Make a SVD implementation in Rust and remove the dependency of openblas

[eddyxu]

Problem Statement

openblas gives us many troubles to build the package in different systems. We only use blas to compute SVD in OPQ now. Because it is only used during indexing, SVD / blas is not performance critical piece of code. It should be safe to remove them.

Desired behavior

We implement SVD in rust, and get rid of openblas-src as dependency.

[I8dNLo]

Would using just nalgebra work?
I think I can do it

[I8dNLo]

@eddyxu do you have any suggestion of exact SVD variation or I can implement any I want?

[eddyxu]

@I8dNLo thanks for your interests. It'd be nice to have a SVD without major dependency.

Also , i dont have strong opinion in SVD. We were thinking about https://www.netlib.org/lapack/explore-html/d1/d7e/group__double_g_esing_ga84fdf22a62b12ff364621e4713ce02f2.html . But not sure whether other implementation will bring major difference. wdyt @changhiskhan @AyushExel

[I8dNLo]

I was thinking to just write my own pure-Rust one

[eddyxu]

@I8dNLo a pure rust one would be great! Looking forward to it

[SarahNasser576]

Hi! I'm a student in the CodePath AI301 program and I'd like to work on this issue. I'll start by reproducing the problem locally this week. Any pointers on where to start in the codebase would be appreciated!