fix jacobian(_, AutoFiniteDiff(fdjtype=Val(:central)))

[oscardssmith]

fixes #983 (comment)
FiniteDiff requires x1==x for central mode autodiff.

[gdalle]

If that's true, this is not the correct fix, because preparation can be reused at different points than the original one. The correct fix would be something like copyto!(prep.cache.x1, x) at the beginning of execution. But this seems like something FiniteDiff should do itself, otherwise the cache is not safe to reuse in FiniteDiff either

[codecov]

Codecov Report

❌ Patch coverage is 0% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 12.35%. Comparing base (a5ecbe0) to head (ec78668).

Files with missing lines	Patch %	Lines
...xt/DifferentiationInterfaceFiniteDiffExt/onearg.jl	0.00%	4 Missing ⚠️

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HEAD has 59 uploads less than BASE

Flag	BASE (a5ecbe0)	HEAD (ec78668)
DIT	12	1
DI	51	3

Additional details and impacted files

@@             Coverage Diff             @@
##             main     #987       +/-   ##
===========================================
- Coverage   98.21%   12.35%   -85.86%     
===========================================
  Files         135      124       -11     
  Lines        8000     7763      -237     
===========================================
- Hits         7857      959     -6898     
- Misses        143     6804     +6661     

Flag	Coverage Δ
DI	6.54% <0.00%> (-92.43%)	⬇️
DIT	27.12% <ø> (-69.11%)	⬇️

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[gdalle]

Also, we would need to fix all operators and add tests

[ChrisRackauckas]

The actual question is just two things, one, are you passing f_in? https://github.com/JuliaDiff/FiniteDiff.jl/blob/master/src/jacobians.jl#L281-L297 If you're passing f(x) but it's the wrong value, yeah that's a problem. If your problem is "but I don't know how to keep it up to date and ..." then... just don't pass it here and let it evaluate it? It's an interface for skipping an f evaluation, and if that interface doesn't apply to DI, then don't use it.

Secondly, the actual issue from the user looks like just uninitialized memory. FiniteDiff doesn't zero things in its non-allocating functions because it assumes the caller has setup the memory appropriately and doesn't touch things it doesn't differentiate. The solution is just to J .= 0.

[oscardssmith]

@ChrisRackauckas the problem isn't the jacobian. It's x1 which when using :central for differentiation is required to be equal to x.