Re: Octave-2.1.50 & Octave-2.9.x

[David Bateman]

Muthiah Annamalai wrote:
> Hello there,
> 
> I have a bundle of code in Octave which use Bessel functions heavily.
> I wanted to run it on a Linux cluster to speed up the Bessel function
> computation.
> 
> But the problem becomes Octave-2.1.50 on the Linux Cluster running
> kernel 2.4.x gives slightly different / inaccurate results. I wonder where
> this difference comes from. Any suggestions here?
> 

I believe the change

2003-09-09  David Bateman  <address@hidden>

        * lo-specfun.cc (zbesj, zbesy, zbesi, zbesk, zbesh1, zbesh2, airy,
        biry): Always request scaled results from AMOS functions and
        perform reverse scaling on results if scaled result not requested
        by user.

is probably relevant. This change meant that the bessel functions could
be calculated to large values than in 2.1.50. As you say it should only
be slightly different. I don't think the results are inaccurate, upto
the point the result given is NaN :-)

> Also I want to know if there is any 'fast' way to compute the Bessel
> functions
> with arguments close to zero. It seems my program spends > 90% time
> doing the Bessel functions.

The book by Abramawitz and Stegun might be a good start. I don't have a
copy in front of me, but if I remember correctly they have asymptotic
expansions large N or X, rather than values close to zero. However, I
believe there was also a series expansion of the bessel functions that
might be useful close to zero. I remember using it more than 10 years ago.

Regards
David



> 
> I am looking to write a multi-threaded C program to compute the part
> involving
>  Bessel functions in parallel. Should I be using MPI? Help me.
> 
> Thanks,
> Muthu
>