Re: strict static pivoting vs pliable static pivoting

i like "restricted  pivoting" in order to describe procedures that do not
change supernodes.

one problem with "static pivoting" is the granularity of the term. does
one imply a particular pivot or the whole factorization? if just one pivot
then "static pivoting" is really obvious. but for the whole factorization
it could be ambiguous. if someone tells me that the whole factorization
uses static pivoting then i would immediately assume that every single
pivot was handled statically. one probably has to be very specific in such
a case. otherwise, "restricted pivoting" does the job.

as for the word dynamic, i know it is redundant but i always prefer
redundancy over ambiguity. no harm in saying dynamic pivoting when there
is some static pivoting around as well. i could say that during a
particular factorization i used static pivoting in column x and dynamic
pivoting in column y. instead of saying that i used static pivoting in
column x and pivoting in column y. the former sounds much better, in my
opinion. of course, if there is no static pivoting involved then i would
never use the term "dynamic pivoting".

the term "delayed pivots" seems to be the right one for describing columns
that are moved from on supernode to its parent, changing thus supernodal
data structures (something not allowed in restricted pivoting). would
"delayed pivoting" be the opposite of "restricted pivoting"? or shall
we use "unrestricted pivoting"?

as for preprocessing, as i said, i would never consider that part of
static pivoting since it could be used without any static pivoting at
all, just to reduce the number of swaps and delayed pivots. i like to
say that there is preprocessing for structural reasons (like fill reducing
orderings) and preprocessing for numerical reasons (like the matching
based codes such as mc64).

the word preassigned does not seem to be a good choice. it is ok if every
single pivot is handled statically. but one can have a scenario where
preassigned does not really describe what i going on. for example column j
might be in position x, within a particular supernode, preassigned by
the preprocessing procedure. let's say that the factorization uses
restricted pivoting. now, when we get to position x we may actually decide
to use dynamic pivoting and bring some other column k, from the same
supernode, into position x. then column j would end up in some other
position y, still within the same supernode, but no longer preassigned.
later, when we get to position y, we may no longer have a choice and
use static pivoting. i don't know if any code does that but it is a
possibility.

florin

On Wed, 13 Sep 2006, Tim Davis wrote:

> I'm pliable enough to accept the rejection of "pliable static pivoting"
> in favor of "restricted pivoting"  :-)
>
> So we could have "static pivoting" to apply to the case
> where no pivoting occurs at all once the pivots are selected during the analysis
> phase.  But aren't there current uses of that phrase to include some minor
> variations on the pivot order determined during the analysis?
>
> Then "restricted pivoting" would be (1) pivot in the analysis phase for reducing
> fill-in and for finding large pivots a priori, followed by (2) minor modifications
> to that pivot order during numerical factorization.
>
> Now, what do you call it when a pivot fails in one frontal matrix, but is
> recovered in, say, its grandparent.  We already call this "delayed pivoting", correct?
> This sounds very much like "restricted pivoting" however.
>
> Thanks,
> Tim
>
> p.s.  Speaking of the naming of pivoting schemes, what do you call a fill-reducing
> ordering followed by a call to a template sparse solver (http://www.netlib.org/templates/),
> when done after 6pm, and when used in the solution of a CFD problem involving argon or
> another one of the noble gases?
>
> answer: "a noble night of the minimum degree order of the templates"
>
> Cleve Ashcraft wrote:
>
>  On Tuesday 12 September 2006 13:33, Tim Davis wrote:
>
>
>  Actually, the fact that there may be row/col swaps hidden inside
> a static scheme fits the word nicely.
>
>
>  Pivoting within a supernode could be called "restricted pivoting".
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