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Warning: Please read this issue before attempting nested differentiation with ForwardDiff.

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.

Here's a simple example showing the package in action:

julia> using ForwardDiff

julia> f(x::Vector) = sum(sin, x) + prod(tan, x) * sum(sqrt, x);

julia> x = rand(5) # small size for example's sake
5-element Array{Float64,1}:
 0.986403
 0.140913
 0.294963
 0.837125
 0.650451

julia> g = x -> ForwardDiff.gradient(f, x); # g = ∇f

julia> g(x)
5-element Array{Float64,1}:
 1.01358
 2.50014
 1.72574
 1.10139
 1.2445

julia> ForwardDiff.hessian(f, x)
5x5 Array{Float64,2}:
 0.585111  3.48083  1.7706    0.994057  1.03257
 3.48083   1.06079  5.79299   3.25245   3.37871
 1.7706    5.79299  0.423981  1.65416   1.71818
 0.994057  3.25245  1.65416   0.251396  0.964566
 1.03257   3.37871  1.71818   0.964566  0.140689

News

• 3/2016: ForwardDiff v0.4.0 has been tagged. There are no API changes, but support for Julia v0.4 has been dropped moving forward.

• 12/2016: ForwardDiff v0.3.0 has been tagged. See our upgrade guide for details regarding user-facing changes.

• 6/2016: ForwardDiff v0.2.0 has been tagged. See our upgrade guide for details regarding user-facing changes.

• 9/2015: We're releasing ForwardDiff v.0.1.0. A lot has changed since the previous version of the package. The best way to get yourself acquainted with the new API is to read our new documentation.

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}
}