Long compile time for differentiation transform test in order SH -> Grid -> SH

[maximilian-gelbrecht]

For some reason the unit test of the the differentiability of the full transform needs a lot of compilation time when starting in spectral space with the OctahedralGaussianGrid.

SpeedyWeather.jl/test/spectral_transform_ad_rules.jl

Lines 159 to 174 in 46849ba

	function transform_identity!(x::LowerTriangularArray{Complex{T}}, S::SpectralTransform{T}) where T
	x_grid = zeros(S.Grid{T}, S.nlat_half, S.nlayers)
	transform!(x_grid, x, S)
	transform!(x, x_grid, S)
	return nothing
	end
	spec = transform(grid, S)
	spec_copy = deepcopy(spec)
	transform_identity!(spec, S)
	@test isapprox(spec, spec_copy)
	dspec = similar(spec)
	fill!(dspec, 1+im)
	autodiff(Reverse, transform_identity!, Const, Duplicated(spec, dspec), Duplicated(S, dS))

This is not an issue when starting in grid space, or with the FullGaussianGrid. The results are correct, and every subsequent execution is also fast. It's the compilation that takes so long.

Not sure why that is. As every subsequent execution is fast, I am not too worried, and I'll just exclude this test from the CI for now, but this might be something to look at it again later.

[milankl]

I'm surprised that there's a difference between the full/octahedral grids. From a software engineering perspective they are super similar. Same definition, same constructors, same place in the type hierarchy just on another branch, same Legendre polynomials, it's just that FFTW plans either 24 (at default resolution) identical plans (full) or 24 different plans (octahedral). But why would that matter?