Switch from Dierckx.jl to Interpolations.jl

[Sbozzolo]

Dierckx does not preserve type kbarbary/Dierckx.jl#48 and it is not GPU compatible. It also has some loading costs that can be avoided.

[szy21]

Yes. I tried to fix it here some time ago: #39. But it didn't work.

[charleskawczynski]

This is an upstream issue: kbarbary/Dierckx.jl#48

[Sbozzolo]

Is it fine to switch to linear interpolation?

If yes, we can move to Interpolations.jl, which is GPU compatible, and stop using Dierckx.

[charleskawczynski]

julia> x = Float32[1,2];

julia> z = Float32[1,2];

julia> Dierckx.Spline1D(z, x; k = 1)(Float32(2))
2.0

[charleskawczynski]

Perhaps we could switch to Interpolations.jl. Although: JuliaMath/Interpolations.jl#598

[charleskawczynski]

Also, it has quite a few dependencies: https://github.com/JuliaMath/Interpolations.jl/blob/master/Project.toml#L6-L17

[charleskawczynski]

I had actually thought about writing our own, e.g., SimpleInterpolations.jl. Make it GPU compatible and type-stable.

[charleskawczynski]

Honestly, we could roll our own very simply interpolation package. Ah right: https://github.com/CliMA/SimpleInterpolations.jl. I just never got it off the ground

[Sbozzolo]

We are already using Interpolations.jl because it is the only package that is GPU compatible and supports 3D interpolations on irregular grids (needed to read in aerosol data for example).

It seems to be type-preserving:

B = Float32[1, 2, 10, 20, 30]
5-element Vector{Float32}:
  1.0
  2.0
 10.0
 20.0
 30.0

julia> A = Float32[1, 2, 10, 20, 30]
5-element Vector{Float32}:
  1.0
  2.0
 10.0
 20.0
 30.0

julia> itp = interpolate((A, ), B, Gridded(Linear()))
5-element interpolate((::Vector{Float32},), ::Vector{Float32}, Gridded(Linear())) with element type Float32:
  1.0
  2.0
 10.0
 20.0
 30.0

julia> itp(2.0)
2.0

julia> itp(2.f0)
2.0f0

[charleskawczynski]

Sure, switching to Interpolations is fine by me. Alternatively, we could wrap types to recover type stability in this package, which might be a quicker solution, but more of a bandaid.

[charleskawczynski]

Should we rename the issue to "Switch from Dierckx.jl to Interpolations.jl"?