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How to quickly do Cholesky factorization for many small matrices?

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Stephan Orzada
Stephan Orzada on 23 Jul 2021
Commented: Stephan Orzada on 1 Aug 2021
In my project, I have to check many small matrices for positive-semidefiniteness (PSDness). I use chol() since it is much faster than using eig() to check for negative eigenvalues. Still it is very slow and the most time consuming part of my calculations, since I have to check 10e6 32x32 matrices over and over again. I already tried to use parfor and batch functions but it doesn't work (I also read this in the forums). However, it occured to me that the processor utilization is very low, so I checked what happens when I run the code on two instances of matlab on the same computer. The processor utilization doubled and each script finished in the same time it would have taken if they had been running alone. So it is possible to let chol() run in parallel on the same system. Any ideas how to do this in the same instance of matlab without incurring the problems you get with chol() in a parfor loop?
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Stephan Orzada
Stephan Orzada on 1 Aug 2021
You are right. For my purpose, I don't care whether it is positive semidefinite or positive definite. Mathematically there is a difference, but it is negligible in many practical cases.

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Answers (1)

Bruno Luong
Bruno Luong on 23 Jul 2021
  2 Comments
Bruno Luong
Bruno Luong on 24 Jul 2021
Indeed mmx only deal with real matrix.
But if you are willing to modify the code, you might change the function dpotrf in line 284 of mmx.cpp to zpotrf
Of course you have to take care of retriving MATLAB complex internal interleaved data.
You might ask the author if he can gives you a hand for such task.

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