Mixed-mode sparse Jacobians

[gdalle]

Implement a new MixedMode backend which allows computing sparse Jacobians with a combination of forward and reverse modes.

---

DI source

• Define MixedMode(forward, reverse) to store a combination of forward mode and reverse mode backends.
• Implement a few traits and getters.

DI extensions

• SparseMatrixColorings: Implement sparse Jacobian for MixedMode backends by computing two compressed matrices Br and Bc from a bidirectional coloring. Each sub-backend (forward and reverse) has its own separate process, the only common part is the joint decompression from SMC.

DI tests

• Test MixedMode on sparse Jacobian scenarios.

DIT source

• Tweak compatibility tests and batch size adaptation for new modes.

Chores

• Bump DI to v0.6.22
• Bump DIT to v0.8.5
• Bump both their SMC compats to v0.4.9 (the release implementing bicoloring)

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 94.18605% with 5 lines in your changes missing coverage. Please review.

Project coverage is 98.29%. Comparing base (efb5acf) to head (42b7ff6).
Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
DifferentiationInterface/src/utils/batchsize.jl	50.00%	2 Missing ⚠️
DifferentiationInterface/src/utils/check.jl	0.00%	2 Missing ⚠️
DifferentiationInterface/src/utils/traits.jl	75.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #554      +/-   ##
==========================================
- Coverage   98.39%   98.29%   -0.11%     
==========================================
  Files         107      109       +2     
  Lines        4739     4813      +74     
==========================================
+ Hits         4663     4731      +68     
- Misses         76       82       +6     

Flag	Coverage Δ
DI	98.47% <94.04%> (-0.16%)	⬇️
DIT	97.90% <100.00%> (+<0.01%)	⬆️

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[codecov]

Codecov Report

Attention: Patch coverage is 94.62366% with 5 lines in your changes missing coverage. Please review.

Project coverage is 97.71%. Comparing base (3094dca) to head (d4f85f9).
Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
...erentiationInterfaceTest/src/scenarios/scenario.jl	37.50%	5 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #554      +/-   ##
==========================================
- Coverage   97.77%   97.71%   -0.06%     
==========================================
  Files         110      112       +2     
  Lines        5439     5522      +83     
==========================================
+ Hits         5318     5396      +78     
- Misses        121      126       +5     

Flag	Coverage Δ
DI	98.95% <100.00%> (+0.02%)	⬆️
DIT	95.35% <37.50%> (-0.25%)	⬇️

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

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