# Parallel rank calculation for sparse matrices -- suggestions?

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I need to calculate the rank of large (> 1 terabyte of non-zero elements) sparse matrices with MATLAB. Exploring the Parallel Toolbox, but can't seem to find anything that convinces me what is offers will be helpful. If I'm wrong, can someone point me in the right direction? Ideally, I'd just want to take my existing code that has "r=sprank(A)" in it and have that library call run in parallel, perhaps with some additional annotation as needed. Would using a GPUARRAY help here, for example? Doesn't seem like it, but perhaps I'm wrong. Hoping someone here can help me out. Thanks!

Barry Fagin

Professor of Computer Science

barry.fagin@afacademy.af.edu

##### 9 Comments

Matt J
on 5 Sep 2022

A = sparse(tall,skinny)

How tall? How skinny? What currently rules out the approach already discussed below of using rank(full(A.'*A))?

Bruno Luong
on 6 Sep 2022

"After doing a little digging, I now believe sprank() merely counts the number of non-zero columns. This is not what I require."

It does something more intelligent than that it match the row to column through Dulmange Mendelsohn permutation. In your case might be all the non-zero column can be matched. But that is exactly what structural rank means.

### Accepted Answer

Bruno Luong
on 30 Aug 2022

Moved: Bruno Luong
on 30 Aug 2022

##### 5 Comments

Bruno Luong
on 31 Aug 2022

IMO the doc should clarify this.

But then I still have some doubt. If user runs multiple sprank in parallel, it will take less worker to work on one sprank. So at the end do we really speed up the whole thing?

Edric Ellis
on 1 Sep 2022

Yes, the "extended capability" description could probably do with some refinement to make it clear exactly what works. (Today, there are a good number of MATLAB functions that cannot be run on a thread pool worker, and this "extended capability" really means simply that the function can run on a thread pool worker).

The performance situation is ... complicated, unfortunately. There is no single simple answer as to whether running N copies of a given function concurrently on workers is faster than running N copies sequentially on the client. It depends on all sorts of details of the implementation of that function - but primarily whether the function is already intrinsically multithreaded by MATLAB itself.

### More Answers (2)

Matt J
on 30 Aug 2022

Bruno Luong
on 5 Sep 2022

For thin and tall sparse matrix A of size (m x n), m>>n and n in the order of 1000s, it might be possible to compute the rank using q-less qr, which is better than rank(A'*A) which has the drawback of square the condition number.

A=sprand(100000,10,0.1)*sprand(10,100,0.1);

R=qr(A,0);

rank(full(R))

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