Anyways, this is moot: Kent asked about "arrays", not linear algebra.
There is a difference between a linear algebraic matrix, and an array data structure.
Even if most scientific code *is* doing linear algebra, the vast majority
of linear algebra is not done with arrays since it is sparse linear algebra. About the
only major exception I can think of is linear algebra on regularly structured
grids in which the data can be represented as arrays.
In my experience, arrays are mostly a non-issue.
Andy
At 11:43 AM 3/28/00 -0500, lums@lsc.nd.edu wrote:
>
>
>I also doubt it. Even in the domain of scientific and engineering
>computing where one would expect much linear algebra, one finds:
>
> o) "Real" applications tend to be PDE based, resulting in sparse
> computations for either finite-difference or finite-element
> solution methods
>
> o) "Real" applications are becoming large, irregular, and dynamic,
> and are including more and more physics
>
> o) In "real" applications, the physics involved dominates the matrix
> solution time. The one application area for which I have
> statistics (of a sort) is circuit simulation. There, device
> evaluation tends to consume 90% of the cycles, versus about 10%
> for the matrix solution.
>
>So, while there are matrix computations in scientific computing, the
>type of the computation tends to be sparse (perhaps with small dense
>blocks), irregular, and iterative -- types of computations that
>fortran is not particular well-suited to. Moreover, the fraction of
>time even spent doing the matrix computations may not be all that
>large.
>
>As another data point, one of the premier scientific computing
>libraries -- Petsc -- does not even have dense solvers per se. And,
>come to think of it, Petsc is written in C.
>
>I think that the focus on dense matrix computations (and
>correspondingly, on arrays) is another of the "baleful effects" of
>computer benchmarking (i.e., the linpack benchmark). Also, when one
>takes even a graduate numerical analysis or matrix computations
>course, the treatment of matrices is always with the dense case
>(much easier for pedagogical purposes).
>
>Best Regards,
>Andrew Lumsdaine
>
>In our last exciting episode Arch Robison wrote:
>
>> Does anyone have statistics to prove that average numerically intensive code
>> spends a majority of time doing matrix math? (Whatever average means here.)
>> I doubt it, for the following reasons:
>
>[list of good reasons]
>
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Dr. Andrew J. Cleary
Computational Scientist
Center for Applied Scientific Computing
Lawrence Livermore National Lab
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