Extrapolation options #356

SouthEndMusic · 2024-11-13T17:35:57Z

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 · 2024-11-13T18:47:31Z

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 · 2024-11-14T10:00:26Z

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 · 2024-11-14T11:49:33Z

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 · 2024-11-16T09:07:51Z

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 · 2024-11-16T09:33:54Z

Can you do the refactors in different PRs?

SouthEndMusic · 2024-11-16T09:54:46Z

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 · 2024-11-16T10:10:22Z

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

…ions

SouthEndMusic · 2024-11-18T11:37:57Z

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

docs/src/extrapolation_methods.md

sathvikbhagavan

A few comments

docs/src/extrapolation_methods.md

src/DataInterpolations.jl

src/interpolation_caches.jl

sathvikbhagavan

Almost there. A few minor comments.

sathvikbhagavan · 2024-11-22T19:02:02Z

src/derivatives.jl

-    return if order == 1
-        _derivative(A, t, iguess)
-    elseif order == 2
+function _extrapolate_derivative_down(A, t, order)


Suggested change

function _extrapolate_derivative_down(A, t, order)

function _extrapolate_derivative_left(A, t, order)

sathvikbhagavan · 2024-11-22T19:02:11Z

src/derivatives.jl

+    end
+end
+
+function _extrapolate_derivative_up(A, t, order)


Suggested change

function _extrapolate_derivative_up(A, t, order)

function _extrapolate_derivative_right(A, t, order)

sathvikbhagavan · 2024-11-22T19:04:55Z

src/derivatives.jl

+function _extrapolate_derivative_down(A, t, order)
+    (; extrapolation_left) = A
+    typed_zero = zero(first(A.u) / one(A.t[1]))
+    if extrapolation_left == ExtrapolationType.none


Slightly knit picky, but I think checking this one line above would prevent a few wasteful computation of typed_zero

sathvikbhagavan · 2024-11-22T19:05:28Z

src/integrals.jl

+    return total
+end
+
+function _extrapolate_integral_down(A, t)


Suggested change

function _extrapolate_integral_down(A, t)

function _extrapolate_integral_left(A, t)

sathvikbhagavan · 2024-11-22T19:05:39Z

src/integrals.jl

+    end
+end
+
+function _extrapolate_integral_up(A, t)


Suggested change

function _extrapolate_integral_up(A, t)

function _extrapolate_integral_right(A, t)

sathvikbhagavan · 2024-11-22T19:07:50Z

src/interpolation_methods.jl

+    end
+end
+
+function _extrapolate_down(A, t)


Suggested change

function _extrapolate_down(A, t)

function _extrapolate_left(A, t)

sathvikbhagavan · 2024-11-22T19:07:59Z

src/interpolation_methods.jl

+    end
+end
+
+function _extrapolate_up(A, t)


Suggested change

function _extrapolate_up(A, t)

function _extrapolate_right(A, t)

sathvikbhagavan · 2024-11-22T19:08:27Z

src/interpolation_methods.jl

+
+function _extrapolate_down(A, t)
+    (; extrapolation_left) = A
+    if extrapolation_left == ExtrapolationType.none


Same as derivative/integral comment

sathvikbhagavan · 2024-11-22T19:09:10Z

test/extrapolation_tests.jl

+    test_constant_extrapolation(LinearInterpolation, u, t)
+
+    for extrapolation_type in [ExtrapolationType.linear, ExtrapolationType.extension]
+        # Down extrapolation


Suggested change

# Down extrapolation

# Left extrapolation

sathvikbhagavan · 2024-11-22T19:09:19Z

test/extrapolation_tests.jl

+        @test DataInterpolations.integral(A, t_eval) == -0.5
+        t_eval = 3.0
+
+        # Up extrapolation


Suggested change

# Up extrapolation

# Right extrapolation

QuadraticSpline POC

b1a751f

SouthEndMusic marked this pull request as draft November 13, 2024 17:36

SouthEndMusic changed the title ~~QuadraticSpline POC~~ Extrapolation options Nov 13, 2024

SouthEndMusic added 3 commits November 14, 2024 07:04

nit

76859cd

Use enumx for extrapolation types

832ca31

Derivative extrapolation POC

ea91f76

SouthEndMusic added 5 commits November 14, 2024 12:50

Integral extrapolation POC

f0efd0e

Apply extrapolation options to all interpolation types

154b755

Fix tests

b1e4bb7

Add docs page

3b3b626

Add some tests, refactor most of integration

c6ab856

SouthEndMusic mentioned this pull request Nov 16, 2024

Refactor integration and QuadraticInterpolation #359

Merged

SouthEndMusic added 2 commits November 17, 2024 14:45

Merge remote-tracking branch 'upstream/master' into extrapolation_opt…

d71ef72

…ions

Complete tests

a562bf7

SouthEndMusic marked this pull request as ready for review November 17, 2024 16:01

Formatting

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sathvikbhagavan reviewed Nov 19, 2024

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SouthEndMusic requested a review from sathvikbhagavan November 22, 2024 11:17

SouthEndMusic mentioned this pull request Nov 22, 2024

Add extrapolation types periodic and reflective #363

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Extrapolation options #356

Extrapolation options #356

SouthEndMusic commented Nov 13, 2024 •

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	function _extrapolate_derivative_down(A, t, order)
	function _extrapolate_derivative_left(A, t, order)

	function _extrapolate_derivative_up(A, t, order)
	function _extrapolate_derivative_right(A, t, order)

	function _extrapolate_integral_down(A, t)
	function _extrapolate_integral_left(A, t)

	function _extrapolate_integral_up(A, t)
	function _extrapolate_integral_right(A, t)

	function _extrapolate_down(A, t)
	function _extrapolate_left(A, t)

	function _extrapolate_up(A, t)
	function _extrapolate_right(A, t)

Extrapolation options #356

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Extrapolation options #356

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SouthEndMusic commented Nov 13, 2024 • edited Loading

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SouthEndMusic commented Nov 13, 2024 •

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