ComplexDiff.jl fully utilize the complex step differentiation to compute accurate and high order derivative.

pkg> add ComplexDiff

While there are round-off error when we are using finite difference to get derivative, by using Complex Step Differentiation, we can obtain extremely high precision derivative.

julia> using ComplexDiff
julia> derivative(sin, 1, 1e-15)
0.5403023058681398

It is also very easy to compute Jacobian matrix and Hessian matrix using complex step differentiation:

julia> jacobian(sin, [1, 2, 3], 0.0000001)
3×3 Matrix{Float64}:
 0.540302   0.0        0.0
 0.0       -0.416147   0.0
 0.0        0.0       -0.989992

If you are also interested in Complex Step Differentiation, please see the following papers:

• Computation of higher-order derivatives using the multi-complex step method

• Using Multicomplex Variables for Automatic Computation of High-Order