Add a pure C interface

[jgillis]

Hi! I'd be interested in interfacing elastiqp with CasADi.
Since we care about C codegeneration, such interface works best when the solver has a C API.

Here is one modeled on daqp's C interface.

[danielpmorton]

Hi @jgillis, great to get in touch! I'm so impressed by your work on CasADi and it would be quite cool to have an CasADi/ElastiQP interface. I ran a few tests on your PR locally and things are looking good already. I'll take a deeper look through the code and get back to you shortly!

[jgillis]

I was working on an experimental slack extension for our nlpsol and conic interfaces, so your elastiQP solver would be a great first fit.

[danielpmorton]

Hi @jgillis ! I made a couple changes to better align the interfaces between the C and C++, and added a small helper function to reduce some extra calls in the C. If you think this looks good to you as well, and what you need for CasADi, I'll merge it in soon. Thanks again for making the PR!

[danielpmorton]

Oh, one question: I noticed that this interface uses row-major matrices, is that preferable for CasADi?

[jgillis]

Good point, CasADi is actually column-major. This merits some extra thought..
From the CasADi side we have hold an ng-by-n column-major (sparse) matrix. With ng spanning equalities and inequalities mixed.

[danielpmorton]

Here's a quick patch to use column-major matrices -- if this branch looks good for your use-cases, let me know and I'll do a final cleanup pass and merge!