Thank you very much Jason, great feedback. I will work through your suggestions and make the changes.
In particular the extensibility argument/pattern is something I've been thinking about as well. Regards, Rob J. Goedman goed...@icloud.com On Mar 30, 2014, at 10:09 AM, Jason Merrill <jwmerr...@gmail.com> wrote: > Cool. I took a quick look over the code, and it looks pretty good to me. You > have an inline comment about wanting understand convert/promote better--one > good place to look is promotions.jl in base: > > https://github.com/JuliaLang/julia/blob/master/base/promotion.jl#L158 > > This defines some fairly generic methods for +, -, *, /, etc. that mean "if > there isn't a more specific method for this combination of argument types, > try promoting the arguments to a common type before doing the operation". By > defining convert and promote_rule, you are participating in this system. > > I didn't look carefully at all the promotions/conversions you define, but if > you have the right ones, this will allow e.g. something like Hyper(0.0, 1.0, > 1.0, 2.0) + Hyper(3//5, 1//2, 1//2, 2//7) to work without you ever having had > to write code specific to the Rational type. > > As for the theory, it seems a little funny to me that this technique > redundantly encodes the first derivative, and I can't see an advantage of > using two variables that both square to 0 over using a single variable that > cubes to 0. Since E1 and E2 are used symmetrically, suppose we make the > change of variables e = E1 + E2. Now we have a single variable with e^2 = > 2E1E2, and e^3 = 0, and you could go through everywhere making the > replacements and end up saving yourself one field in your type, and a bit of > redundant arithmetic. > > After the replacement, it's easier to see how to extend to higher derivatives > too. If e^3 = 0 is a variable that helps us compute second derivatives, then > f^4=0 is a variable that helps us compute third derivatives, g^5 = 0 helps us > compute 4th derivatives, and so on. This is the theory behind the truncated > power series in PowerSeries.jl > > Instead of talking about a lot of different variables with special > properties, it's also possible to say that you're working modulo some > polynomial. Dual numbers are equivalent to computing mod x^2, 2nd order > truncated series are equivalent to computing mod x^3, 3rd order series to mod > x^4 and so on. In this way of thinking, complex numbers are polynomials mod > (x^2 + 1), and the split-complex numbers, which come up in the hyperbolic > geometry of the plane, are polynomials mod (x^2 - 1). > > On Saturday, March 29, 2014 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
