Home > Science > Math > Numerical Analysis > Automatic Differentiation
From Wikipedia, the free encyclopedia ------ In mathematics and computer algebra, automatic differentiation, or AD, sometimes alternatively called algorithmic differentiation, is a method to numerically evaluate the derivative of a function specified by a computer program. [...] AD exploits the fact that any computer program that implements a vector function y = F(x) (generally) can be decomposed into a sequence of elementary assignments, any one of which may be trivially differentiated by a simple table lookup. These elemental partial derivatives, evaluated at a particular argument, are combined in accordance with the chain rule from derivative calculus to form some derivative information for F (such as gradients, tangents, the Jacobian matrix, etc.). This process yields exact (to numerical accuracy) derivatives. ------ This also means that AD can only be applied to augment an existing computer program to make it calculate derivatives in addition to usual results. There are two different implementation strategies for AD (Source transformation and Operator overloading) which are used in so called AD tools to modify the source code in question.
http://www.autodiff.org/
Overview, resources and examples on Automatic Differentiation, as well as and index of conferences and publications.
http://www.bt.pa.msu.edu/index_cosy.htm
A system for the use of automatic differentiation and Taylor Models in Fortran and C++, developed by the Michigan State University, USA. While site contains links to manual and description, the tool is only available through registration.
http://www.coin-or.org/CppAD/
A Package for Differentiation of C++ Algorithms developed by the COmputational INfrastructure for Operations Research (COIN-OR) project. Windows and Linux Binaries are available for download as well as documentation and source code.
http://www.fastopt.de/
Company provides tools for Automatic Differentiation and their application in Geoscience, Economics, Engineering and Mathematics. Home of the commercial tools TAF (Fortran) and TAC++ (C++).
http://www.ti3.tu-harburg.de/rump/intlab/
INTerval LABoratory is the Matlab toolbox for self-validating algorithms, developed by the Hamburg University of Technology, Germany. Along with examples and related publications, the source code can be downloaded freely for private and academic use. Commercial applications require a license.
http://www-unix.mcs.anl.gov/~utke/OpenAD/
A flexible, modular, open source tool that can generate adjoint codes of numerical simulation programs written in C and Fortan. Along with examples, case studies, documentation and related publications, Test Binaries can be downloaded from freely from CVS tree.
http://autodiff.com/tamc/
A source-to-source translator that generates Fortran routines for computation of the first-order derivatives out of Fortran routines. Site contains documentation and references to publications. Usage is restricted to non-commercial and educational applications remotely via email.
http://en.wikipedia.org/wiki/Automatic_differentiation
In mathematics and computer algebra, automatic differentiation is a method to numerically evaluate the derivative of a function specified by a computer program.
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