BLIS.jl VS 18335

It doesn't look like you're measuring factorization performance? OpenBLAS matrix-matrix multiplication is fine, it just falls apart when going to things like Cholesky and LU.

> not the default, I've now checked

Whatever the Julia default build is doing, so probably not the recursive LAPACK routines then if that's how it's being built. If there's a better default that's worth an issue.

> That said, I don't understand why people avoid AMD's BLAS/LAPACK

There just isn't a BLIS wrapper into Julia right now, and it's much easier to just write new BLAS tools than to build wrappers IMO. It makes it very easy to customize to nonstandard Julia number types too. But I do think that BLIS is a great project and I would like to see it replace OpenBLAS as the default. There's been some discussion to make it as easy as MKL (https://github.com/JuliaLinearAlgebra/BLIS.jl/issues/3).

I would say Fortran is a pretty great language for teaching beginners in numerical analysis courses. The only issue I have with it is that, similar to using C+MPI (which is what I first learned with, well after a bit of Java), the students don't tend to learn how to go "higher level". You teach them how to write a three loop matrix-matrix multiplication, but the next thing you should teach is how to use higher level BLAS tools and why that will outperform the 3-loop form. But Fortran then becomes very cumbersome (`dgemm` etc.) so students continue to write simple loops and simple algorithms where they shouldn't. A first numerical analysis course should teach simple algorithms AND why the simple algorithms are not good, but a lot of instructors and tools fail to emphasize the second part of that statement.

On the other hand, the performance + high level nature of Julia makes it a rather excellent tool for this. In MIT graduate course 18.337 Parallel Computing and Scientific Machine Learning (https://github.com/mitmath/18337) we do precisely that, starting with direct optimization of loops, then moving to linear algebra, ODE solving, and implementing automatic differentiation. I don't think anyone would want to give a homework assignment to implement AD in Fortran, but in Julia you can do that as something shortly after looking at loop performance and SIMD, and that's really something special. Steven Johnson's 18.335 graduate course in Numerical Analysis (https://github.com/mitmath/18335) showcases some similar niceties. I really like this demonstration where it starts from scratch with the 3 loops and shows how SIMD and cache-oblivious algorithms build towards BLAS performance, and why most users should ultimately not be writing such loops (https://nbviewer.org/github/mitmath/18335/blob/master/notes/...) and should instead use the built-in `mul!` in most scenarios. There's very few languages where such "start to finish" demonstrations can really be showcased in a nice clear fashion.