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‎README.md

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<a href="https://github.com/codespaces/new?hide_repo_select=true&ref=main&repo=563952901&machine=standardLinux32gb&devcontainer_path=.devcontainer%2Fdevcontainer.json&location=EastUshttps://github.com/codespaces/new?hide_repo_select=true&ref=main&repo=563952901&machine=standardLinux32gb&devcontainer_path=.devcontainer%2Fdevcontainer.json&location=EastUs"><img src="https://github.com/codespaces/badge.svg" alt="Open in GitHub Codespaces" /></a>
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</p>
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Please see [Documentation](https://juliadiff.org/TaylorDiff.jl) and [Benchmarks](https://benchmark.tansongchen.com/TaylorDiff.jl) for more information.
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[TaylorDiff.jl](https://github.com/JuliaDiff/TaylorDiff.jl) is an automatic differentiation (AD) package for efficient and composable higher-order derivatives, implemented with operator-overloading on Taylor polynomials.
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Disclaimer: this project is still in early alpha stage, and APIs can change any time in the future. Discussions and potential use cases are extremely welcome!
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## Features
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TaylorDiff.jl is designed with the following goals in head:
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- Linear scaling with the order of differentiation (while naively composing first-order differentiation would result in exponential scaling)
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- Same performance with [ForwardDiff.jl](https://github.com/JuliaDiff/ForwardDiff.jl) on first order and second order, so there is no penalty in drop-in replacement
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- Capable for calculating exact derivatives in physical models with ODEs and PDEs
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- Composable with other AD systems like [Zygote.jl](https://github.com/FluxML/Zygote.jl), so that the above models evaluated with TaylorDiff can be further optimized with gradient-based optimization techniques
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TaylorDiff.jl is fast! See our dedicated [benchmarks](https://benchmark.tansongchen.com/TaylorDiff.jl) page for comparison with other packages in various tasks.
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## Installation
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```bash
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] add TaylorDiff
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```
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## Usage
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```julia
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using TaylorDiff
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x = 0.1
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derivative(sin, x, 10) # scalar derivative
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v, direction = [3.0, 4.0], [1.0, 0.0]
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derivative(x -> sum(exp.(x)), v, direction, 2) # directional derivative
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```
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Please see our [documentation](https://juliadiff.org/TaylorDiff.jl) for more details.
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## Related Projects
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- [TaylorSeries.jl](https://github.com/JuliaDiff/TaylorSeries.jl): a systematic treatment of Taylor polynomials in one and several variables, but its mutating and scalar code isn't great for speed and composability with other packages
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- [ForwardDiff.jl](https://github.com/JuliaDiff/ForwardDiff.jl): well-established and robust operator-overloading based forward-mode AD, where higher-order derivatives can be achieved by nesting first-order derivatives
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- [Diffractor.jl](https://github.com/PumasAI/SimpleChains.jl): next-generation source-code transformation based forward-mode and reverse-mode AD, designed with support for higher-order derivatives in mind; but the higher-order functionality is currently only a proof-of-concept
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- [`jax.jet`](https://jax.readthedocs.io/en/latest/jax.experimental.jet.html): an experimental (and unmaintained) implementation of Taylor-mode automatic differentiation in JAX, sharing the same underlying algorithm with this project
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## Citation
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```bibtex
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@software{tan2022taylordiff,
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author = {Tan, Songchen},
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title = {TaylorDiff.jl: Fast Higher-order Automatic Differentiation in Julia},
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year = {2022},
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publisher = {GitHub},
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journal = {GitHub repository},
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howpublished = {\url{https://github.com/JuliaDiff/TaylorDiff.jl}}
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}
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```

‎benchmark/runbenchmarks.jl

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branch = headname(repo)
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config = BenchmarkConfig(id = branch)
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results = benchmarkpkg(TaylorDiff, config)
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results.name = "TaylorDiff.jl"
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endpoint = "https://benchmark.tansongchen.com"
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put(endpoint; body = json(results))
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end

‎docs/src/index.md

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# TaylorDiff.jl
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[TaylorDiff.jl](https://github.com/JuliaDiff/TaylorDiff.jl) is an automatic differentiation (AD) library for efficient and composable higher-order derivatives, implemented with forward evaluation of overloaded function on Taylor polynomials. It is designed with the following goals in head:
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[TaylorDiff.jl](https://github.com/JuliaDiff/TaylorDiff.jl) is an automatic differentiation (AD) package for efficient and composable higher-order derivatives, implemented with operator-overloading on Taylor polynomials.
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Disclaimer: this project is still in early alpha stage, and APIs can change any time in the future. Discussions and potential use cases are extremely welcome!
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## Features
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TaylorDiff.jl is designed with the following goals in head:
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- Linear scaling with the order of differentiation (while naively composing first-order differentiation would result in exponential scaling)
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- Same performance with [ForwardDiff.jl](https://github.com/JuliaDiff/ForwardDiff.jl) on first order, so there is no penalty in drop-in replacement
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- Same performance with [ForwardDiff.jl](https://github.com/JuliaDiff/ForwardDiff.jl) on first order and second order, so there is no penalty in drop-in replacement
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- Capable for calculating exact derivatives in physical models with ODEs and PDEs
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- Composable with other AD systems like [Zygote.jl](https://github.com/FluxML/Zygote.jl), so that the above models evaluated with TaylorDiff can be further optimized with gradient-based optimization techniques
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This project is still in early alpha stage, and APIs can change any time in the future. Discussions and potential use cases are extremely welcome!
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TaylorDiff.jl is fast! See our dedicated [benchmarks](https://benchmark.tansongchen.com/TaylorDiff.jl) page for comparison with other packages in various tasks.
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## Installation
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```bash
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] add TaylorDiff
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```
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## Usage
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# Related Projects
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```julia
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using TaylorDiff
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This project start from [TaylorSeries.jl](https://github.com/JuliaDiff/TaylorSeries.jl) and re-implement the Taylor mode automatic differentiation primarily for high-order differentiation in solving ODEs and PDEs.
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x = 0.1
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derivative(sin, x, 10) # scalar derivative
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v, direction = [3.0, 4.0], [1.0, 0.0]
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derivative(x -> sum(exp.(x)), v, direction, 2) # directional derivative
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```
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Please see our [documentation](https://juliadiff.org/TaylorDiff.jl) for more details.
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## Related Projects
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- [TaylorSeries.jl](https://github.com/JuliaDiff/TaylorSeries.jl): a systematic treatment of Taylor polynomials in one and several variables, but its mutating and scalar code isn't great for speed and composability with other packages
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- [ForwardDiff.jl](https://github.com/JuliaDiff/ForwardDiff.jl): well-established and robust operator-overloading based forward-mode AD, where higher-order derivatives can be achieved by nesting first-order derivatives
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- [Diffractor.jl](https://github.com/PumasAI/SimpleChains.jl): next-generation source-code transformation based forward-mode and reverse-mode AD, designed with support for higher-order derivatives in mind; but the higher-order functionality is currently only a proof-of-concept
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- [`jax.jet`](https://jax.readthedocs.io/en/latest/jax.experimental.jet.html): an experimental (and unmaintained) implementation of Taylor-mode automatic differentiation in JAX, sharing the same underlying algorithm with this project
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## Citation
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```bibtex
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@software{tan2022taylordiff,
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author = {Tan, Songchen},
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title = {TaylorDiff.jl: Fast Higher-order Automatic Differentiation in Julia},
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year = {2022},
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publisher = {GitHub},
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journal = {GitHub repository},
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howpublished = {\url{https://github.com/JuliaDiff/TaylorDiff.jl}}
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}
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```

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