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From Gilles Sadowski <gil...@harfang.homelinux.org>
Subject Re: [math] Exposing the Lanczos approximation in o.a.c.m3.special.Gamma?
Date Tue, 08 May 2012 21:09:25 GMT
> > I've spent quite some time on MATH-753 [1], and I think I now have a
> > satisfactory solution.
> > The problem was to overcome the overflows which arise when computing
> > the density of the Gamma distribution for large values of the argument
> > and/or the scale parameter.
> > 
> > As I initially feared, what was proposed in the JIRA ticket leads to
> > high floating point errors. I adapted a method proposed in BOOST [2]
> > with acceptable errors. Meanwhile, I've also managed to improve the
> > accuracy of the computation of the density for the range of parameters
> > where the previous implementation was already working: in this range,
> > the accuracy *was* about 300 ulps, and is now 1-2 ulps! I think this
> > improvement is worth implementing.
> > 
> > The downside is that I need to expose the Lanczos implementation
> > internally used by o.a.c.m3.special.Gamma. This approximation is so
> > standard that I don't see it as a problem. I don't think that it
> > reveals too much of the Gamma internals, since the javadoc of
> > Gamma.logGamma states that it uses this approximation. So what I
> > propose is the addition of two methods in Gamma:
> > double getLanczosG(): returns the g constant
> > double getLanczos(double): returns the value of the Lanczos sum.

Is that something useful only inside the "Gamma" class?
If not, maybe that it can become a stand-alone class, or a method in one of
the "utility" classes (in package "util").

> > 
> > If you do not like this option, I can copy/paste the Lanczos
> > approximation in the GammaDistribution class. I'm adverse to the
> > latter option, as it leads to code duplication.

No "copy/paste" for me, thank you. :-)


Best,
Gilles

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