Re: Algorithmic Differentiation (Using a C++ library)

[Joel Dahne]

Brad Bell writes:

> What is the advantage of re-programming Taylor arithmetic in Octave as
> apposed to using
>      CppAD::AD< IntervalType >
> where IntervalType is a C++ interval type ?
>
> On 03/08/2017 01:27 PM, Joel Dahne wrote:
> ... snip ...
>> Hi,
>>
>> One way to implement automatic differentiation would be to do it with
>> Taylor arithmetic. For single variable functions this would allow for
>> computing arbitrarily order derivatives in an effective way. It can also
>> be generalized to multi-variable functions but I am not sure how much
>> work this is (though two variables should be no problem). This also fits
>> nicely with Olivers idea of integrating it with the interval
>> package. Taylor expansions are very suitable for evaluation with
>> integrals, one example of this can be found in [1]. Adding that
>> functionality to Octave would allow for very powerful interval methods.
>>
>> I have created a proof-of-concept implementation of Taylor arithmetic
>> which is available at GitHub, [2]. So far it implements a constructor
>> and some basic operations, +, -, .*, ./, exp, log, .^, sin and cos. As
>> of yet there is no functions to actually make use of the result. It is
>> meant to work with the interval package and should then generate
>> guaranteed results.
>>
>> I would be very interested in continuing this work as a
>> GSoC-student. Especially I am interested it developing it alongside the
>> interval package, it is in this environment I have used Taylor
>> arithmetic it before.
>>
>> Regards,
>> Joel Dahne
>>
>> [1] http://www2.math.uni-wuppertal.de/~xsc/preprints/prep_05_4.pdf
>> [2] https://github.com/Urathai/octave-taylor-POC
>>

That might be another possibility, I am not familiar enough with CppAD
to know how well it would work. I do think however that it might be hard
to get proper support for Octaves interval-type, especially the
decorated intervals.

Regards,
Joel Dahne