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Landau distribution
- To: GSL mailing list <gsl-discuss at sourceware dot cygnus dot com>
- Subject: Landau distribution
- From: Dave Morrison <dave at bnl dot gov>
- Date: Thu, 15 Mar 2001 10:39:21 -0500
Hi folks,
At first, I thought I only had a specific question about getting a
Landau distribution into both the special functions and random number
distribution parts of GSL, but then I realized this raised a more
general issue for me. The specific bit first:
I'd like to see a Landau distribution in GSL. For those that don't use
this distribution everyday, it's used to describe the energy loss of a
particle passing through a thin(ish) piece of material. It's a
specialization of the more general Vavilov distribution, but Landau's
the one people tend to use. The technique that everyone seems to use to
calculate the value of the distribution, or more to the point, the
inverse of the cumulative Landau distribution, is taken from a 1974
paper by Schorr. Truncate the tails, Fourier series in the middle, that
sort of thing. There may be more clever ways to do it, but this is the
technique you see in practice. I'm willing to do the work to get it in
GSL.
OK, now the more general issue. Schorr's technique is fairly fast, but
not astoundingly precise. In his paper he claims it's good to a few
significant digits in the middle of the approximation interval, but only
good to about 5% or so at the end of that range. That's not exactly the
sort of stuff numerical analysts write home about. However, it's fine
for describing many physical situations, and that's how it's typically
used. The question then is GSL interested in having some distributions
that are "good enough" for some, but not all, purposes. This case would
satisfy many physicists but few mathematicians (I think).
Dave
--
David Morrison Brookhaven National Laboratory phone: 631-344-5840
Physics Department, Bldg 510 C fax: 631-344-3253
Upton, NY 11973-5000 email: dave@bnl.gov