From c0e2efe5e1360c6e9a3444afa2798e9d9b551540 Mon Sep 17 00:00:00 2001 From: ouyangjiahong Date: Mon, 19 Oct 2026 11:12:42 +0800 Subject: [PATCH] Add a Chinese translation of the README Adds README.zh-CN.md, a Simplified Chinese translation of README.md, and links between the two files. The Julia code blocks are copied verbatim, so the examples and their output are unchanged; only the prose is translated. No source or CI configuration is affected. --- README.md | 2 ++ README.zh-CN.md | 91 +++++++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 93 insertions(+) create mode 100644 README.zh-CN.md diff --git a/README.md b/README.md index 4e79ddb8..a27c9b56 100644 --- a/README.md +++ b/README.md @@ -4,6 +4,8 @@ [![](https://img.shields.io/badge/docs-stable-blue.svg)](https://juliadiff.org/ForwardDiff.jl/stable) [![](https://img.shields.io/badge/docs-dev-blue.svg)](https://juliadiff.org/ForwardDiff.jl/dev) +[English](README.md) | [简体中文](README.zh-CN.md) + # ForwardDiff.jl ## Upgrading to ForwardDiff.jl 1.0 diff --git a/README.zh-CN.md b/README.zh-CN.md new file mode 100644 index 00000000..74cabcd3 --- /dev/null +++ b/README.zh-CN.md @@ -0,0 +1,91 @@ +[English](README.md) | [简体中文](README.zh-CN.md) + +[![CI](https://github.com/JuliaDiff/ForwardDiff.jl/actions/workflows/ci.yml/badge.svg?branch=master)](https://github.com/JuliaDiff/ForwardDiff.jl/actions/workflows/ci.yml?query=branch%3Amaster) +[![codecov](https://codecov.io/gh/JuliaDiff/ForwardDiff.jl/graph/badge.svg?token=SzHfhyoxUa)](https://codecov.io/gh/JuliaDiff/ForwardDiff.jl) + +[![](https://img.shields.io/badge/docs-stable-blue.svg)](https://juliadiff.org/ForwardDiff.jl/stable) +[![](https://img.shields.io/badge/docs-dev-blue.svg)](https://juliadiff.org/ForwardDiff.jl/dev) + +# ForwardDiff.jl + +> 本文是 [README.md](README.md) 的中文翻译。两者如有出入，以英文原文为准。 + +## 升级到 ForwardDiff.jl 1.0 + +`Dual` 数上的相等比较（`==`）现在要求实部和对偶部都相同（https://github.com/JuliaDiff/ForwardDiff.jl/pull/481）。 +这修复了一大批 bug：这些 bug 源于程序会去检查例如数组中非零值之类的“结构”，从而得到错误的导数。 +这可能会让程序行为略有变化，但总体上比之前更正确。 + +--------------------------- + +ForwardDiff 使用**前向模式自动微分（AD）**，对原生 Julia 函数（实际上对任何可调用对象都适用）计算**导数**、**梯度**、**雅可比矩阵**、**黑塞矩阵**以及更高阶导数。 + +性能会随所计算的函数而变化，但总体而言，ForwardDiff 实现的算法在速度和精度上都优于非 AD 算法（例如有限差分）。 + +下面是一个简单示例： + +```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 +``` + +像 `f` 这样把向量映射为标量的函数，是反向模式自动微分的最佳场景；但如果 `x` 不太大，ForwardDiff 可能仍是更好的选择，因为它简单得多。 +前向模式微分的最佳场景是把标量映射为向量的函数，例如下面的 `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 +``` + +使用说明详见 [ForwardDiff 文档](https://juliadiff.org/ForwardDiff.jl/stable)。 +许多简单函数（例如 `sin`）的导数由 [DiffRules](https://github.com/JuliaDiff/DiffRules.jl) 提供。 + +其他自动微分包见 [JuliaDiff 主页](https://juliadiff.org)。 + +## 论文与引用 + +如果 ForwardDiff 对你的工作有帮助，我们恳请你引用[这篇论文](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} +} +```