|
A.1.8 Parallelization with ssi links
In this example, we demonstrate how ssi links can be used to
parallelize computations.
To compute a standard basis for a zero-dimensional ideal in the
lexicographical ordering, one of the two powerful routines
stdhilb
(see stdhilb)
and stdfglm
(see stdfglm)
should be used. However, in general one cannot predict
which one of the two commands is faster. This very much depends on the
(input) example. Therefore, we use ssi links to let both commands
work on the problem independently and in parallel, so that the one which
finishes first delivers the result.
The example we use is the so-called "omndi example". See Tim
Wichmann; Der FGLM-Algorithmus: verallgemeinert und implementiert in
Singular; Diplomarbeit Fachbereich Mathematik, Universitaet
Kaiserslautern; 1997 for more details.
| ring r=0,(a,b,c,u,v,w,x,y,z),lp;
ideal i=a+c+v+2x-1, ab+cu+2vw+2xy+2xz-2/3, ab2+cu2+2vw2+2xy2+2xz2-2/5,
ab3+cu3+2vw3+2xy3+2xz3-2/7, ab4+cu4+2vw4+2xy4+2xz4-2/9, vw2+2xyz-1/9,
vw4+2xy2z2-1/25, vw3+xyz2+xy2z-1/15, vw4+xyz3+xy3z-1/21;
link l_hilb,l_fglm = "ssi:fork","ssi:fork"; // 1.
open(l_fglm); open(l_hilb);
write(l_hilb, quote(stdhilb(i))); // 2.
write(l_fglm, quote(stdfglm(eval(i))));
list L=list(l_hilb,l_fglm); // 3.
int l_index=waitfirst(L);
if (l_index==1)
{
"stdhilb won !!!!"; size(read(L[1]));
close(L[1]); close(L[2]);
}
else // 4.
{
"stdfglm won !!!!"; size(read(L[2]));
close(L[1]); close(L[2]);
}
==> stdfglm won !!!!
==> 9
| Some explainatory remarks are in order:
-
Instead of using links of the type
ssi:fork , we alternatively
could use ssi:tcp links such that the two "competing"
SINGULAR processes run on different machines. This has the
advantage of "true" parallel computing since no resource sharing is
involved (as it usually is with forked processes).
-
Notice how quoting is used in order to prevent local evaluation
(i.e., local computation of results). Since we "forked" the two
competing processes, the identifier
i is defined and has
identical values in both child processes. Therefore, the innermost
eval can be omitted (as is done for the l_hilb link),
and only the identifier i needs to be communicated to the
children. However, when ssi:tcp links are used, the inner
evaluation must be applied so that actual values, and not the
identifiers are communicated (as is done for the l_fglm link
in our example).
-
We wait until one of the two children
finished the computation. The main process sleeps
(i.e., suspends its execution) in the intermediate time.
-
The child which has won delivers the result and is terminated with the usual
close command. The other child which is still computing needs to
be terminated by an explicit (i.e., system) kill command if running on a different computer. For ssi:fork a close is sufficient.
|