Levenberg-Marquart + SLSQP for Proximity

[jzwar]

Overview

Adds Levenberg-Marquart and SLSQP for proximity. Current implementation wouldn't work for some situations (see #389). Source for SLSQP is from current scipy's fortran version. To avoid difficulties of fortran-compiler-setup in CI systems, the source is translated to c using f2c. Then, removed some static variables and add const keywords.

Now, the search looks like this:

Initial guess
|
Newton
|
Converged? -- yes -- return
|
No
|
Reset initial guess, max_iterations *= 5
|
SLSQP
|
Converged? -- yes -- return
|
No
|
Reset initial guess, max_iterations *= 5
|
LM

Also, SLSQP can incorporate bounds. Nice.

Addressed Issues

• fixes #389
• Sometimes, newton iterations does not converge
• Sometimes, we needed to sample a lot of points for k-d tree
• Sometimes, we really want to get correct values at any cost.

Checklists

• [ ] Documentations are up-to-date.
• [ ] Added example(s)
• [ ] Added test(s)

[j042]

super cool!

[j042]

Do you have scripts/notes of the origin of this implementation?

[j042]

never mind, found it in #389

[j042]

one thing to note in general is that we probably had to call system.ResetRowOrder(); at each iteration.

[j042]

one thing to note in general is that we probably had to call system.ResetRowOrder(); at each iteration.

On the other hand, it would have iterated through this order and reordered it, so maybe it is irrelevant

[j042]

If you get a chance, I'd appreciate if you can take a look at proximity.hpp / proximity.cpp @danielwolff1 :)

[danielwolff1]

Thanks for incorporating the changes, from my point of view this can be merged! 🚀

[j042]

Thanks for the review @danielwolff1 !