We need to phase out InverseRTransform

[marco-2023]

InverseRTransform currently duplicates functionality already provided by BaseTransform (see #307), in particular the inverse transformation derivatives. This class should therefore be deprecated and removed.

At present, InverseRTransform is used by solve_poisson_bvp and solve_poisson_ivp. These functions use a transformation mapping $( r \in [0, \infty) \rightarrow [0, 1] )$, i.e. the inverse of the mapping used to construct the grid. Therefore, accepting the inverse transform as an argument.

• This design should be revised to consistently use the forward transformation (from finite to infinite domain), and compute inverse-related quantities via BaseTransform where needed.

• Similar changes will be required in the ode module.

• Corresponding tests must also be refactored to reflect the updated transformation convention and ensure consistency with the new API.

[Ao-chuba]

Hi @marco-2023,
My implementation will need to be build on top of #307, so Id need that merged into main first before I can open my PR. so ill start working on it ones it get merged, or maybe we can branch directly off #307 and work on it as stacked PR though there is chances of it getting a little messy

[Ao-chuba]

also .

• after the refactor, should solve_poisson_bvp and solve_poisson_ivp accept the forward transform directly, and internally call deriv_inverse?
• will the scope of ode.py change? as in does solve_ode_bvp/solve_ode_ivp also need their public API updated, or is it just the internal _transform_solution_to_original_domain helper that needs adjusting?