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As computational challenges in optimization and statistical inference growever harder, algorithms that utilize derivatives are becoming increasingly moreimportant. The implementation of the derivatives that make these algorithms sopowerful, however, is a substantial user burden and the practicality of thesealgorithms depends critically on tools like automatic differentiation thatremove the implementation burden entirely. The Stan Math Library is a C++,reverse-mode automatic differentiation library designed to be usable, extensiveand extensible, efficient, scalable, stable, portable, and redistributable inorder to facilitate the construction and utilization of such algorithms.  Usability is achieved through a simple direct interface and a cleanlyabstracted functional interface. The extensive built-in library includesfunctions for matrix operations, linear algebra, differential equation solving,and most common probability functions. Extensibility derives from astraightforward object-oriented framework for expressions, allowing users toeasily create custom functions. Efficiency is achieved through a combination ofcustom memory management, subexpression caching, traits-based metaprogramming,and expression templates. Partial derivatives for compound functions areevaluated lazily for improved scalability. Stability is achieved by taking carewith arithmetic precision in algebraic expressions and providing stable,compound functions where possible. For portability, the library isstandards-compliant C++ (03) and has been tested for all major compilers forWindows, Mac OS X, and Linux.

The Stan Math Library: Reverse-Mode Automatic Differentiation in C++