Make distances autodiffable

[kskyten]

Basically I just changed the AbstractFloat types to Real for ForwardDiff and ReverseDiff compatibility. The tests still pass. Is there some reason to use the AbstractFloat type?

I just did the following quick check for AD functionality.

using Distances
import ForwardDiff
import ReverseDiff

X = rand(3, 10);
f(w) = sum(pairwise(WeightedSqEuclidean(w), X))
df(w) = ForwardDiff.gradient(f, w)
df2(w) = ReverseDiff.gradient(f, w)

df([1., 2., 3.])
df2([1., 2., 3.])

How do I verify that the AD is working properly? ReverseDiff documentation says that mutation of the input is not allowed. There are some updating assignments in the code, but as far as I know these are not mutations in Julia. Is it safe to assume that if I get results, they are correct (i.e. I wont get wrong results silently)?

[KristofferC]

Could put a test dependency on forwarddiff, and use it to test that AD works. Then use either analytic or numeric differentiation to test for correctness.

[ararslan]

Bump! Still to do here:

• Fix conflicts (in particular this will require switching parametric syntaxes)
• Add correctness tests

Once that's done we'll be good to go. Thanks for the contribution!

[KristofferC]

Should be fixed in #74