@(@ \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-20160528: A Package for Differentiation of C++ Algorithms
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# include <cppad/cppad.hpp>

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 is dedicated to research about, and promoting the use of, AD.
  1. 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.
  2. 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).
  3. 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 .
  4. A set of programs for doing speed comparisons between Adolc , CppAD, Fadbad , and Sacado are included.
  5. 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.
  6. 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 , .

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_.

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.

_contentsTable of Contents
InstallCppAD Download, Test, and Install Instructions
IntroductionAn Introduction by Example to Algorithmic Differentiation
ADAD Objects
ADFunADFun Objects
preprocessorCppAD API Preprocessor Symbols
multi_threadUsing CppAD in a Multi-Threading Environment
utilitySome General Purpose Utilities
ipopt_solveUse Ipopt to Solve a Nonlinear Programming Problem
speedSpeed Test an Operator Overloading AD Package
_referenceAlphabetic Listing of Cross Reference Tags
_indexKeyword Index
_searchSearch This Web Site
_externalExternal Internet References

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