Re: strict static pivoting vs pliable static pivoting

Actually, the fact that there may be row/col swaps hidden inside
a static scheme fits the word nicely.

Think of watching static on TV, or a white noise signal.  Its
constant and unchanging, in one sense.  Its character doesn't change.

But underneath, it can be simmering and shifting a bit.  Still white
noise, and still "constant", but in fact its possible for any one
item in the sequence to flip back and forth.

Perhaps the phrase "strict static pivoting" could be used if there
is *no* change to the original ordering.  Then "static pivoting"
could refer generically either to strict
static pivoting, or to the "noisy" kind of static pivoting, where
things can deviate a bit from the original ordering.

So ... "strict static pivoting" means no change at all to the ordering.
Just "static pivoting" could allow for changes, such as swaps within
a supernode or frontal matrix, even if usually no changes are made.

"dynamic pivoting" sounds a little funny ... that's just "pivoting"
in my mind.  No need for the word "dynamic."

Is there a need for a specific name for "white-noise static pivoting"?
"loose static pivoting"?  "updatable static pivoting?"
"bendable static pivoting?"  "stiff pivoting?"

"pliable static pivoting?"

The last one is kind of nice.  It's static, but it can bend a bit
if needed.  There ... "pliable static pivoting".  What do you think ...?

Or maybe we only need "strict static pivoting" and "static pivoting".

Thanks,
Tim

Florin Dobrian wrote:
> iain,
> 
> i kept asking myself the same questions but somehow i got used to the term
> static pivoting. the word static clearly describes the use of a pivot
> without any row/column swaps. the only problem is that sometimes there
> could be row/column swaps hidden behind this word. for example you don't
> want to change the data structure for a supernode but you may still allow
> some dynamic pivoting, combining it with static pivoting. that is, you may
> allow some swaps when you start processing the supernode but then switch
> to static pivoting when you no longer have a choice. or any other kind of
> combination. so in this case it would probably not be correct to call the
> entire procedure static pivoting but rather a combination of
> static/dynamic pivoting with no data structure changes. i think the word
> static should describe only what happens to a particular pivot and if you
> use it for the whole factorization it would necessarily mean that any
> pivot was statically processed (no swaps at all).
> 
> another small problem comes from the distinction between static and
> dynamic. usually you would say pivoting and if you use the term dynamic
> pivoting without any mention of static pivoting then the discussion
> becomes a bit confusing. so if i would have to explain this i would first
> describe pivoting in general, which could determine row/column swaps, then
> i would say that because of certain constraints it is useful to call such
> pivoting dynamic. only after that i would introduce the concept of static
> pivoting. so the confusion comes from the "equivalence" between the term
> pivoting and dynamic pivoting. the latter would be more appropriate if
> static pivoting is involved as well.
> 
> one other small confusion also comes from any preprocessing performed for
> pivoting reasons. such as the processing performed by mc64. sometimes one
> may think that that is part of static pivoting but it is not and it is not
> only static pivoting that benefits from it. dynamic pivoting can benefit
> as well (fewer swaps, fewer delays).
> 
> so overall i think the terms static and dynamic pivoting are ok because
> they really describe what is going on, but they should be used explicitly
> in order to avoid any confusion. in addition, one should be careful not to
> associate any form of preprocessing with static pivoting.
> 
> florin
> 
> On Mon, 11 Sep 2006 [email protected] wrote:
> 
>> Dear Colleagues,
>>
>> Here are some questions posed by Iain Duff ([email protected])  to stimulate
>> some discussion in the CSC list serve. Please prove that you are back from
>> your vacations and getting back to fun and CSC by your contribution :-)
>> --Alex
>>
>>
>> Several direct codes, notably SuperLU, PARDISO, and MA57 in different ways
>> restrict the pivoting during numerical factorization so that the
>> structures determined during the analysis can be respected.  This clearly
>> has important implications for limiting storage and for parallelism.
>> Normally if it is necessary to use a pivot that does not satisfy the
>> numerical criterion it is replaced by some suitable value (conventionally
>> ||A||*sqrt(epsilon)) and the factorization proceeds.  This will of course
>> result in the factorization of a perturbed matrix but hopefully
>> perturbations are small and so the solution is obtained by a simple
>> iterative method.
>>
>> My question to the group is what term should we use to describe this kind
>> of strategy.  We [1] have used the term "static pivoting" and believe that
>> this was first used in [2]. Is this indeed the first reference to this
>> term and when was the term first used in a journal paper?  Is it an
>> appropriate term to use or is there a more appropriate term?  The debate
>> is open.
>>
>> [1]
>> @techreport{dupr:05a,
>>     author = {Iain S. Duff and St\'ephane Pralet},
>>     title = {Towards a stable static pivoting strategy for the sequential
>> and
>>              parallel solution of sparse symmetric indefinite systems},
>>     institution = RAL,
>>     number = {RAL-TR-2005-007},
>>     notes  = {Also appeared as report TR/PA/05/26, CERFACS, Toulouse
>>               and report RT/TLSE/05/08, IRIT, ENSEEIHT, Toulouse},
>>     year = {2005} }
>>
>> [2]
>> @inproceedings{lide:98,
>>     AUTHOR = {Xiaoye S. Li and James W. Demmel},
>>     TITLE = {Making Sparse {G}aussian Elimination Scalable by Static
>>                   Pivoting},
>>     BOOKTITLE = {Proceedings of Supercomputing},
>>     ADDRESS = {Orlando, Florida},
>>     YEAR = {1998},
>>     MONTH = {November}
>> }
>> -------------------------------------------------------------------------------------------
>>
>>
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