[boost] Ann: Statistics/Special Functions/Numeric Methods Toolkit

From: John Maddock (john_at_[hidden])
Date: 2006-03-31 13:40:00

Gentlemen,

This is to announce a new library added to the file vault, it is a work in 
progress and is intended to fulfil two needs:

1) To provide a small number of high quality special functions, initially 
these will be concentrated on functions used in statistical applications 
(with a strong nod towards Paul Bristow's existing work in this area).

The functions currently implemented are the gamma/beta/erf functions along 
with the incomplete gamma and beta functions (four variants of each).

All the implementations are fully generic and support the use of arbitrary 
"real-number" types, although they are optimised for use with types with 
known-about mantissa sizes: typically float, double or long double.

Use of these functions with interval arithmetic (Boost.Interval) isn't quite 
supported yet, but it's something I want to investigate soon.

2) To provide at least some of the tools required to implement mathematical 
special functions, hopefully the presence of these will encourage other 
authors to contribute more special function implementations in the future.

Currently implemented are helpers for the evaluation of infinite series, 
continued fractions and rational approximations.

There are also classes for the manipulation of polynomials, for testing a 
special function against tabulated test data, and for the rapid generation 
of test data and/or data for output to an external graphing application.

I've been keeping deliberately quiet about this for a while (with apologies 
to Paul Bristow), as I wanted to be certain that these special function 
implementations would offer something over and above what is available 
elsewhere.  I still have some way to go here: erf and lgamma in particular 
still need work, but the incomplete gamma and beta functions already 
typically have 10 times lower error bounds than Cephes and GSL, and in one 
spectacular case 10^11 times more accurate (which is to say there is a 
domain of the incomplete gamma where Cephes and GSL have hardly any 
significant digits correct).

Preliminary documentation is available here: 
http://www.johnmaddock.co.uk/toolkit and includes quite a lot of information 
already, including descriptions of implementation methodologies etc. 
There's also a roadmap of future work, open issues, and what needs to be 
done before a final release etc: 
http://www.johnmaddock.co.uk/toolkit/libs/math/doc/html/math_toolkit/status_and_roadmap.html

The actual source code, is available for download in the vault: 
http://boost-consulting.com/vault/index.php?action=downloadfile&filename=math-toolkit.zip&directory=&

Regards,

John Maddock.