[diff] Rework evaluation in diff

[alexfikl]

Right now, calling

df = diff(method, func, points)

will evaluate the fractional derivative of func on all the points, e.g. $D_C^\alpha[f](x_n)$ for all $x_n$. Ideally, we want to be more coarse grained here

• diff(method, func, points): left as now to evaluate at all points, but mainly just a simple wrapper around diffs.
• weights(method, x): just computes the quadrature weights for x points, i.e. to integrate from x[0] to x[-1].
• diffs(method, func, points): only evaluates at $x_n$. (extra s for single?)

[alexfikl]

We also want to separate these:

• so that we could presumably reuse the weights for the ODE solvers: currently very copy pasted :(
  • Would need to also expand the interface to support $f: \mathbb{R} \to \mathbb{R}^d$.
• so that we can use diffs to compute the gradient at a given point: currently pycaputo.grad just evaluates everything and takes the last point :(
  • For some definition of the gradient? This should just work.