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ssiccha committed May 5, 2021
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Expand Up @@ -4,38 +4,30 @@ This package implements the algorithm described in "A parallel algorithm for Gau
The algorithm divides a given matrix into smaller submatrices (blocks) and carries out steps of the Gaussian elimination block by block.
The paper identifies the minimal dependencies between processing different blocks. Independent steps can be performed simultaneously, allowing for high levels of parallelism.
We provide two main functions <Ref Func="EchelonMatBlockwise"/>
and <Ref Func="EchelonMatTransformationBlockwise"/>, where the latter additionally computes the transformation matrix in parallel. The naming conventions are chosen in accordance with the "Gauss"-package
and <Ref Func="EchelonMatTransformationBlockwise"/>, where the latter additionally computes the transformation matrix in parallel. The naming conventions are chosen in accordance with the "Gauss"-package
@BeginLatexOnly
\footnote{\url{https://www.gap-system.org/Packages/gauss.html}}
@EndLatexOnly
, which provides an implementation of the sequential GAUSS algorithm. Our functions do currently not support sparse matrices.

@Chapter Gaussian Elimination
@Section Gaussian Elimination

This section describes the different variants of our implementation
of the Gaussian algorithm.

NOTES FOR US BELOW


Note that the value of the option <A>numberBlocks</A> described below has a big
impact on the performance of our algorithms.
For information on how to choose a suitable value for <A>numberBlocks</A> see
Chapter <Ref Chap="Chapter_Finding_a_suitable_number_of_blocks"/>.

TODO: move this to the right place.
The value of <A>numberBlocks</A> has a big impact on the perfomance of the
algorithms implemented in the GaussPar.
@Chapter Finding a suitable number of blocks

Experiments with matrices over fields of sizes 2 to 11 and dimensions 500 to
10.000 have found values for <A>numberBlocks</A> from 6 to 15 to be acceptable.
Note though, that this highly depends on the calculation, the number of used
threads and the machine itself.

The function <Ref Func="GAUSS_MeasureContention"/> in Chapter
<Ref Chap="Chapter_Finding_a_suitable_number_of_blocks"/>
can be used to find a suitable value systematically.

@Chapter Gaussian Elimination
@Section Gaussian Elimination

This section describes the different variants of our implementation
of the Gaussian algorithm.

@Chapter Finding a suitable number of blocks
@Section Measure Contention

@Chapter Using the task framework provided by HPC-GAP
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