linear least squares/mldivide for large matrices in parallel?

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I have a really large system to solve using linear least squares. The A matrix can have 2-3 million rows and 2000-3000 columns. The B matrix has same row size but with a single column.
I have access to a supercomputer, and I want to run the x = A\B (or) mldivide(A,B) command in parallel, since I can easily run out of RAM even on workstations with lots of memory.
Any ideas? I am able to run EIG and SVD without any issues in parallel, since I assume it is automatically parallelized by MATLAB. What about linear least squares? Suggestions outside of MATLAB are also welcome. Thanks.

Accepted Answer

Edric Ellis
Edric Ellis on 8 Apr 2015
Edited: Edric Ellis on 8 Apr 2015
If you have access to a cluster of machines, you could use distributed arrays to solve the large system in parallel using the multiple memories. You'll need MATLAB Distributed Computing Server worker licenses on the cluster, and Parallel Computing Toolbox on the client machine. Something like this:
parpool();
A = distributed.rand(20000,2000);
b = sum(A, 2);
x = A\b;
  3 Comments
Sean de Wolski
Sean de Wolski on 27 Jul 2016
David, please ask this in a new question - the answer will end up being to use codistributed arrays inside of spmd.

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More Answers (1)

Mahdiyar
Mahdiyar on 8 Apr 2015
Hi Arvind
Parallel computing helps you to use more amount of CPU to run your simulation in a shorter time. As well as I know, when you have memory problem, it does not help you.
What I can suggest you is that you can implement the "x=A\B" by your own code.
I mean that write the m-file to calculate this x = A\B. The only difference is that you have to save your data and delete another one when you do not need it to avoid Memory problem.
For example, to calculate the A\B, you need to calculate A^(-1). Thus, first, JUST load matrix A and calculate A^(-1) and then save that matrix as a matrix and delete matrix A (be cause you do not need it anymore).
I hope it helps you.
Regards,

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