Extrapolation options

[SouthEndMusic]

Fixes #355.

This is what I have in mind:

using DataInterpolations
using Plots
using Random

Random.seed!(2)

t = cumsum(rand(5))
u = rand(5)

t_eval = range(-1, 3.5, length = 100)
p = scatter(t,u; label = "data")
title!("Extrapolation types")

for extrapolation_type in [:constant, :linear, :extension]
    A = QuadraticSpline(u,t; extrapolation_up = extrapolation_type, extrapolation_down = extrapolation_type)
    plot!(t_eval, A.(t_eval); label = string(extrapolation_type))
end

p

Let me know whether this is a good approach before I apply it to all interpolation types, integrals, derivatives.

[ChrisRackauckas]

This looks like a great idea. It should be an EnumX enum though instead of just symbols in order to autocomplete and spellcheck properly.

[SouthEndMusic]

Derivative extrapolation now also looking good:

using DataInterpolations
using CairoMakie
using Random

Random.seed!(2)

t = cumsum(rand(5))
u = rand(5)

t_eval = range(-1, 3.5, length = 1000)
fig = Figure()
ax_itp = Axis(fig[1,1]; title = "(inter/extra)polation")
ax_deriv = Axis(fig[2,1]; title = "(inter/extra)polation first derivative")
ax_deriv2 = Axis(fig[3,1]; title = "(inter/extra)polation second derivative")
scatter!(ax_itp, t,u; label = "data")

for extrapolation_type in [ExtrapolationType.constant, ExtrapolationType.linear, ExtrapolationType.extension]
    A = QuadraticSpline(u,t; extrapolation_up = extrapolation_type, extrapolation_down = extrapolation_type)
    lines!(ax_itp, t_eval, A.(t_eval); label = string(extrapolation_type))
    lines!(ax_deriv, t_eval, DataInterpolations.derivative.(Ref(A), t_eval); label = string(extrapolation_type))
    lines!(ax_deriv2, t_eval, DataInterpolations.derivative.(Ref(A), t_eval, 2); label = string(extrapolation_type))
end

axislegend(ax_itp)
axislegend(ax_deriv)
axislegend(ax_deriv2)
fig

[SouthEndMusic]

And the integral:

using DataInterpolations
using CairoMakie
using Random

Random.seed!(2)

t = cumsum(rand(5))
u = rand(5)

t_eval = range(-2, 5.5, length = 1000)
fig = Figure()
ax_itp = Axis(fig[1,1]; title = "(inter/extra)polation")
ax_antideriv = Axis(fig[2,1]; title = "(inter/extra)polation antiderivative")
scatter!(ax_itp, t,u; label = "data")

for extrapolation_type in [ExtrapolationType.constant, ExtrapolationType.linear, ExtrapolationType.extension]
    A = QuadraticSpline(u,t; extrapolation_up = extrapolation_type, extrapolation_down = extrapolation_type)
    lines!(ax_itp, t_eval, A.(t_eval); label = string(extrapolation_type))
    lines!(ax_antideriv, t_eval, DataInterpolations.integral.(Ref(A), t_eval); label = string(extrapolation_type))
end

axislegend(ax_itp)
axislegend(ax_antideriv)
fig

[SouthEndMusic]

I've found myself in a refactoring rabbit hole again 😅

• I'm refactoring integration because I found the previous implementation, where _integral gives the antiderivative unintuitive. With my refactor _integral integrates over an interval that lies between 2 consecutive data points, which also allows for some simplification / reduction of operations
• I also want to refactor QuadraticInterpolation because the way we compute it now is unnecessarily computationally intensive and cumbersome. I wonder how many people actually use that one anyway

[sathvikbhagavan]

Can you do the refactors in different PRs?

[SouthEndMusic]

Not really, or I have to do them before this one. Is it fine by you if I wrap up what I'm doing here and make some follow-up issues?

[sathvikbhagavan]

Thats alright, refactors that are not strictly needed in this one can have follow up issues/PRs.

[SouthEndMusic]

@sathvikbhagavan sorry for the spam but just to let you know that this PR is ready for review

[sathvikbhagavan]

A few comments

[sathvikbhagavan]

Almost there. A few minor comments.

[sathvikbhagavan]

LGTM!