I'm not especially defending the Romberg code, and deprecating the
double-float version is fine, if it is really totally superceded by better
stuff. I am sure I can come up with problems that quadpack fails on, too.
It is not clear what you are advocating here, But deprecating the
(bigfloat) version of it seems to me would be a BIG mistake. What
distinguishes Maxima from Fortran, C, Matlab ... is that numerical programs
can, at least in principle, be run to arbitrary precision. What
distinguishes Maxima from MPFR is that the specification of calculations can
be done interactively. Deprecating the Maxima facility to do bigfloat
integration is exactly the wrong direction.
There are other things to do: how about replacing bigfloats (which I wrote)
by MPFR (which I did not write, but is actively under development and
appears to be fast). I don't see offhand an MPFR numerical integrator (but
one could be built with Romberg).. Another possibility is to use
quad-double integration which has been studied by Sherry Li:
http://crd.lbl.gov/~xiaoye/fp.html
and could be put into my generic arithmetic package easily, and into Maxima
too, though not without some effort. This brings up the foreign function
interface issue in whatever CL you are using, as well as the cross-platform
compilation issues for libraries --- which lack of standardization seems to
be a disqualification for Maxima. (I would prefer this to not be a
disqualification, but I am unwilling personally to fix all lisps! And
recompile everything in C or C++ for Mac, Linux, Windows, Solaris...)
RJF
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu [mailto:maxima-
> bounces at math.utexas.edu] On Behalf Of Daniel Lakeland
> Sent: Thursday, January 04, 2007 8:02 AM
> To: maxima at math.utexas.edu
> Subject: Re: [Maxima] romberg
>
> > I think that throwing away the bigfloat version of Romberg without
> replacing
> > it with a bigfloat version of some better numerical integration program
> > would be a bad choice. Both Maple and Mathematica have bigfloat
> numerical
> > integration.
>
> I tend to think that the romberg code should stay as an alternative to
> the quadpack, but that the third option (can't remember the name) is
> superfluous since it performed worst among the three that Robert
> tested. The Romberg code should be documented as having been
> superseded for most purposes by quadpack.
>
> > Removing a feature from Maxima on the grounds that [someone thinks that]
> > most people are generally happy without it, would remove quite a few
> > features! :)
>
> True enough. I think one of Robert's concerns is that it's not
> completely robust, having failed some of his tests. If a bigfloat
> version of quadpack were available it would probably be wise to
> deprecate romberg as suggested. For now, perhaps it's best to
> deprecate Romberg in the documentation but leave it available in the
> code.
>
>
> --
> Daniel Lakeland
> dlakelan at street-artists.org
> http://www.street-artists.org/~dlakelan
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