Commons Math
  1. Commons Math
  2. MATH-785

Numerical Underflow in ContinuedFraction

    Details

    • Type: Bug Bug
    • Status: Closed
    • Priority: Major Major
    • Resolution: Fixed
    • Affects Version/s: 3.0
    • Fix Version/s: 3.1
    • Labels:
      None
    • Environment:

      Description

      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.

      1. patch.txt
        2 kB
        Colin J. Fuller

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          Hide
          Thomas Neidhart added a comment -

          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.

          Show
          Thomas Neidhart added a comment - 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.
          Hide
          Thomas Neidhart added a comment -

          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.

          Show
          Thomas Neidhart added a comment - 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.
          Hide
          Thomas Neidhart added a comment -

          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.

          Show
          Thomas Neidhart added a comment - 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.
          Hide
          Colin J. Fuller added a comment -

          Patch to fix the numerical underflow problem in ContinuedFraction.

          Show
          Colin J. Fuller added a comment - Patch to fix the numerical underflow problem in ContinuedFraction.

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            • Assignee:
              Unassigned
              Reporter:
              Colin J. Fuller
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              Dates

              • Created:
                Updated:
                Resolved:

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