How to quickly do Cholesky factorization for many small matrices?
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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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Bruno Luong
2021년 7월 31일
편집: Bruno Luong
2021년 7월 31일
In real life 0 eigen value does not exist exactly. CHOL, EIG, EIGS all might fail due to round off.
And Stephan Orzada end up programming his own Cholesky decomposition for his own need, not MATLAB CHOL.
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Bruno Luong
2021년 7월 23일
It requires MEX, but it should be fast
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Bruno Luong
2021년 7월 24일
편집: Bruno Luong
2021년 7월 24일
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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