4 ms·

lapack does expose a full pivoting lu as far as i can tell? https://netlib.org/lapack/explore-html/d8/d4d/group__getc2_gab40de248b52eae8c638d72d951631795.html h

• bee_rider 2y ago
  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.
  • sarah-ek 2y ago
    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
    • adgjlsfhk1 2y ago
      it might be interesting to add butterfly lu https://arxiv.org/abs/1901.11371 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.
      • sarah-ek 2y ago
        looks interesting! thanks for sharing
      • bee_rider 2y ago
        It looks like they are describing a preconditioner there.
        • adgjlsfhk1 2y ago
          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.
• heinrichhartman 2y ago
  Thanks for pointing this out. Looks like only the python bindings are not included in nunpy.