Add jacobian function

[ChrisRackauckas]

Fixes #98

[CarloLucibello]

needs a test and a mention in the docs

[mcabbott]

This would be good to have, but shouldn't it behave like gradient and return a 1-tuple for one argument? Then the extension to several arguments need not break anything.

[cossio]

Bump? Would be nice to have.

[MasonProtter]

If we split out OneHotVector from Flux.jl, we could have this simpler implementation that's sometimes more performant and has less weird edge cases:

using Flux: OneHotVector

"""
jacobian(f,x)
Construct the Jacobian of `f` where `x` is a real-valued array
and `f(x)` is also a real-valued array.
"""
function jacobian(f, x)
    y, ∂f = Zygote.pullback(f,x)
    n, m  = length(x), length(y)
    mapreduce(i -> ∂f(OneHotVector(i, m)), hcat, 1:m)
end

[DhairyaLGandhi]

Looks good, but needs tests

[DhairyaLGandhi]

Also probably something that should hook into the forward mode

[ChrisRackauckas]

Forward mode Jacobian should be kept as a separate call: which one is better depends on the application so both are required. What this should really connect to is SparseDiffTools for sparse Jacobians, but what will happen there is that SparseDiffTools will have a... more intense version that handles all of that extra machinery.

[DhairyaLGandhi]

This is due to it detecting sparsity patterns I assume?

[ChrisRackauckas]

This is due to it detecting sparsity patterns I assume?

Well this could be made to accept a color vector even without SparseDiffTools.