Revamp batch size handling

[gdalle]

Versions

• Bump DI to v0.6.13

DI source

• Define BatchSizeSettings to store every necessary information about batches:
  • batch size B
  • whether we need a single batch or several
  • whether the batch size is aligned with the input size (zero remainder)
• Revamp jacobian and hessian to use these BatchSizeSettings. Add a custom out-of-place jacobian and hessian for the single-batch case which does not use mapreduce
• Add reasonable batch size selector borrowed from ForwardDiff, to use in Enzyme so that x = ones(17) requires 2 batches of 9 instead of 2 batches of 16.
• Throw errors on traits and batch size selection for AutoSparse and SecondOrder

DI extensions

• ForwardDiff (and PolyesterForwardDiff): Implement BatchSizeSettings
• Enzyme: Implement BatchSizeSettings
• StaticArrays:
  • Implement custom row stacking (only column stacking was available so far)
  • Override BatchSizeSettings for x::StaticArray and backend::Union{AutoForwardDiff{nothing},AutoEnzyme} to take batch size = input length
• SparseMatrixColorings:
  • Revamp jacobian and hessian to use BatchSizeSettings
  • Perform batch size selection based on the number of groups, not the total number of dimensions!!!

DI docs

• Discuss batching in the advanced explanations

DIT source

• Improve scenario batch size thresholding

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 96.60194% with 7 lines in your changes missing coverage. Please review.

Project coverage is 97.48%. Comparing base (fd7580c) to head (0e43dd5).

Files with missing lines	Patch %	Lines
...fferentiationInterface/src/first_order/jacobian.jl	93.47%	3 Missing ⚠️
...DifferentiationInterfacePolyesterForwardDiffExt.jl	33.33%	2 Missing ⚠️
...raysExt/DifferentiationInterfaceStaticArraysExt.jl	71.42%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #575      +/-   ##
==========================================
- Coverage   97.52%   97.48%   -0.04%     
==========================================
  Files         108      109       +1     
  Lines        4970     5050      +80     
==========================================
+ Hits         4847     4923      +76     
- Misses        123      127       +4     

Flag	Coverage Δ
DI	98.59% <96.46%> (-0.09%)	⬇️
DIT	95.17% <100.00%> (+0.01%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.