# Sparse matrix inversion in parallel

33 views (last 30 days)
Alex on 7 Jun 2012
Commented: Remington Reid on 12 Oct 2016
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.

Jill Reese on 8 Jun 2012
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

Show 1 older comment
Jill Reese on 20 Jun 2012
Alex, thanks for the additional information. I'm not sure if it will speed things up for you at all, but there is one workaround that you could try.
N = 10,000;
density = 1.0e-4;
A = sprand(N, N, density); % Your sparse matrix here. Do not distribute it.
SparseEye = distributed.speye(N); % distribute the sparse identity matrix
X = A\SparseEye; % explicitly compute the inverse
X will be a distributed array containing the inverse of your sparse matrix A. The important thing here is not to distribute the matrix you want to invert, but rather distribute the second input to mldivde. Again, I'm not sure if this will provide better performance than regular mldivide, but it is the only way that you can invert a sparse matrix in parallel right now.
Hope this helps,
Jill
Sid on 1 Aug 2012
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 on 12 Oct 2016
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.