JuliaApproximation / JuliaApproximation/ApproxFun.jl

Spline basis for data interpolation.

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Julia
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Description

Hello! I'm trying to use ApproxFun for some Functional Data Analysis, as it has a lot of quite nice features for the work I'm doing.

From other issues, I see that I can use ApproxFun.transform to fit some data to a certain space.
For example, using one of the samples I'm working with, obtain the following fit.

Fun(Chebyshev(-1..1), ApproxFun.transform(Chebyshev(-1..1), reverse(tecator[:,1])))

image

However, for my applications I need to be able to use a prioritise closely fitting the data. Looking at Interpolations.jl it seems to be quite helpful for this.

Using a spline, I get:
image

This is much more useful for my purposes.

Would it be possible for me to use this as a basis?

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Research direction

Start with the ApproxFun.transform and Chebyshev examples shown in the issue, then compare the desired spline behavior with the Interpolations.jl example. Define what a supported spline basis would need to provide and how completion would be demonstrated by fitting the sample data more closely.

Written by the indexing model from the issue text.

Assessment

Tech stack
julia
Domain
data
Issue type
Feature
Difficulty
5/5
Estimated time
Over a week
Activity status
Stale
Clarity
Needs clarification
Newbie friendliness
35/100

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