Adding pchip interpolator to pybamm.Interpolant class.

[martinjrobins]

Discussed in #4589

^{Originally posted by MartinFuentetaja November 15, 2024}
Hello everyone! I am trying to use Akima1D interpolator to interpolate the OCPs of gr/LFP cell. I have tried to use pchip instead of cubic spline (due to the flatness of the OCP of LFP). However, the following error arises:

NotImplementedError: The interpolator 'pchip' is not supported by CasAdi. Use 'linear' or 'cubic' instead. Alternatively, set 'model.convert_to_format = 'python'' and use a non-CasADi solver.

Therefore, I have also tried to implement Akima1D interpolator from scratch. However, I did not success.

I have to mention that it works with linear interpolator, however I would prefer to use another one.

[martinjrobins]

Discussed in #4589

This is possible, the main piece of work would be to implement the pchip interpolant in the file pybamm/expression_tree/operations/convert_to_casadi.py. There is an issue on the casadi repo that gives an example of how to do this: casadi/casadi#2489