Any plans for adjoint operators?

[JeffFessler]

Is there a plan to provide adjoint operators for the interpolators here?

Currently I am using
https://github.com/emmt/LinearInterpolators.jl
because it provides adjoints.

But of course I'd like the best of both worlds: speed and adjoints.

(Note to self: If I have time, I'd like to extend the speed comparison to compare to that package too btw.)

[mgyoo86]

Thanks for the interest — this is a really nice idea.

Funny timing: I actually just released v0.4.0, and it now supports the duck-typing, so computing adjoints via AD (AutoDiff) become possible. The details are documented here: . 📖 Adjoint-via-AD

This AD workaround might not cover everything you need yet, but I hope this can be a basic starting point. Please give it a try, and I would appreciate any feedbacks.

A more native adjoint-focused API also seems technically feasible and would likely be a nice addition. If you’d like (and if it’s easy), could you share a small example of your typical workflow—even a simplified case? That would help a lot when thinking through the API design and later setting performance targets/benchmarks.

[JeffFessler]

Thanks for the quick reply and the nice documentation on adjoint-via-AD. I was actually going to try that but you did it already!

My primary use case is SPECT image reconstruction, which is an inverse problem where the (linear) forward model includes an interpolator as part of an image rotation step, and we need the adjoint of that operator. Here's the repo:
https://github.com/JuliaImageRecon/SPECTrecon.jl

The details are here, where the A' in mul! is the adjoint of the interpolator from the package linked above
https://github.com/JuliaImageRecon/SPECTrecon.jl/blob/11cc7e3111e7a02ac988b21c54d38d3f61273718/src/rotatez.jl#L407-L411

I will make a MWE and do some timing tests and get back to you.

[mgyoo86]

v0.4.2 has just been released with native Adjoint API and AD support for cubic interpolation.
I’m leaving this issue open for now since linear interpolation is still not supported yet and seems to be the main use case here.
Please feel free to try it out and let us know if you notice anything unexpected.

Support for linear and the other methods is planned for future releases.

[mgyoo86]

FYI, v0.4.5 has been released — this issue is now fully resolved.

All four interpolant types now have complete adjoint support:

• Native adjoint operators: constant_adjoint, linear_adjoint, quadratic_adjoint, cubic_adjoint — matrix-free Wᵀȳ in both 1D and ND
• AD integration: Zygote and Enzyme rrules registered for all four types (1D + ND), using the native adjoint operators internally

This should cover the most use cases (inverse problems, data fitting, etc.).
If you run into any edge cases where the rrules don't fire correctly or produce unexpected results, please open a new issue and I'll look into it.

CC @stevengj @lxvm — adjoint support has been generalized beyond cubic to all interpolant types, in case useful for your workflows.

[lxvm]

Thanks @mgyoo86 ! I've wrapped the cubic and linear interpolants and adjoints into a SciML-like API and so far it is working really well.
https://github.com/NanoComp/SSP/pull/2/changes#diff-7f8e8be3fa4bc565b0838c4540fdceb1388a9d4c3b2b6607ba16e1c96b601e8cR1-R201