Sparse matrix inversion in parallel

Question

Alex 2012-6-7

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评论： Remington Reid 2016-10-12

Is there a way to invert a sparse matrix using MATLAB's Parallel Computing Toolbox? For instance, if I type:

>> matlabpool open
>> matlabpool size
ans =
        12
>> A = distributed.sprand(1000,1000,0.01) ;
>> b = distributed.rand(1000,1) ;
>> spmd; x = A\b; end

I get the error message:

Error stack:
mldivide.m at 51
Sparse input arguments are not yet supported.

Is this a fundamental limitation in MATLAB, or am I missing something? I would like to harness parallel computing to invert a large, sparse matrix.

Thanks for your time, Alex

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Answer 1

Jill Reese 2012-6-8

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Hi Alex. Unfortunately, distributed/mldivide is currently limited to solving full linear systems. Thanks for pointing out that this limitation has not been explicitly stated in the help or documentation.

We are continually adding new features to distributed arrays, and we would like to expand our support for sparse linear algebra. Is the example shown in your question representative of the size and sparsity of the linear systems you want to solve? Are there are other linear algebra functions that you would want to use with sparse distributed arrays? We would appreciate any additional information that you might provide.

Best,

Jill

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Sid 2012-8-1

Jill, I have a similar problem. I can run Matlab with about N=200,000 and density about 1.0e-5 on my desktop. I would like to scale up to around N=1000,000 with density around the same or a bit less 1.0e-6. mldivide with sparse matrices in parallel would be the way to go short of writing my own MPI code.

Remington Reid 2016-10-12

I have run into the same issue. I'm simulating diffraction using the Finite Difference Frequency Domain method, and solving very large sparse systems. Parallel support for mldivide would be ideal. In my case the sparse matrix has N~10^6, with a density of 10^-6, is complex and not positive semi-definite.

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