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From Thomas Neidhart <thomas.neidh...@gmail.com>
Subject Re: [math] Exposing the Lanczos approximation in o.a.c.m3.special.Gamma?
Date Tue, 08 May 2012 19:55:27 GMT
On 05/08/2012 05:26 PM, S├ębastien Brisard wrote:
> Hi,
> 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.
> 
> 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.
> 
> What do you think?

Hi S├ębastien,

this sounds pretty good.

After looking at the current Gamma function implementation, it looks
like it consists mainly of public static methods. Could you attach your
changes to the issue so I can have a look at them?

Thanks,

Thomas

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