Good to see LU decomposition with full pivoting being implemented here (which is missing from BLAS/LAPACK). This gives a fast, numerically stable way to compute the rank of a matrix (with a basis of the kernel and image spaces). Details: https://www.heinrichhartmann.com/posts/2021-03-08-rank-decom....
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.
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.
Is there a collection of algorithms published somewhere, in a coherent manner? It seems like to me, there should be a collection of matrix algebra, symbolic algebra, etc. algorithms somewhere that makes it easy to implement these in any language or system. As it is, it seems you need to already be an expert or researcher in the space to make any movement.
>The BLAS-like Library Instantiation Software (BLIS) framework is a new infrastructure for rapidly instantiating Basic Linear Algebra Subprograms (BLAS) functionality. Its fundamental innovation is that virtually all computation within level-2 (matrix-vector) and level-3 (matrix-matrix) BLAS operations can be expressed and optimized in terms of very simple kernels.
That can be argued, but they're pretty esoteric. For example, what language are they written in? Fortran, assembly, etc.? Probably nothing the majority of developers or mathematicians can't understand. And creating bindings for them is non-trivial. I don't even know where to start from the website. And on the website, all the links to the routines are broken. https://www.netlib.org/blas/
The naming convention is a bit esoteric, but once you figure it out it's not too bad. I don't think writing bindings is too hard once you know what's going on. You most likely would want to write some kind of wrapper on top of that in order to make things a little more user-friend.
I will agree with you on the routines being broken. That happened within the past year. Not sure why it happened, but it's annoying. If you know the name of the routine you can usually find documentation on another site.