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https://github.com/JuliaDiff/ForwardDiff.jl
Forward Mode Automatic Differentiation for Julia
https://github.com/JuliaDiff/ForwardDiff.jl
automatic-differentiation calculus julia
Last synced: about 2 months ago
JSON representation
Forward Mode Automatic Differentiation for Julia
- Host: GitHub
- URL: https://github.com/JuliaDiff/ForwardDiff.jl
- Owner: JuliaDiff
- License: other
- Created: 2013-04-13T10:19:04.000Z (over 11 years ago)
- Default Branch: master
- Last Pushed: 2024-07-28T11:26:49.000Z (about 2 months ago)
- Last Synced: 2024-07-28T12:44:02.256Z (about 2 months ago)
- Topics: automatic-differentiation, calculus, julia
- Language: Julia
- Homepage:
- Size: 3.32 MB
- Stars: 879
- Watchers: 28
- Forks: 141
- Open Issues: 157
-
Metadata Files:
- Readme: README.md
- License: LICENSE.md
Awesome Lists containing this project
- awesome-sciml - JuliaDiff/ForwardDiff.jl: Forward Mode Automatic Differentiation for Julia
README
[](https://github.com/JuliaDiff/ForwardDiff.jl/actions/workflows/ci.yml)
[](https://coveralls.io/github/JuliaDiff/ForwardDiff.jl?branch=master)
[](https://juliadiff.org/ForwardDiff.jl/stable)
[](https://juliadiff.org/ForwardDiff.jl/dev)
# 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 (such as finite-differencing) in both speed and accuracy.
Here's a simple example showing the package in action:
```julia
julia> using ForwardDiff
julia> f(x::Vector) = sin(x[1]) + prod(x[2:end]); # returns a scalar
julia> x = vcat(pi/4, 2:4)
4-element Vector{Float64}:
0.7853981633974483
2.0
3.0
4.0
julia> ForwardDiff.gradient(f, x)
4-element Vector{Float64}:
0.7071067811865476
12.0
8.0
6.0
julia> ForwardDiff.hessian(f, x)
4×4 Matrix{Float64}:
-0.707107 0.0 0.0 0.0
0.0 0.0 4.0 3.0
0.0 4.0 0.0 2.0
0.0 3.0 2.0 0.0
```
Functions like `f` which map a vector to a scalar are the best case for reverse-mode automatic differentiation,
but ForwardDiff may still be a good choice if `x` is not too large, as it is much simpler.
The best case for forward-mode differentiation is a function which maps a scalar to a vector, like this `g`:
```julia
julia> g(y::Real) = [sin(y), cos(y), tan(y)]; # returns a vector
julia> ForwardDiff.derivative(g, pi/4)
3-element Vector{Float64}:
0.7071067811865476
-0.7071067811865475
1.9999999999999998
julia> ForwardDiff.jacobian(x) do x # anonymous function, returns a length-2 vector
[sin(x[1]), prod(x[2:end])]
end
2×4 Matrix{Float64}:
0.707107 0.0 0.0 0.0
0.0 12.0 8.0 6.0
```
See [ForwardDiff's documentation](https://juliadiff.org/ForwardDiff.jl/stable) for full details on how to use this package.
ForwardDiff relies on [DiffRules](https://github.com/JuliaDiff/DiffRules.jl) for the derivatives of many simple function such as `sin`.
See the [JuliaDiff web page](https://juliadiff.org) for other automatic differentiation packages.
## Publications
If you find ForwardDiff useful in your work, we kindly request that you cite [the following paper](https://arxiv.org/abs/1607.07892):
```bibtex
@article{RevelsLubinPapamarkou2016,
title = {Forward-Mode Automatic Differentiation in {J}ulia},
author = {{Revels}, J. and {Lubin}, M. and {Papamarkou}, T.},
journal = {arXiv:1607.07892 [cs.MS]},
year = {2016},
url = {https://arxiv.org/abs/1607.07892}
}
```