Go to ForwardDiff on GitHub

ForwardDiff.jl

ForwardDiff implements methods to take derivatives, gradients, Jacobians, Hessians, and higher-order derivatives of native Julia functions (or any callable object, really) using forward mode automatic differentiation (AD).

While performance can vary depending on the functions you evaluate, the algorithms implemented by ForwardDiff generally outperform non-AD algorithms in both speed and accuracy.

This wikipedia page on automatic differentiation is a useful resource for learning about the advantages of AD techniques over other common differentiation methods (such as finite differencing).

Publications

If you find ForwardDiff useful in your work, we kindly request that you cite the following paper:

@article{RevelsLubinPapamarkou2016,
   title = {Forward-Mode Automatic Differentiation in Julia},
  author = {{Revels}, J. and {Lubin}, M. and {Papamarkou}, T.},
 journal = {arXiv:1607.07892 [cs.MS]},
    year = {2016},
    url = {https://arxiv.org/abs/1607.07892}
}