Adept (C++ library)

{{Infobox software

| name = Adept C++ Library

| logo =

| logo size = 300

| developer = Robin Hogan

| latest release version = 2.1.2

| latest release date = {{start date and age|df=yes|paren=yes|2023|10|03}}

| latest preview version =

| latest preview date =

| programming language = C++

| operating system = Cross-platform

| genre = Library

| license = Apache 2.0 (open source)

| website = {{URL|http://www.met.reading.ac.uk/clouds/adept/}}

}}

Adept is a combined automatic differentiation and array software library for the C++ programming language. The automatic differentiation capability facilitates the development of applications involving mathematical optimization. Adept is notable for having applied the template metaprogramming technique of expression templates to speed-up the differentiation of mathematical statements.{{cite journal|last=Hogan|first=Robin J.|title=Fast reverse-mode automatic differentiation using expression templates in C++|journal=ACM Trans. Math. Softw.|year=2014|volume=40|issue=4|pages=26:1–26:16|url=http://www.met.reading.ac.uk/%7Eswrhgnrj/publications/adept.pdf|doi=10.1145/2560359|s2cid=9047237}}{{cite journal|first=Andreas|last=Griewank|year=2014|title=On automatic differentiation and algorithmic linearization|journal=Pesquisa Operacional|volume=34|issue=3|pages=621–645|doi=10.1590/0101-7438.2014.034.03.0621|doi-access=free|s2cid=54059078 }} Along with the efficient way that it stores the differential information, this makes it significantly faster than most other C++ tools that provide similar functionality (e.g. ADOL-C, CppAD and FADBAD),{{cite arXiv|first=Bob|last=Carpenter|title=The Stan Math Library: Reverse-Mode Automatic Differentiation in C++|eprint=1509.07164|class=cs.MS|year=2015}}{{cite web|url=https://www.xcelerit.com/computing-benchmarks/software/aad/|title=Sensitivities in Quantitative Finance: Libor Swaption Portfolio Pricer (Monte-Carlo)|accessdate=2017-10-21|date=2016-12-02}}{{cite thesis|title=Discrete controls and constraints in optimal control problems|type=PhD Thesis|first=Matthias|last=Rieck|publisher=Technical University of Munich|accessdate=2017-10-21|url=https://mediatum.ub.tum.de/doc/1316413/1316413.pdf}}{{cite thesis|title=Stochastic volatility models with applications in finance|url=http://ir.uiowa.edu/cgi/viewcontent.cgi?article=6780&context=etd|archive-url=https://web.archive.org/web/20170718074806/http://ir.uiowa.edu/cgi/viewcontent.cgi?article=6780&context=etd|url-status=dead|archive-date=July 18, 2017|first=Ze|last=Zhao|accessdate=2017-10-27|publisher=University of Iowa}} although comparable performance has been reported for Stan and in some cases Sacado. Differentiation may be in forward mode, reverse mode (for use with a Quasi-Newton minimization scheme), or the full Jacobian matrix may be computed (for use with the Levenberg-Marquardt or Gauss-Newton minimization schemes).

Applications of Adept have included computer functionality in the financial field,{{cite arXiv|first1=Gilles|last1=Pagès|first2=Olivier|last2=Pironneau|first3=Guillaume|last3=Sall|title=Vibrato and automatic differentiation for high order derivatives and sensitivities of financial options|eprint=1606.06143|class=q-fin.CP|year=2016}} computational fluid dynamics,{{cite conference|first1=T.|last1=Albring|first2=M.|last2=Sagebaum|first3=N. R.|last3=Gauger|year=2016|title=A Consistent and Robust Discrete Adjoint Solver for the SU2 Framework—Validation and Application|editor-first=A.|editor-last=Dillmann|editor2-first=G.|editor2-last=Heller|editor3-first=E.|editor3-last=Krämer|editor4-first=C.|editor4-last=Wagner|editor5-first=C.|editor5-last=Breitsamter|series=New Results in Numerical and Experimental Fluid Mechanics X. Notes on Numerical Fluid Mechanics and Multidisciplinary Design|volume=132|publisher=Springer, Cham|doi=10.1007/978-3-319-27279-5_7}} physical chemistry,{{cite journal|first1=Kyle E.|last1=Niemeyer|first2=Nicholas J.|last2=Curtis|first3=Chih-Jen|last3=Sung|title=pyJac: Analytical Jacobian generator for chemical kinetics|journal=Comput. Phys. Commun.|volume=215|year=2017|pages=188–203|arxiv=1605.03262|bibcode=2017CoPhC.215..188N|doi=10.1016/j.cpc.2017.02.004|s2cid=19675513}} parameter estimation{{cite journal|title=Boosting Bayesian parameter inference of nonlinear stochastic differential equation models by Hamiltonian scale separation|first1=Carlo|last1=Albert|first2=Simone|last2=Ulzega|first3=Ruedi|last3=Stoop|journal=Phys. Rev. E|volume=93|issue=43313|pages=043313|year=2016|arxiv=1509.05305|doi=10.1103/PhysRevE.93.043313|pmid=27176434|bibcode=2016PhRvE..93d3313A|s2cid=4479221}} and meteorology.{{cite journal|first1=S.|last1=Mason|first2=J.-C.|last2=Chiu|first3=R. J.|last3=Hogan|first4=D.|last4=Moisseev|first5=S.|last5=Kneifel|title=Retrievals of riming and snow particle density from vertically-pointing Doppler radars|journal=J. Geophys. Res.|volume=123|doi=10.1029/2018JD028603|year=2018|url=http://centaur.reading.ac.uk/80877/1/manuscript.pdf|doi-access=free}} Adept is free software distributed under the Apache License.

Example

Adept implements automatic differentiation using an operator overloading approach, in which scalars to be differentiated are written as adouble, indicating an "active" version of the normal double, and vectors to be differentiated are written as aVector. The following simple example uses these types to differentiate a 3-norm calculation on a small vector: