FiniteDiffCheck

Checks analytic vs finite difference gradient + hessian using central differencing.
While the Calculus.jl package does
lots more & takes one-sided differences, it won’t do Jacobians (though Calculus2.jl does). Also, FiniteDiffCheck.jl can use AbstractVectors like MVector from StaticArrays.jl.

Example:

using FiniteDiffCheck
function fgh!(x::AbstractVector, dx::AbstractVector, d2x::AbstractMatrix)
    length(x) == 2 || throw(DimensionMismatch())
    f = x[1]^2. + 3.*x[1]*x[2] + x[2]^2.
    if length(dx) > 0
        dx[1] = 2.*x[1] + 3.*x[2]
        dx[2] = 3.*x[1] + 2.*x[2]
    end
    if length(d2x) > 0
        d2x[1,1] = 2.
        d2x[2,1] = 3.
        d2x[1,2] = 3.
        d2x[2,2] = 2.
    end
    return f
end
θ0 = rand(2)
# when defining tmp struct
tmp = jacchecktmp(θ0)
@show out = jac_hess_check!(tmp, fgh!, θ0)
@show all(out .< 3e-10)
# without
@show jac_hess_check(fgh!, θ0)