Just a note to avoid confusion: ForwardDiff.jl doesn't use complex numbers at all. It uses its own implementation of dual number/hyper-dual number "ensembles" for computing multiple partial derivatives simultaneously. There is no additional error term in ForwardDiff.jl's formulation.
-- Jarrett On Tuesday, September 29, 2015 at 12:21:26 AM UTC-4, Rob J Goedman wrote: > > Hi Nitin, > > Thanks for the note and references. The recent upgrade of ForwardDiff.jl > certainly shows the value of these methods. > > Did you (re-)implement MultiComplexNumbers from the 2nd reference, or used > one of the two (Fortran and Matlab) prototype modules? Did you use it from > within Julia? Do you know the license that comes with the implementation > you used? > > Sorry for all the questions! > > Regards, > Rob > > > On Sep 28, 2015, at 18:11, Nitin Arora <nitin...@gmail.com <javascript:>> > wrote: > > There is another method to calculate any order derivatives, very similar > to this one, known as Multi-complex differentiation. This method can > calculate derivatives up-to any order. > > > http://www.autodiff.org/Docs/euroad/13rd%20EuroAd%20Workshop%20-%20Thierry%20Dargent%20-%20Using%20Multicomplex%20Variables%20for%20Automatic%20Computation%20of%20High-Order%20Derivatives.pdf > > > http://delivery.acm.org/10.1145/2170000/2168774/a16-lantoine.pdf?ip=207.151.221.1&id=2168774&acc=ACTIVE%20SERVICE&key=6405B83BDA580DC2%2E4D4702B0C3E38B35%2E4D4702B0C3E38B35%2E4D4702B0C3E38B35&CFID=717380051&CFTOKEN=25446753&__acm__=1443489222_ee3f3d4c7ee41030aaba536e14d6a6ab > > I have used this in my field and it seems to work nicely. > > thanks, > Nitin > > On Saturday, March 29, 2014 at 5:43:05 PM UTC-7, Rob J Goedman wrote: >> >> Hi, >> >> As a first 'jump into the fray' exercise I've attempted to translate >> Jeffrey Fike's hyper-dual numbers code from c++ to Julia, more or less >> following the DualNumbers package. >> >> The c++ code can be found at >> http://adl.stanford.edu/hyperdual/hyperdual.h . The paper itself at >> http://adl.stanford.edu/hyperdual/Fike_AIAA-2011-886.pdf . >> >> The Julia package can be found at: >> https://github.com/goedman/HyperDualNumbers.jl.git . >> >> Of course, I'm pretty new at this so I'm sure there will be errors and >> poor practices. So any feedback is appreciated. >> >> Also, I'm wondering if the type should be called Hyper or a better name >> would be HyperDual. >> >> This work was triggered by the interesting threads around openPP, >> TaylorSeries.jl, Calculus2, PowerSeries.jl (and at some time I hope >> MCMC.jl). >> >> Rob J. Goedman >> goe...@icloud.com >> >> >> >> >>
