Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!uunet!mstan!amull
From: amull@Morgan.COM (Andrew P. Mullhaupt)
Newsgroups: comp.lang.apl
Subject: Syntax for extended matrix operations
Keywords: APL primitives, beyond quad-divide
Message-ID: <539@s5.Morgan.COM>
Date: 27 Nov 89 05:27:10 GMT
Organization: Morgan Stanley & Co. NY, NY
Lines: 32

I would like to solicit suggestions for primitives to be added to
the APL lexicon which would update the representation of linear
algebraic concepts. In particular I have in mind a way to deal
with the concept of matrix factorizations; Cholesky, QR, and
SVD. The point is that if you use quad-divide, you have to factor
the matrix every time you come up with a right hand side (left
hand side in APL terms) that needs evaluating. Having access to
the factored form of the matrix, especially in a storage efficient
form is quite desirable. In particular, since I am using SVD to
implement quad-divide in a version of APL, I think it's a stupid
shame to have to junk the matrix factors. It is also desirable to
have the choice of more than one decomposition available to the
programmer, and in the case of the LU; why should double the
storage be required?

At present, the implementation is going to bail out of APL for
almost all of this stuff. This will have the same result that 
it had for us on APL2 on the mainframe: there, quad divide is 
not competitive with the ESSL SVD, so we never use it for much
anymore. (In fact I checked around our group of programmers, and
I think it is never used in new code.) 

Now HP calculators keep track of whether or not a given matrix
has been factored in place or not, but this doesn't give much 
insight into what to do with the SVD. 

Thanks in advance,
Andrew Mullhaupt

P.S. Sparse and band matrix tricks, and updates (Cholesky and
QR) would seem very desirable if they can be embedded comfortably
in the APL syntax.