[jira] [Commented] (MATH-785) Numerical Underflow in ContinuedFraction

["Thomas Neidhart (JIRA)" <ji...@apache.org>]

    [ https://issues.apache.org/jira/browse/MATH-785?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13272797#comment-13272797 ] 

Thomas Neidhart commented on MATH-785:
--------------------------------------

I have looked into this patch, and it looks very reasonable.

My original experiments with the epsilon were just scraping on the symptom but this seems to deal with the actual cause of the numerical instability problems.

Results of distributions using this fix also greatly improved to the situation before.
                
> Numerical Underflow in ContinuedFraction
> ----------------------------------------
>
>                 Key: MATH-785
>                 URL: https://issues.apache.org/jira/browse/MATH-785
>             Project: Commons Math
>          Issue Type: Bug
>    Affects Versions: 3.0
>         Environment: Issue seen in both 3.0 release binary version as well as a fresh checkout of the subversion trunk.
> java -version output:
> java version "1.6.0_26"
> Java(TM) SE Runtime Environment (build 1.6.0_26-b03)
> Java HotSpot(TM) 64-Bit Server VM (build 20.1-b02, mixed mode)
> (On Ubuntu 12.04)
>            Reporter: Colin J. Fuller
>         Attachments: patch.txt
>
>
> The ContinuedFraction calculation can underflow in the evaluate method, similar to the overflow case already dealt with.  I encountered this problem while trying to evaluate the inverse cumulative probability of an F distribution with a large number of degrees of freedom.
> I would guess this has the same cause as MATH-718 and MATH-738, though I am not experiencing inaccurate results but rather an exception.
> For instance, the following test case fails:
> double prob = 0.01;
> FDistribution f = new FDistribution(200000, 200000);
> double fails = f.inverseCumulativeProbability(prob);
> This produces a NoBracketingException with the following stack trace:
> org.apache.commons.math3.exception.NoBracketingException: function values at endpoints do not have different signs, endpoints: [0, 1], values: [-0.01, -∞]
> 	at org.apache.commons.math3.analysis.solvers.BrentSolver.doSolve(BrentSolver.java:118)
> 	at org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver.solve(BaseAbstractUnivariateSolver.java:190)
> 	at org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver.solve(BaseAbstractUnivariateSolver.java:195)
> 	at org.apache.commons.math3.analysis.solvers.UnivariateSolverUtils.solve(UnivariateSolverUtils.java:77)
> 	at org.apache.commons.math3.distribution.AbstractRealDistribution.inverseCumulativeProbability(AbstractRealDistribution.java:156)
> I could avoid the issue as in the comment to MATH-718 by relaxing the default value of epsilon in ContinuedFraction, although in my test case I can't see any reason the current default precision shouldn't be attainable.
> I fixed the issue by implementing underflow detection in ContinuedFraction and rescaling to larger values similarly to how the overflow detection that is already there works.  I will attach a patch shortly.
> One possible issue with this fix is that if there exists a case where there is a legitimate reason for p2 or q2 to be zero (I cannot think of one), it might break that case.

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