[Feature Request] Integration procedures for Interpolation and LinearRegression #291

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1. github-actions

   added

   enhancement

   on Mar 23, 2026
2. github-actions

   added a commit that references this issue on Apr 13, 2026

   feat: add integrate function to LinearSpline, Step, and CubicSpline

   ...

   6d91d6c
3. github-actions commented on Apr 13, 2026

   

   github-actionsbot

   on Apr 13, 2026 – with GitHub Actions

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   🤖 This is an automated response from Repo Assist.

   I've created a draft PR implementing several of the integration functions from this checklist. Here's the current status:

   Interpolation

   • Step interpolation — implemented in this PR
   • Akima interpolation — Akima.integrate already existed ✓
   • Hermite interpolation — still missing
   • Polynomial interpolation — Polynomial.integrate already existed ✓
   • Cubic spline interpolation — implemented in this PR

   I also added LinearSpline.integrate (not in the original checklist but a natural addition).

   Regression — these remain unimplemented (simple linear regression, polynomial regression, smoothing spline).

   The PR uses closed-form antiderivatives for all three new functions and includes 5 tests against known analytical results (1198/1198 pass). The Hermite case is more involved since it requires expressing the integral in terms of the cubic Hermite basis functions; happy to tackle that in a follow-up if useful.

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4. annacwe commented on Jul 21, 2026

   

   annacwe

   on Jul 21, 2026

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   PR #375 added functions to calculate definite integrals for LinearSpline, Step, and CubicSpline. Akima also has definite integrals already.
   I also think that for Polynomial interpolation, both the integral function as well as the definite integrals have been added in 6a9038e. Unit tests for that seem to be missing though.

   @bvenn Just to better my understanding going forward, is this issue specifically asking to implement calculations for definite integrals or for integral functions (or both)?
5. bvenn commented on Oct 11, 2026

   

   bvenn

   on Oct 11, 2026

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   @annacwe Originally this issue targeted the solution addressed in e.g. #375 to enable calculation of definite integrals from the given functions. Could you rephrase what you mean with "integral functions"?

   If my understanding is correct the current approach calculates the definite integral via

   let integralValue: float = getIntegralBetween coefficients lowerBound upperBound

   With integral function do you mean:

   let integralFun lowerBound upperBound: (float  -> float -> float) = getIntegral coefficients

   where the integral function itself is returned?

   If so, this could easily be realized using closures and the current implementation

   let integralFun = 
   	fun a b -> getIntegralBetween coefficients a b

   Or do you mean a standard interval starting at 0.0 as integral function?
6. annacwe commented on Oct 11, 2026

   

   annacwe

   on Oct 11, 2026

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   By "integral function" I meant the antiderivative. My thinking was that if the goal was to support both the antiderivative and the calculation of definite integrals, that could influence in what order we approach implementation.

   The question came up because I felt that the existing implementation wasn't entirely consistent.
   For Polynomials, there are both, if I understand correctly:

   • integrate, which returns the coefficients of the antiderivative
   • getIntegral, which computed a definite integral

   Whereas for Akima subsplines:

   • integrate, which returns the integral from 0.0 to xVal
   • definiteIntegral, which returns the integral from xVal1 to xVal2

   And with the solution from #375, there is only the definite integral.

   That's why I was unsure what the overall intention was or whether this is simply the result of a historical development.
7. bvenn commented on Oct 11, 2026

   

   bvenn

   on Oct 11, 2026

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   Okay, now I see you point. It's a valid concern. Naturally I think both would be a great to have.

   Naturally getIntegral a b or integrate a b should be the definite integral between both boundaries. I'm currently don't have a strong opinion regarding the naming. The antiderivative coefficient is a whole new use case that I haven't had in mind. Whatever the member would be called, as you mentioned it just should be coherent across the library