In message from "M. Edward (Ed) Borasky" <
znmeb@...> (Sun, 10
Aug 2008 08:58:36 -0700):
>On Sun, 2008-08-10 at 07:50 -0500, Clint Whaley wrote:
>> Guys,
>>
>> My paper on the benefits of empirically tuning LAPACK's
>>ILAENV-controlled NB
>> has been accepted for CANA'08. You can see a draft of it at:
>>
http://www.cs.utsa.edu/~whaley/papers/lanb.pdf>>
>> It shows the advantage you get from tuning NB for several different
>>BLAS
>> an a couple of platforms. Depending on problem size and
>>architecture,
>> you can be leaving as much as 30% (or 75%, if on the Itanium :) on
>>the table
>> if you use stock lapack's ILAENV. It also highlights two new tools
>>available
>> in ATLAS (lapack timer/tuner and a tool that takes ATLAS timer
>>output,
>> does some simple statistics, and prints it out in a spreadsheet
>>friendly
>> format).
>>
>> We can apply this tuning to pretty much any blocked LAPACK routine.
>> ATLAS
>> presently handles tuning the factorizations. My guess is that the
>>next
>> most important routines are the eigencodes. Does anyone want to
>>nominate
>> particular routines that they use a lot?
>
>Real symmetric eigensolvers are a big workhorse in lots of areas ...
>even undergraduate chemistry. :)
I want to support this proposal - about real (double precision :-))
symmetric matrix diagonalization. To be more exact for quantum
chemistry, they solve often also generalized eigenvectors problem,
i.e. Ax=lambda*Bx, where B is positive defined simmetric matrix. This
task may be reduced to usual diagonalization.
What is about sparse matrixes, in quantum chemistry, there is special
LINEAR scaling algorithms which avoids usual diagonalization.
Mikhail
> Singular Value Decomposition is
>another
>workhorse -- gotta have it.
>
>Question -- is anybody putting this much effort into tuning *sparse*
>linear algebra? Something approaching ATLAS performance on huge
>sparse
>matrix-vector multiplies would give significant improvements in many
>areas, including my personal favorite, Markov chains.
>>
>> Cheers,
>> Clint
>>
>> **************************************************************************
>> ** R. Clint Whaley, PhD ** Assist Prof, UTSA **
>>www.cs.utsa.edu/~whaley **
>> **************************************************************************
>>
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https://lists.sourceforge.net/lists/listinfo/math-atlas-devel>--
>M. Edward (Ed) Borasky
>ruby-perspectives.blogspot.com
>
>"A mathematician is a machine for turning coffee into theorems." --
>Alfréd Rényi via Paul Erdős
>
>
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