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From "Thomas Neidhart (JIRA)" <>
Subject [jira] [Resolved] (MATH-785) Numerical Underflow in ContinuedFraction
Date Mon, 21 May 2012 20:01:43 GMT


Thomas Neidhart resolved MATH-785.

       Resolution: Fixed
    Fix Version/s: 3.1

The problem has fixed together with MATH-718. Instead of applying the attached patch, the
evaluation of the continued fraction has been changed to the modified Lentz-Thompson algorithm
which does not suffer from underflow/overflow problems as the original implementation. A test
case for the described problem has been added too.

Thanks for the report.
> 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
>             Fix For: 3.1
>         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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