Add test_with_logabsdet_jacobian

[oschulz]

No description provided.

[devmotion]

IMO the tests should be simplified and users should just provide a suitable Jacobian function. The implementation seems too complicated to me, and I assume it could still fail for types of x that are not covered here explicitly.

[codecov]

Codecov Report

Merging #2 (cabe46d) into master (cb0d3b1) will decrease coverage by 15.55%.
The diff coverage is 100.00%.

@@             Coverage Diff              @@
##            master       #2       +/-   ##
============================================
- Coverage   100.00%   84.44%   -15.56%     
============================================
  Files            1        2        +1     
  Lines           31       45       +14     
============================================
+ Hits            31       38        +7     
- Misses           0        7        +7     

Impacted Files	Coverage Δ
src/with_ladj.jl	77.41% <ø> (-22.59%)	⬇️
src/test.jl	100.00% <100.00%> (ø)

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[oschulz]

IMO the tests should be simplified and users should just provide a suitable Jacobian function.

Yes, simpler and more lightweight now with the optional rv_and_back argument (and this way users can just plug in functions like ParameterHandling.flatten in many cases - once that one learns to support dual numbers).

[oschulz]

Fine with you like this, @devmotion ?

[devmotion]

I think it's still too confusing, I don't get what exactly one has to do even after reading the code and the docstring multiple times 😄 Can't we just drop the back stuff completely and let users just specify a function that computes the Jacobian returned by with_logabsdet_jacobian as second argument properly?

(BTW the AD vector + back functionality already exists as FiniteDifferences.to_vec: https://github.com/JuliaDiff/FiniteDifferences.jl/blob/main/src/to_vec.jl, so I don't think one should push for its support in ParameterHandling too hard)

[oschulz]

I think it's still too confusing [...] specify a function that computes the Jacobian returned by with_logabsdet_jacobian as second argument properly?

All right, you win. :-) How about now?

(BTW the AD vector + back functionality already exists as FiniteDifferences.to_vec:

Oh, right! Yes, it really think it's a fundamental thing, I think (hence JuliaGaussianProcesses/ParameterHandling.jl#43).

[oschulz]

Ok, doctests for example are in too now. Good with you, @devmotion ? If so, would release a v0.1.1 based on this and then prepare a PR on LogExpFunctions to support InverseFunctions and ChangesOfVariables.