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lapack does expose a full pivoting lu as far as i can tell? https://netlib.org/lapack/explore-html/d8/d4d/group__getc2_g...

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If you are going to include vs MKL benchmarks in your repo, full pivoting LU might be one to consider. I think most people are happy with partial pivoting, so I sorta suspect Intel hasn’t heavily tuned their implementation, might be room to beat up on the king of the hill, haha.

funny you mention that, the full pivoting. it's one of the few benchmarks where faer wins by a huge margin

n faer mkl openblas

1024 27.06 ms 186.33 ms 793.26 ms

1536 73.57 ms 605.71 ms 2.65 s

2048 280.74 ms 1.53 s 8.99 s

2560 867.15 ms 3.31 s 17.06 s

3072 1.87 s 6.13 s 55.21 s

3584 3.42 s 10.18 s 71.56 s

4096 6.11 s 15.70 s 168.88 s

it might be interesting to add butterfly lu https://arxiv.org/abs/1901.11371. it's a way of doing a numerically stable lu like factorization without any pivoting, which allows it to parallelize better.

looks interesting! thanks for sharing

It looks like they are describing a preconditioner there.

the key point is that the preconditioner allows you to skip pivoting which is really nice because the pivoting introduces a lot of data dependence.

Thanks for pointing this out. Looks like only the python bindings are not included in nunpy.

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