RecursiveArrayTools.jl VS SciPy

You're not really supposed to be using StaticArraysCore anymore, but here's a somewhat older PR that shows the siginificance of moving StaticArray functionality on a smaller library, moving it from 6228ms to 292ms load time (https://github.com/SciML/RecursiveArrayTools.jl/pull/217).

> > This gives the package authors a tool to basically "profile" the loading time of their package, which will help them optimize the loading time. So there _will_ be downstream improvement to package loading for us users too.

It lead to https://github.com/SciML/RecursiveArrayTools.jl/pull/217 . 6228.5 ms to 292.7 ms isn't too shabby.

The load times on some core packages were reduced by an order of magnitude this month. For example, RecursiveArrayTools went from 6228.5 ms to 292.7 ms. This was due to the new `@time_imports` in the Julia v1.8-beta helping to isolate load time issues. See https://github.com/SciML/RecursiveArrayTools.jl/pull/217 . This of course doesn't mean load times have been solved everywhere, but we now have the tooling to identify the root causes and it's actively being worked on from multiple directions.

I guess it is a rite of passage to rewrite it. I'm doing it for SciPy too together with Propack in [1]. Somebody already mentioned your repo. Thank you for your efforts.

[1]: https://github.com/scipy/scipy/issues/18566

Fortran codes have caused many problems for the Python package Scipy, and some of them are now being rewritten in C: e.g., https://github.com/scipy/scipy/pull/19121. Not only does R have many Fortran codes, there are also many R packages using Fortran codes: https://github.com/r-devel/r-svn, https://github.com/cran?q=&type=&language=fortran&sort=. Modern Fortran is a fine language but most legacy Fortran codes use the F77 style. When I update the R package quantreg, which uses many Fortran codes, I get a lot of warning messages. Not sure how the Fortran codes in the R ecosystem will be dealt with in the future, but they recently caused an issue in R due to the lack of compiler support for Fortran: https://blog.r-project.org/2023/08/23/will-r-work-on-64-bit-arm-windows/index.html. Some renowned packages like glmnet already have their Fortran codes rewritten in C/C++: https://cran.r-project.org/web/packages/glmnet/news/news.html

There are several lessons here: a) vanilla conda-forge numpy and scipy versions come with openblas, and it works pretty well, b) do not use netlib unless your matrices are small and you need to do a lot of SVDs, or idek why c) Apple's veclib/accelerate is super fast, but it is also numerically unstable. So much so that the scipy's devs dropped any support of it back in 2018. Like dang. That said, they are apparently are bring it back in, since the 13.3 release of macOS Ventura saw some major improvements in accelerate performance.

First, if you read through that scipy issue (https://github.com/scipy/scipy/issues/18118 ) the author was willing and able to relicense PRIMA under a 3-clause BSD license which is perfectly acceptable for scipy.

For the numerical recipes reference, there is a mention that scipy uses a slightly improved version of Powell's algorithm that is originally due to Forman Acton and presumably published in his popular book on numerical analysis, and that also happens to be described & included in numerical recipes. That is, unless the code scipy uses is copied from numerical recipes, which I presume it isn't, NR having the same algorithm doesn't mean that every other independent implementation of that algorithm falls under NR copyright.

Reading the discussions under a previous thread titled "More Descent, Less Gradient"( https://news.ycombinator.com/item?id=23004026 ), I guess people might be interested in PRIMA ( www.libprima.net ), which provides the reference implementation for Powell's renowned gradient/derivative-free (zeroth-order) optimization methods, namely COBYLA, UOBYQA, NEWUOA, BOBYQA, and LINCOA.

PRIMA solves general nonlinear optimizaton problems without using derivatives. It implements Powell's solvers in modern Fortran, compling with the Fortran 2008 standard. The implementation is faithful, in the sense of being mathmatically equivalent to Powell's Fortran 77 implementation, but with a better numerical performance. In contrast to the 7939 lines of Fortran 77 code with 244 GOTOs, the new implementation is structured and modularized.

There is a discussion to include the PRIMA solvers into SciPy ( https://github.com/scipy/scipy/issues/18118 ), replacing the buggy and unmaintained Fortran 77 version of COBYLA, and making the other four solvers available to all SciPy users.

if that makes your eyes bleed, what do you think about this? https://github.com/scipy/scipy/blob/main/scipy/special/specfun/specfun.f (heh)