Poor performance for calculating eigenvalues and eigenvectors on GPU

Question

In some code we need to get auto vectors and auto values for the generalized eigenvalue problem with symmetric real matrices (Ax=lamba Bx). This code uses DSPGVX from LACPACK. We wanted to speed it up on GPU using a MAGMA function. We asked on this forum and got the answer about this

http://icl.cs.utk.edu/magma/docs/zhegvx_8cpp.html

The size of our matrices (N) goes from 100 to 50000 and even more, related to the number of atoms in a molecule. We observe:

a) for N bigger than 2500 (approx), MAGMA just does not work; segmentation fault b) MAGMA runs always slower than LAPACK sequential, around 10 times slower

Is this behavior normal and could we overcome it? Can anybody report any reference where anybody working on this similar problems gets a decent speedup?

Thanks

What do you mean "does not work"...does it not run? Does it produce the wrong results, does it crash and burn at runtime? — prelic, Mar 16 '12 at 19:06
N is 50000 and you want an NxN matrix? For floats: 50000 * 50000 * 4 Byte > 4 GByte. — knivil, Mar 18 '12 at 18:53
Are you talking about sparse matrices? I mean, 50K x 50K looks really terrifically complex problem. But if you talk about sparse matrice (i.e. most of the elements are zero) - the algorithms implemented is software may solve it by appropriate means — valdo, Mar 18 '12 at 19:12
Err DSPGVX is a real valued eigenvalue solver, but ZHGEVX is a *complex* eigenvalue solver. Are you sure you know what you are doing here? — talonmies, Mar 18 '12 at 19:50
ZHGEVX is the only thing that can help solve my problem; there is no other thing on GPU for the general eigenvalue problem (otherwise, please tell me). It is designated for complex, but of course, can be used for real — Open the way, Mar 18 '12 at 21:16
So can you clarify which serial lapack routine you are comparing performance with? — talonmies, Mar 18 '12 at 23:05
You might be interested in this research: http://www.dgp.toronto.edu/~lessig/mrrr/index.html — harrism, Mar 18 '12 at 23:45
@harrism; that is not for the generalized symmetric real eigenvalue problem — Open the way, Mar 20 '12 at 08:20
@David; that looks really good, I am going to test it, you should change your comment to asnwer — Open the way, Mar 20 '12 at 08:21
Link in this question is dead. Please include as much info as possible in the question itself. — Richard, Oct 11 '17 at 13:10

score 4 · Accepted Answer · answered Mar 20 '12 at 09:46

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In my experience you may be able to gain greater performance benefits by switching to a better eigensolver. The best solver that I know of is ARPACK. You will gain most benefit it your matrices have some structure, for example if they are sparse. This solver is also most efficient if you only need to extract a small fraction of the total number of eigenpairs.

I would start off by trying this solver on your problems running just on the CPU. You may find that this alone gives sufficient performance for your needs. If not then it is relatively easy to move the calculation core for ARPACK to the GPU. Or, there are parallel versions of ARPACK available.

answered Mar 20 '12 at 09:46

David Heffernan

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do you think ARPACK can be applied to the case of dense matrices? IF so, could you point to some example? thanks – Open the way Mar 20 '12 at 17:40
It makes no assumptions on the type of matrices. Read about the reverse passing interface and you will understand why this is so. – David Heffernan Mar 20 '12 at 18:04
you deserve to win the bounty, not only because your inspiring answer but also given your excellent picture, thanks – Open the way Mar 24 '12 at 18:40
Ha ha. You really gave a big laugh there! ;-) Did you give arpack a go yet? Any luck with it. I found it pretty tricky to get on top of but once I got it working its performance blew me away. – David Heffernan Mar 24 '12 at 18:55

score 2 · Answer 2 · answered Mar 22 '12 at 03:16

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Have you tried CULA http://www.culatools.com/ ? CULA is Lapack converted for CUDA by NVIDIA, so at least in theory it should have one of the best implementation for the generalized eigenvalue problem. I think the single precision version is free so you could give it a try.

answered Mar 22 '12 at 03:16

mmisu

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I had a look but I did not see any information related with implementations of the generalized eigenvalue problem. Only information about the simple eigenvalue problem is reported there, am I right? – Open the way Mar 22 '12 at 11:04
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@flow You are right. I've used CULA only for solving a symmetric eigenvalue problem not for the generalized problem. Sorry the misunderstanding. – mmisu Mar 22 '12 at 15:18

Poor performance for calculating eigenvalues and eigenvectors on GPU

2 Answers2