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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 ([email protected]).
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,y2hyper_showrealpart,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.