Backend-based AbstractFFTs interface

[nHackel]

Hello @jipolanco,

over at MRIOperators we discussed a limitation of AbstractNFFTs interface. Mainly, its inability to allow for both NFFT and NonuniformFFTs (or any second package) to be loaded at the same time in such a way that a user can chose which NFFT provider/package to use.

I've provided a potential solution to this problem over at this PR and I've implemented the necessary changes for NonuniformFFTs in this PR. I'd be happy to hear your feedback to this approach

[jipolanco]

Hi @nHackel, thank you for proposing these changes to the AbstractNFFTs interface. I'd be happy to make the required changes to adapt to the new interface.

I raised the same issue you mention some time ago, and I think what you propose based on backends is a nice and elegant solution to this problem. If you don't mind, I'll wait for JuliaMath/NFFT.jl#149 to be merged and for AbstractNFFTs.jl v0.9.0 to be released before merging this PR in some form.

As a minor comment, I'd replace NonuniformFFTBackend with NonuniformFFTsBackend (note the extra s) for consistency with the name of this package.

[nHackel]

Hello @jipolanco, I've finally had some time to merge and release AbstractNFFTs v0.9 with the proposed changes and I think this PR is now ready for review

[nHackel]

@jipolanco would it be possible to add the precompute keyword argument here.

Something like:

Base.@constprop :aggressive function NFFTPlan(
        xp::AbstractMatrix{T}, Ns::Dims;
        # working keyword arguments ...
        precompute = nothing,
        kws...,
    ) where {T <: AbstractFloat}

if !isnothing(precompute)
  @warn "Precompute flags are not yet supported and will be ignored"
end

I'm currently propagating the AbstractNFFTs changes up to MRIReco.jl and I'm testing to see if one can just use NonuniformFFTs as a drop-in replacement. So far I am failing on the keyword argument.

I can gladly make a seperate PR for all the changes I'd need for that and then we can decide seperately from this PR

[codecov]

Codecov Report

❌ Patch coverage is 85.71429% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 89.66%. Comparing base (a4b957e) to head (2ee6edd).
⚠️ Report is 3 commits behind head on master.

Files with missing lines	Patch %	Lines
src/abstractNFFTs.jl	80.00%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##           master      #68   +/-   ##
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  Coverage   89.66%   89.66%           
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  Files          24       24           
  Lines        1838     1839    +1     
=======================================
+ Hits         1648     1649    +1     
  Misses        190      190           

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[jipolanco]

@jipolanco would it be possible to add the precompute keyword argument here.

Yes, that would be fine. I would just slightly change the warning message to something like "Precompute flags are not supported by the NonuniformFFTs backend and will be ignored", since I don't think NonuniformFFTs will ever support a precompute option. I will include it in this PR to make things simple.