JacVec_VecJac.jl

using ReverseDiff, ForwardDiff
using Test

"""
    vecjac(f, x, v) -> u

``v'J(f(x))``
"""
function vecjac(f, x, v)
    tp = ReverseDiff.InstructionTape()
    tx = ReverseDiff.track(x, tp)
    ty = f(tx)
    ReverseDiff.increment_deriv!(ty, v)
    ReverseDiff.reverse_pass!(tp)
    return ReverseDiff.deriv(tx)'
end
"""
    jacvec(f, x, v) -> u

``J(f(x))*v``
"""
function jacvec(f, x, v)
    du = ForwardDiff.Dual{:___jacvec_tag}.(x, v)
    ForwardDiff.partials.(f(du), 1)
end

f = cumprod
x = rand(300)
v = rand(300)

@test jacvec(f, x, v) ≈ ForwardDiff.jacobian(f, x)*v
@test vecjac(f, x, v) ≈ v'ForwardDiff.jacobian(f, x)