Special Functions [was: improving special functions in GSoC 2017]

[Robert T. Short]

On 06/28/2016 02:29 AM, Marco Caliari wrote:
> On Sun, 26 Jun 2016, Robert T. Short wrote:
>
> > On 06/25/2016 11:52 PM, John W. Eaton wrote:
> > > On 06/26/2016 02:08 AM, Colin Macdonald wrote:
> > > > On 25/06/16 02:54, Marco Caliari wrote:
> > > > > "Special functions are expected by users to just work".
> > > >
> > > > So I just found that our "besselj" gives NaNs for values like "1e10".
> > > >
> > > >  >> besselj(1, 1e9)
> > > > ans = -5.21042264155388e-06
> > > >  >> besselj(1, 1e10)
> > > > ans = NaN + NaNi
> > > >
> > > >
> > > > https://savannah.gnu.org/bugs/index.php?48316
> > > >
> > > >
> > > > That's not some wild exotic function: its a common Bessel function!
> > > >
> > > >
> > > > Why are we not just calling some free-licensed library that nails 
> > > > these
> > > > things?
> > >
> > > Amos was the best thing I knew of at the time.  If there is 
> > > something better now, or a standard library solution, then perhaps 
> > > we should be using it.  Propose a patch and a test suite.
> > >
> > > jwe
> > There was some discussion of this a few years ago (something like 
> > 2011 or 2012).  At the time Amos was still the best option that we 
> > could find.  I don't remember all the details, but other libraries 
> > (including boost) didn't handle things like complex arguments or 
> > other some other crucial element.
>
> Yes, for instance boost, GSL, and Cephes require both the arguments of 
> gammainc to be nonnegative. Matlab allows x negative, and in this case 
> the result is complex.
>
> > Hopefully things have changed since then, but that was the conclusion 
> > at that time.  I was not able to find that thread so my memory is not 
> > refreshed.  I put in a bunch of tests at the time we had the 
> > discussion.  It seems, though, that I didn't do any for complex 
> > arguments.  I have no clue how I missed that.
>
> Should we start with *the* list of special functions with the domain 
> of application?
>
> specfun1: A1 x B1 x ... x Z1 -> complex_field
>
> where the domain is taken from the equivalent Matlab function.
>
> Marco
Marco, jwe

Attached is a list of MATLAB special functions.  I started with

http://www.mathworks.com/help/matlab/special-functions-1.html

I think it is correct, but I could easily have some mistakes.

Bob

ListOfSpecialFunctions.pdf
Description: Adobe PDF document