Path: csiph.com!newsfeed.hal-mli.net!feeder3.hal-mli.net!newsfeed.hal-mli.net!feeder1.hal-mli.net!npeer01.iad.highwinds-media.com!news.highwinds-media.com!feed-me.highwinds-media.com!postnews.google.com!glegroupsg2000goo.googlegroups.com!not-for-mail
From: boruun@gmail.com
Newsgroups: comp.graphics.apps.gnuplot
Subject: Special functions in gnuplot
Date: Fri, 10 Aug 2012 20:34:54 -0700 (PDT)
Organization: http://groups.google.com
Lines: 82
Message-ID: <1694fa1b-c5e4-4561-8594-40d67337d065@googlegroups.com>
NNTP-Posting-Host: 128.101.221.168
Mime-Version: 1.0
Content-Type: text/plain; charset=ISO-8859-1
Content-Transfer-Encoding: quoted-printable
X-Trace: posting.google.com 1344656094 27385 127.0.0.1 (11 Aug 2012 03:34:54 GMT)
X-Complaints-To: groups-abuse@google.com
NNTP-Posting-Date: Sat, 11 Aug 2012 03:34:54 +0000 (UTC)
Complaints-To: groups-abuse@google.com
Injection-Info: glegroupsg2000goo.googlegroups.com; posting-host=128.101.221.168; posting-account=GvZkAQkAAAAolYpA2729ei7GxSNWZjCy
User-Agent: G2/1.0
X-Received-Bytes: 4186
Xref: csiph.com comp.graphics.apps.gnuplot:1314

Can someone give me some pointers on how can I figure out:

a) what ALGORITHMS (files/codes either gnuplot specific or system specific)=
 gnuplot is ACCESSING to calculate special functions like gamma, or lgamma,=
 igamma, ibeta etc..... and WHERE are these algorithms/files located

and,

b) (if possible) tell me (or guide me on how to find) how accurate are thes=
e estimates and over what range of values for their arguments.

I am using these functions in the "fit" command and not merely for plotting=
. Hence it is extremely important for me to know the error bounds of these =
estimates and the range of values over which they are valid.=20


Any help will be much appreciated. [Please read the background below before=
 responding].

I am using: Scientific Linux 6.2 (Kernel Linux 2.6.32-220.23.1.el6.x86_64)


BACKGROUND:
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
I hunted for this information a bit and have come across a file called spec=
fun.c in the gnuplot /src directory. The file contains lines of code with:

ifdef ..., ifndef... and ifdef HAVE_function

I think that something like HAVE_LGAMMA indicates that if a function called=
 LGAMMA exists then that one is preferred.=20

BUT, WHERE is GNUPLOT looking for such pre-existing LGAMMA (and other funct=
ion definitions)?=20

[I dont understand what "HAVE_function" type references really mean. I sear=
ched a lot but could not really understand what it is doing and WHERE exact=
ly is it looking so that I can go to that file and take a look at the algor=
ithm used to define that function].

Also is LGAMMA the same as "log gamma" or is it "gamma in long format/type =
(i.e. double precision)". If it is "log gamma" then why is a call to gamma(=
x) referred to lgamma(x) without any 'exponentiation'?=20

This link indicates that lgamma is log(gamma) and not just gamma in double-=
precision.

http://www.kernel.org/doc/man-pages/online/pages/man3/lgamma.3.html

But I am not sure if gnuplot is accessing this one or not. I also do not kn=
ow WHERE to find this lgamma in my system files.

I also checked the GNU scientific library, but here gamma is referred to di=
fferently and not as lgamma:
http://www.gnu.org/software/gsl/manual/html_node/Gamma-Functions.html

Further, the GNU scientific library also has igamma defined:
http://www.gnu.org/software/gsl/manual/html_node/Incomplete-Gamma-Functions=
.html

BUT, the GNUPLOT specfun.c file does not seem to use this function even if =
it exists in the GNU scientific library. Anyone knows why? Is the gnuplot v=
ersion of igamma more accurate than that in the GNU scientific library?

Please give me as specific info as possible (given my operating system..see=
 above). Like if you say system file, then let me know whether you are refe=
rring to:

usr/lib/x86_64-redhat.....=20

OR

usr/include/ etc..

And once again, I dont just want to know what it is doing, I want to know (=
and see for myself) what ALGORITHM it is accessing and if possible get some=
 idea of what are the errors in estimation of these special functions and o=
ver what range of values for its arguments.

Thank you very much for your help in advance!
Kind regards,
Barun.