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From "Thomas Neidhart (JIRA)" <>
Subject [jira] [Commented] (MATH-785) Numerical Underflow in ContinuedFraction
Date Sun, 20 May 2012 21:40:41 GMT


Thomas Neidhart commented on MATH-785:

I looked further into it and am not convinced anymore that this really to solve the numerical
stability problems. In fact the results are pretty much random depending on the choice of
the scaling factor.

In fact I implemented the modified Lentz-Thompson algorithm to do the continued fraction evaluation
and the results are much much better. All the unit tests run through and the probability evaluations
for the different distributions for large trials are stable and return correct values.
> Numerical Underflow in ContinuedFraction
> ----------------------------------------
>                 Key: MATH-785
>                 URL:
>             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(
> 	at org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver.solve(
> 	at org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver.solve(
> 	at org.apache.commons.math3.analysis.solvers.UnivariateSolverUtils.solve(
> 	at org.apache.commons.math3.distribution.AbstractRealDistribution.inverseCumulativeProbability(
> 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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