the interpolator can be used slightly out of the current step,
> so slightly shifting the end date after it has been computed of the order of magnitude
> of the convergence threshold in the event handler is safe.
> 
> It is guaranteed that the event handler is called after the step handler, in fact it
is
> exactly because we need to make sure the isLast boolean is properly set to true when
an
> events ask the integrator to stop.
> 
>> Any help would be greatly appreciated.
> 
> Hope this helps,
> 
> Luc
> 
>> Thanks,
>> Dennis
>>
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