JuliaDiff/HyperDualNumbers

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Hyper-dual numbers can be used to compute first and second derivatives numerically without the cancellation errors of finite-differencing schemes.

The initial Julia implementation (up to v3.0.1) is directly based on the C++ implementation by Jeffrey Fike and Juan J Alonso, both of Stanford University, department of Aeronautics and Astronautics as described in the paper:

The Development of Hyper-Dual Numbers for Exact Second Derivative Calculations

Up to v3.0.1 the Julia versions have been derived/written by Rob J Goedman (goedman@icloud.com).

HyperDualNumbers.jl v4.0.0 has been completely redone by Benoit Pasquier and follows the structure of the JuliaDiff/DualNumbers package.

For a quick intro, see STEPBYSTEP.md

Latest tagged versions:

• v1.1.0 (Julia 0.5 & 0.6, Oct 2017)
• v2.0.0 (Julia v0.7-, Oct 2017)
• v3.0.1 (Julia v0.7 & Julia v1.0), Aug 2018, Pkg(3))
• v4.0.0 (Julia v1.0, Nov 2018)
• v4.0.9 (Julia 1.9-DEV, May 2022)

For details see VERSION.md

The following functions are specific to hyperdual numbers:

• Hyper,
• Hyper256,
• Hyper128,
• ishyper,y2
• hyper_show
• realpart,
• ε₁part(), replaces eps1,
• ε₂part(), replaces eps2,
• ε₁ε₂part(), replaces eps1eps2

In the future it is my intention to deprecate:

• hyper,
• hyper256,
• hyper128,
• eps1,
• eps2,
• eps1eps2

• STABLE — documentation of the most recently tagged version.
• DEVEL — documentation of the in-development version.

Question and contributions are very welcome, as are feature requests and suggestions. Please open an issue if you encounter any problems or have a question.