"Parallelize" and Symbolic computation

[John Hattersley]

Hi All,

I apologies if this is an idiotic question. Essentially, I've a complex
Taylor series expansion that keeps running out of memory and as I've
upgraded to Mathematica 7 of late, and we've a few machines idling away, I
was wondering if the parallel stuff could help.

The documentation for Parallel Tools hints that it's only applicable for
numeric problems, but doesn't state that symbolic is out of the question.

At a recent Mathematica demo I went to recently it was suggested that the
parallel architecture didn't exclude all symbolic calculations. Has anyone
seen any documentation on this? Or have any experience of it?

Thanks,

JHatt

[Jens-Peer Kuska]

Hi,

a) you will probably need more memory with parallel execution
b) no it work for any algorithm, but you should have a problem with
few input data, few output data and a huge number of operations on it
c) with computers you have in many cases the choice speed xor memory.
Since parallel computing is for speed, you need probably more memory

Regards
Jens

[David Bailey]

The parallelize mechanism in 7, works by starting extra kernels, that
can each do any calculation they want, but I can't quite see how that
will help you with your calculation.

It might be an idea to post the problem, because if there is a way round
your difficulty, someone here will suggest it!

Memory problems can be greatly eased by moving to a 64-bit architecture.
Many modern computers are already 64-bit capable, and in that case,
all that is needed is to change to a 64-bit operating system and
re-install Mathematica. However, I'd start by posting your actual
problem if possible.

David Bailey
http://www.dbaileyconsultancy.co.uk

[John Hattersley]

Thanks for your replies gents.

Jens, I'm not sure I agree with your statements; whilst parallel computing
does introduce over head, in terms of process communication, depending on
how the problem is split, multiple machines should surely offer increased
resource for memory and CPU. Returning the result to a single process is an
interesting problem though, but without knowing how the Parallel arch works
in Mathematica I've really no idea. This is however a little to abstract
for me.

The documentation of parallelize says expressions like
"Parallelize[Integrate[1/(x - 1), x]]" cannot be 'parallelized', so I'm
guessing "D[]" is also out.

David, the 64-bit isn't an approach I can use at the moment due to
licensing, but I'll try and break down the problem, see if the group can
point out the error of my ways.

Essentially, I've a system of ODEs (12 states in all) I'm only observing
(measuring) a single state so have a single output (y(t)) that I'd like to
produce a Taylor series expansion of (for those that are interested I'm
trying to determine the identifiability of the system parameters)

My normal way of getting the Taylor series co-effs is brute force, e.g.
given a system

S1'[t_]:=-p2*S1[t]*S2[t]+p1*S1[t] ...
S2'[t_]:= p2*S1[t]*S2[t]-p2*S1[t] ...
...
Send'[t] := -k7*Send[t]*S1[t] ...

Define the output

y[t_] := {Send[t]}

Then trundle along getting the derivatives

y[0]
yDer=D[y[t],t]
yDer2=D[yDer,t]
...

For the problem I'm currently working with, the 12 state-system, this runs
out of memory by the 5th Taylor series coeff and I need a few more.

I hope this makes sense, any help or suggestions would be much appreciated.

Thanks again,
John

-----Original Message-----
From: David Bailey [mailto:da...@removedbailey.co.uk]
Sent: 10 June 2009 10:32
Subject: Re: "Parallelize" and Symbolic computation