🚀 go-pugleaf

bevan@cs.man.ac.uk (Stephen J Bevan) writes:
: In article <17n6fjINNhvt@network.ucsd.edu> mbk@lyapunov.ucsd.edu (Matt Kennel) writes:
:    I have no idea what Mr Rubin really wants but here are a couple of 
:    easy ones of the top of my head:
: 
:     P, D, Q <- singular_value_decomposition(A);
: 
: How about :-
: 
: (p,d,q) = singular_value_decomposition A

This is perfectly sensible.

:    Array index notation:
: 
:    for all i <= j: a(i,j) <- sum over (k) ( b(i,k)*c(j,N,k) )
: 
: I'm not _exactly_ sure what the above does (e.g. is N constant?), so
: the following may be wrong (but it is better than my previous attempt
: which I hopefully cancelled correctly :-)

What I mean is that the upper triangular part of "a" is equal to B *
transpose("C"), but where the matrix "C" is "spread" out through different
parts of a 3tensor arrays.

: 
: foo b c = array bds vs
:   where
:     vs = [ (i,j) := f i j | (i,j) <- range bds, i <= j ]
:     f i j = sum [ b!(i,k)*c!(j,n,k) | k <- range (klb,kub) ]
:     bds = ((ilb,jlb),(iub,jub))
:     ((ilb,klb),(iub,kub)) = bounds b
:     ((jlb,_,_),(jub,n,_)) = bounds c

This is perfectly ridiculous!  I have no clue what that means.
I don't think one should have to write a subroutine to implement each simple
array statement.

: An alternative (and possibly more efficient) version of _vs_ is :-
: 
:   vs = [ (i,j) := f i j | i <- range (ilb,iub), j <- range (i,jub) ]
: 
: Note this is untested as I currently don't have a compiler installed.
: As to the notation, I'll do you a deal: you explain the one you're
: using and I'll explain the one I'm using :-)

What's called "implied summation convention" means "sum over repeated
indices"on the right hand side of the assignment
and iterate over covarying indices on both sides.  (No I didn't invent
this...heard it's also called "Einstein summation convention" as it's
very useful in relativity calculations).

So if C(i,j,k) is a 3-tensor, then 

T(i) = C(i,j,j)

means for each matrix C(i,*,*) compute its trace and assign to T(i).
(Yes the indices should automatically figure out their bounds).

I think it wouldn't be so bad to allow you to explicitly say these things:

for all i T(i) = sum_over(j) C(i,j,j)

sum_over or sum or whatever is the of course just the traditional capital
sigma symbol used in math, and of course all it means is add everything
up.

:    I won't bore you with the obvious complex numbers, exponentiation, etc.
: 
: Why not, you may be pleasantly suprised.
: 
: bevan

--
-Matt Kennel  		mbk@inls1.ucsd.edu
-Institute for Nonlinear Science, University of California, San Diego
-*** AD: Archive for nonlinear dynamics papers & programs: FTP to
-***     lyapunov.ucsd.edu, username "anonymous".