Implement `interp`

[ClaudiaComito]

Feature functionality
https://numpy.org/doc/stable/reference/generated/numpy.interp.html

Additional context
Climate Use case @kleinert-f

[mrfh92]

Stil open and particularly of interest since related to a particular use-case.
Also possible connection to #1183 possible.

Reviewed within #1109

[samadpls]

Hey @ClaudiaComito and @mrfh92, for this should we use np.interp or create a custom implementation for interp?

[samadpls]

@ClaudiaComito May I work on this issue😋? Just to confirm, is this file where the function needs to be implemented?

[mrfh92]

@samadpls sry for the late answer, I was in vacation.

I think it would be best to add the function to the file heat/heat/core/arithmetics.py.

Regarding your first question, the function ht.interp should exhibit the same behaviour (and API) as numpy.interp. However, since local arrays in Heat are PyTorch-tensors and we need to cover the (memory-)distributed case, we cannot make direct use of numpy.interp and need to write our own custom implementation; in particular, numpy.interp could not be used on GPUs (which is a highly important case for Heat) at all... However, to get our implementation as fast as possible, one should high-level routines from PyTorch (at a first look, I guess that torch.lerp could be interesting) wherever possible because these implementations are highly optimized in the single-process context. In a very condensed way: we want to "glue together" highly optimized single-process PyTorch-routines using mpi4py (wrapped in heat.communication) to obtain a (memory-)distributed routine for our overall DNDarray.

[mrfh92]

Don't hesitate to ask, if you need more infos or help :)

[github-actions]

Branch features/832-Implement_interp created!

[samadpls]

hey @mrfh92, While looking for possible implementations, I came across this implementation in the PyTorch community, which can provide valuable insights into the interpolation process and strategies: PyTorch Interpolation Implementation-1 & PyTorch Interpolation Implementation-2. This approach might allows us to take advantage of PyTorch's optimized operations while addressing the distributed nature of our data.