Add support for ChangesOfVariables.with_logabsdet_jacobian

[oschulz]

This PR adds support for ChangesOfVariables.test_with_logabsdet_jacobian to functions in LogExpFunctions that already support InverseFunctions.inverse.

This complements #29: InverseFunctions and ChangesOfVariables were designed in tandem (both are extremely lightweight packages) to support variable transformations. Applications that perform variable transformations often need the volume element of the transformation in addition to the result and the inverse of the transformation. ChangesOfVariables.with_logabsdet_jacobian(f, x) delivers that capability, it returns the equivalent of f(x), logabsdet(jacobian(f, x))

With this PR, fun stuff like this works out of the box:

using LogExpFunctions, InverseFunctions, ChangesOfVariables

X = rand(5)
trafo = Base.Fix1(broadcast, logit)

Y, ladj = with_logabsdet_jacobian(trafo, X)

X2, ladj2 = with_logabsdet_jacobian(inverse(trafo), Y)

@assert X ≈ X2 ≈ logistic.(Y) && ladj ≈ -ladj2

Packages like Bijectors that use logistic and logit in transformations can profit directly from implementing with_logabsdet_jacobian in LogExpFunctions (Bijectors will support InverseFunctions and ChangesOfVariables soon, see TuringLang/Bijectors.jl#199).

This PR has no significant effect on the load time of LogExpFunctions (@time using LogExpFunctions showed 0.47 s without and 0.45 s with this PR).

CC @devmotion, @torfjelde, @willtebbutt

[oschulz]

Thanks for the improvements @devmotion . Can you start CI?

[oschulz]

Can you start CI again?

[oschulz]

Looks good.

[devmotion]

Looks good, thanks @oschulz!

[oschulz]

Thanks!