Cubic interpolation

[ajwheeler]

We are currently linearly interpolating partition functions and equilibrium constants. I recently went to change this, but quickly realized that Interpolations.jl does not support cubic interpolation over a non-regular grid, even in 1D. At one point there was some effort to fix this, but it seems to have stagnated. I tested CubicSplines.jl and can verify that it works and plugs easily into SSSynth, but it's not a popular package and I worry that it might have undiscovered bugs or go unmaintained. I see a few options:

• Try to get what we need into Interpolations.jl by doing it ourselves (probably not worth it)
• Using CubicSplines.jl
• Writing our own cubic spline into SSSynth. This is probably easier than getting it into interpolations, and it would reduce our dependencies.
• Wait. Maybe the problem will solve itself? Maybe linear interpolation is fine? I believe the Barklem & Collet data is intended to be interpolated with a cubic spline, but I'm not sure if we need that level of precision.

[ajwheeler]

Another option: DataInterpolations.jl supports 1D cubic splines, and supports derivatives via ChainRules.jl (it would still be autodiff-able if it didn't but this is faster and more accurate).

edit: Unfortunately, DataInterpolations has very heavy dependencies.

[ajwheeler]

This is partially addressed by #104 , but only for partition functions and equilibrium constants. (There are now lots of other instances of interpolation in the code.)

A differentiable cubic spline implementation and a 2D implementation would be very useful to have still.