cppad-20171217: A Package for Differentiation of C++ Algorithms

@(@ \newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} } @)@, cppad-20171217: A Package for Differentiation of C++ Algorithms

	One section per web page	All sections in one web page
	(fast to load)	(slow to load)
Math displayed using MathJax	cppad.htm	_printable.htm
Math displayed using MathML	cppad.xml	_printable.xml

Syntax



# include <cppad/cppad.hpp>

Introduction
We refer to the step by step conversion from an algorithm that computes function values to an algorithm that computes derivative values as Algorithmic Differentiation (often referred to as Automatic Differentiation.) Given a C++ algorithm that computes function values, CppAD generates an algorithm that computes its derivative values. A brief introduction to Algorithmic Differentiation can be found in wikipedia . The web site autodiff.org is dedicated to research about, and promoting the use of, AD.

CppAD uses operator overloading to compute derivatives of algorithms defined in C++. It is distributed by the COIN-OR Foundation with the Eclipse Public License EPL-1.0 or the GNU General Public License GPL-3.0 . Testing and installation is supported for Unix, Microsoft, and Apple operating systems. Extensive user and developer documentation is included.
An AD of Base operation sequence is stored as an AD function object which can evaluate function values and derivatives. Arbitrary order forward and reverse mode derivative calculations can be preformed on the operation sequence. Logical comparisons can be included in an operation sequence using AD conditional expressions . Evaluation of user defined unary discrete functions can also be included in the sequence of operations; i.e., functions that depend on the independent variables but which have identically zero derivatives (e.g., a step function).
Derivatives of functions that are defined in terms of other derivatives can be computed using multiple levels of AD; see mul_level.cpp for a simple example and mul_level_ode.cpp for a more realistic example. To this end, CppAD can also be used with other AD types; for example see mul_level_adolc_ode.cpp .
A set of programs for doing speed comparisons between Adolc , CppAD, Fadbad , and Sacado are included.
Includes a set of C++ utilities that are useful for general operator overloaded numerical method. Allows for replacement of the testvector template vector class which is used for extensive testing; for example, you can do your testing with the uBlas template vector class.
See whats_new for a list of recent extensions and bug fixes.

You can find out about other algorithmic differentiation tools and about algorithmic differentiation in general at the following web sites: wikipedia , autodiff.org .

Example
The file get_started.cpp contains an example and test of using CppAD to compute the derivative of a polynomial. There are many other examples .

Include File
The following include directive



     # include <cppad/cppad.hpp>

includes the CppAD package for the rest of the current compilation unit.

Preprocessor Symbols
All the preprocessor symbols used by CppAD begin with eight CppAD or CPPAD_.

Namespace
All of the functions and objects defined by CppAD are in the CppAD namespace; for example, you can access the AD types as



     size_t n = 2;

     CppAD::vector< CppAD::AD<

Base> > x(n

You can abbreviate access to one object or function a using command of the form



     using CppAD::AD

     CppAD::vector< AD<

Base> > x(n

You can abbreviate access to all CppAD objects and functions with a command of the form



     using namespace CppAD

     vector< AD<

Base> > x(n

If you include other namespaces in a similar manner, this can cause naming conflicts.

Contents

_contents	Table of Contents
Install	CppAD Download, Test, and Install Instructions
Introduction	An Introduction by Example to Algorithmic Differentiation
AD	AD Objects
ADFun	ADFun Objects
preprocessor	CppAD API Preprocessor Symbols
multi_thread	Using CppAD in a Multi-Threading Environment
utility	Some General Purpose Utilities
ipopt_solve	Use Ipopt to Solve a Nonlinear Programming Problem
Example	Examples
speed	Speed Test an Operator Overloading AD Package
Appendix	Appendix
_reference	Alphabetic Listing of Cross Reference Tags
_index	Keyword Index
_search	Search This Web Site
_external	External Internet References

Input File: doc.omh