Make domain representation explicit across sampling and random-walk interfaces

[Akash504-ai]

Sampling and random-walk code currently rely on implicit assumptions about the domain.

Different parts of the code treat the domain in different ways:

• Polytope objects are passed and changed directly by the algorithms,
• Unconstrained domains(R^d) are assumed implicitly in some of the samplers,
• Domain meaning is encoded inside the algorithm logic instead of being explicit.

This mixes the domain meaning with the algorithm logic and makes the code hard to understand, reason about and extend. Also in several places algorithm behavior changes based on hidden domain assumptions without making this clear to the caller.

In my opinion we should avoid implicit domain handling. Instead of the domain (R^d) should be represented explicitly and the domain logic should live inside a clear domain abstraction rather than being spread across sampling, random-walk, and preprocessing code.

[Akash504-ai]

Thanks for converting this to a discussion...huge respect to your decision. I know that this is more of a design level topic. If u want my opinion, my main goal is to make the domain assumptions explicit and try to avoid the hidden behavior inside algorithms. I am happy to hear your thoughts on possible designs and tradeoffs...if you think this needs to be solved.