Add SmoothedConstantInterpolation

[SouthEndMusic]

Fixes #364.

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

using DataInterpolations
using Plots
using Random

N = 10
Random.seed!(8)
u = rand(N)
t = cumsum(rand(N))
A1 = ConstantInterpolation(u, t)

p = plot()
plot!(A1)

for d_max in 00.05:0.05:0.2
    A2 = SmoothedConstantInterpolation(u, t, cache_parameters = true; d_max)
    plot!(A2)
end

p

[SouthEndMusic]

Fun feature; if SmoothedConstantInterpolation is used with extrapolation = ExtrapolationType.Periodic, then the transitions are also smooth:

using DataInterpolations
using Plots
using Random

N = 4
Random.seed!(8)
u = rand(N)
t = cumsum(rand(N))
Δt = t[end] - t[1]
t_eval = range(first(t) - Δt, last(t) + Δt, length = 500)

A = SmoothedConstantInterpolation(u, t; extrapolation = ExtrapolationType.Periodic, d_max = 0.2)

plot(t_eval, A.(t_eval))
scatter!(t[1:end-1], u[1:end-1]; label = "data")
scatter!(t[1:end-1] .+ Δt, u[1:end-1]; label = "data one period forward")
scatter!(t[1:end-1] .- Δt, u[1:end-1]; label = "data one period back")

[ChrisRackauckas]

Conflicts?

[SouthEndMusic]

I don't understand why the derivative tests are failing 🤔

[SouthEndMusic]

fixed it 👍

[ChrisRackauckas]

I think I'm happy. @sathvikbhagavan ?

[sathvikbhagavan]

A couple of clarifications

[SouthEndMusic]

A tangentially related gripe regarding periodic extrapolation: calendars are a mess, making it difficult to periodically extrapolate timeseries in a way that does not get out of sync with them

[sathvikbhagavan]

Format and then can be merged!

[SouthEndMusic]

@sathvikbhagavan not sure why but formatting locally doesn't make the check pass

[sathvikbhagavan]

It might be the version. Are you using v1 or v2? CI tries to check in v1

[SouthEndMusic]

That did it 🥳 Btw, is there a way to set compat bounds on packages in your base env?

[ChrisRackauckas]

SciML/.github#25 let's just get that fixed.

[ChrisRackauckas]

Let's update the formatting in a follow up, seems like it takes time to propagate.