How can I solve linear equation system in parallel?
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Javier Alaminos
el 14 de En. de 2020
Comentada: Heiko Weichelt
el 14 de En. de 2020
I am solving a linear equation system, , where A is a sparse square matrix and B is a sparse column vector. Before solving the system I use the command
dA = decomposition(A);
to return a decomposition of matrix A that I can use to solve the linear system more efficiently. In my case, it is Cholesky decomposition. Then I solve the system
x = dA\B;
and it works perfectly. My question is: how can I do it in parallel computing? or What is the best way to solve it in a cluster?
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John D'Errico
el 14 de En. de 2020
You already are doing that!
That is, decomposition uses all of the cores you have available for large problems.
Watching my activity monitor while the decomposition was being done:
A = sprand(10000,10000,.001);
tic,DA= decomposition(A);toc
Elapsed time is 8.250635 seconds.
All 8 cores were being used. MATLAB does try to multithread many large computations, especially those involving linear algebra.
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Christine Tobler
el 14 de En. de 2020
As John says, if you are using decomposition on one computer with several cores, the solver used already will use those cores if appropriate.
If you are working on a distributed system, and the matrix A is a distributed matrix, as of R2019b decomposition is also supported for this (see here).
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Heiko Weichelt
el 14 de En. de 2020
Notice that decomposition of distributed arrays has a slightly limited subset for the underlying algorithms. Right now, sparse Cholesky, e.g., is not yet supported. Compare
>> help parallel.distributed.Decomposition.Type
and
>> help parallel.distributed.Decomposition
for the limitations.
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