🚀 go-pugleaf

From article <855@cresswell.quintus.UUCP>, by ok@quintus.UUCP (Richard A. O'Keefe):
> In article <1315@hubcap.UUCP>, steve@hubcap.UUCP ("Steve" Stevenson) writes:
> (1) Mathematics and numerical programming are not co-extensive.

Agreed - I forgot "numerical"

> (2) If by "arrays" one means the rectangular structures found in Fortran
>     ... large-scale numerical programming is a matter of fighting 
>     around the limitations of such arrays ...

Agreed - Fortran is not coextensive with numerical :-).  The obvious thing
is to realize that fact.  The idea is to straighten the problem out
not ignore it.


> (4) The same absence of constant-time update is to be found in functional
>     languages such as ML.  Does this mean that it is 'impossible to
>     consider "numerical functional programming"'?

Last time I checked, that was the case.  I have been away from functional
models for a while.

> (5) It turns out that assignment to individual array elements is one of
>     the principal reasons for there being so little potential parallelism
>     in Fortran programs.  There was a study which claimed to show that if

Sorry, but you  seem to have this fixation about Fortran and numerical
processes be the same.  It certainly is not.  I don't recall seeing
anything in Isaacson and Keller to that effect.  But certainly the
problems of updating and misshaping of arrays comes about from
such a limited model. BTW, APL is not much help and LINPACK is even worse.

My question remains.  Why not include "matrix" processing.  Let's
call them matrices to differentiate from the data structure.  There
very elegant proofs in real and complex analysis which use matrices
and certainly seem to work just fine.  Perhaps you mean the "unrestricted
use of assignment in array structures."

It's easy enough to think about a linear solver in prolog, but I
want you to do Gauss-Seidel with a normal PDE in mind.  Normal being
LARGE and SPARSE.

-- 
Steve (really "D. E.") Stevenson           steve@hubcap.clemson.edu
Department of Computer Science,            (803)656-5880.mabell
Clemson University, Clemson, SC 29634-1906