Switch SplineBouleImpurityDensity to FritschCarlsonMonotonicInterpolation

[hervasa2]

Continuing the discussion on #545 @fhagemann suggested to switch to FritschCarlsonMonotonicInterpolation.
This provides an elegant solution which is built into Interpolations.

[fhagemann]

Looks good to me.

For reference, this is what the examples in the previous PR #545 look like now:

z = [1,5,6,10]
ρ = [1,2,3,4]
scatter(z, ρ)
plot!(range(extrema(z)..., length = 100),z ->  spline(z))

z = [1,5,6.5,10]
ρ = [1,2,3,4]
ρ = [1,2,3,2]
scatter(z, ρ)
plot!(range(extrema(z)..., length = 100),z ->  spline(z))

z = [1,5,7.6,10]
ρ = [1,2,3,2]
scatter(z, ρ)
plot!(range(extrema(z)..., length = 100),z ->  spline(z))

[fhagemann]

Also, seems like we can decrease the bound for Interpolations back to 0.14 then, as we don't require the use of cubic_spline_interpolation anymore.

[fhagemann]

The only thing that does not (yet) work with this PR: FritschCarlsonMonotonicInterpolation does not seem to extrapolate, so if the user were to evaluate this impurity density outside the z range where it is defined, this method will result in a wordy error message:

z = [1,5,6,10]
ρ = [1,2,3,4]
plot!(0:1e-3:11, z ->  spline(z))

ERROR: BoundsError: attempt to access 4-element interpolate(::SVector{4, Float64}, ::SVector{4, Float64}, FritschCarlsonMonotonicInterpolation()) with element type Float64 with indices SOneTo(4) at index [0.0]
Stacktrace:
  [1] throw_boundserror(A::Interpolations.MonotonicInterpolation{…}, I::Tuple{…})
    @ Base ./essentials.jl:14
  [2] (::Interpolations.MonotonicInterpolation{…})(x::Float64)
    @ Interpolations ~/.julia/packages/Interpolations/dR5oF/src/monotonic/monotonic.jl:211
  [3] (::var"#1#2")(z::Float64)
    @ Main ./REPL[16]:1
  [4] iterate
    @ ./generator.jl:48 [inlined]
  [5] _collect(c::StepRangeLen{…}, itr::Base.Generator{…}, ::Base.EltypeUnknown, isz::Base.HasShape{…})
    @ Base ./array.jl:811
  [6] collect_similar(cont::StepRangeLen{…}, itr::Base.Generator{…})
    @ Base ./array.jl:720
  [7] map(f::Function, A::StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}, Int64})
    @ Base ./abstractarray.jl:3371
  [8] _compute_y
    @ ~/.julia/packages/RecipesPipeline/BGM3l/src/series.jl:72 [inlined]
  [9] _compute_xyz(x::StepRangeLen{…}, y::Function, z::Nothing, nice_error::Bool)
    @ RecipesPipeline ~/.julia/packages/RecipesPipeline/BGM3l/src/series.jl:86
 [10] macro expansion
    @ ~/.julia/packages/RecipesPipeline/BGM3l/src/series.jl:140 [inlined]
 [11] apply_recipe(plotattributes::AbstractDict{Symbol, Any}, ::Type{RecipesPipeline.SliceIt}, x::Any, y::Any, z::Any)
    @ RecipesPipeline ~/.julia/packages/RecipesBase/BRe07/src/RecipesBase.jl:300
 [12] _process_userrecipes!(plt::Any, plotattributes::Any, args::Any)
    @ RecipesPipeline ~/.julia/packages/RecipesPipeline/BGM3l/src/user_recipe.jl:38
 [13] recipe_pipeline!(plt::Any, plotattributes::Any, args::Any)
    @ RecipesPipeline ~/.julia/packages/RecipesPipeline/BGM3l/src/RecipesPipeline.jl:72
 [14] _plot!(plt::Plots.Plot, plotattributes::Any, args::Any)
    @ Plots ~/.julia/packages/Plots/8ZnR3/src/plot.jl:223
 [15] plot!(::Plots.Plot, ::Any, ::Vararg{Any}; kw...)
    @ Plots ~/.julia/packages/Plots/8ZnR3/src/plot.jl:213
 [16] plot!(::Plots.Plot, ::Any, ::Any)
    @ Plots ~/.julia/packages/Plots/8ZnR3/src/plot.jl:208
 [17] plot!(::Any, ::Vararg{Any}; kw...)
    @ Plots ~/.julia/packages/Plots/8ZnR3/src/plot.jl:202
 [18] plot!(::Any, ::Any)
    @ Plots ~/.julia/packages/Plots/8ZnR3/src/plot.jl:194
 [19] top-level scope
    @ REPL[16]:1
Some type information was truncated. Use `show(err)` to see complete types.

Should we add some catch for this (e.g. if z < zmin, just take the first value of ρ and if z > zmax, take the last value of ρ), throw an explicit warning or just leave this as is?

[hervasa2]

Should we add some catch for this (e.g. if z < zmin, just take the first value of ρ and if z > zmax, take the last value of ρ), throw an explicit warning or just leave this as is?

With the cubic spline it was the same story. But I would put the check in get_impurity_density. If the user use idm.spline manually there should be no check.

[fhagemann]

Perfect, thanks!

[fhagemann]

Tests pass locally, I am going to merge this now.