why SVD is so so slow??!

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why SVD is so so slow??!

Postby zhangft » Fri Apr 09, 2010 8:50 pm

I implemented SVD decomposition with culaDeviceSgesvd in CULA 1.3 and the test matrix is a positive definite matrix size of 4000*4000. This operation cost me 41282ms on my GTX280 GPU card. This function should be optimized I think!
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Re:why SVD is so so slow??!

Postby kyle » Sat Apr 10, 2010 6:09 am

Hi zhangft,

I have a few questions.

1) Have you tried this on the CPU? SVD is a very intense algorithm. A 6 minute runtime isn't unheard of for large sizes.

Here is our expected performance chart for SVD: http://www.culatools.com/performance/svd

Here we show over a 3x speed up with a GPU runtime of about 40 seconds compared to about 150 seconds on the CPU.

2) Have you tried the non-device interface? A 4000x4000 matrix will see improvements with our regular interface.

-Kyle
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Re:why SVD is so so slow??!

Postby kyle » Sat Apr 10, 2010 6:25 am

I just noticed you mentioned that your matrix is positive definite. Have you considered symmetric eigenvalue routines instead? Here is some information on SVD's relation to eigenvalues if you aren't familiar with that:

http://en.wikipedia.org/wiki/Singular_v ... omposition

In your case: SVD's A=U*S*V' is equal to SYEV's A=V*W*V'

For performance this is a massive reduction in work. SYEV is a less computationally complex algorithm and our performance of a 4K Eigenproblem results in about a 12 second runtime.

http://www.culatools.com/performance/sy ... enproblems

Hope this helps as well!

-Kyle
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Re:why SVD is so so slow??!

Postby zhangft » Thu Apr 15, 2010 6:26 pm

thanks Kyle! 12 second runtime is wonderful.
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Re:why SVD is so so slow??!

Postby kyle » Thu Apr 15, 2010 6:32 pm

Glad to hear it! This should be even lower come CULA 2.0. We've put a lot more effort into symmetric eigenvalues for the upcoming release!
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