Discussion: Deprecate overloading `__new__` for operator application?

[inducer]

Suppose x is a numpy object array of densities.

Now: S(x) returns a vector of single-layer potentials.

A possible future: componentwise(S, x) returns a vector of single-layer potentials.

Context/motivation: #245 (comment)

cc @alexfikl

[alexfikl]

I would argue for:

• Adding a num_reference_derivative function for the corresponding NumReferenceDerivative class that does this vectorization. Similarly for the other overloaded classes.
• Adding a little @componentwise decorator (or something like that) that automatically does that (a la for_each_kernel in loopy).

I don't know if being explicit with componentwise(Something, operand, **kwargs) in a lot of places is worth it..

[inducer]

D'oh! Yes, you're right of course. That sounds like a good plan. Let's deprecate the __new__ thing and have a vectorizing function.