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The Stan Math Library is a C++, reverse-mode automatic differentiation library designed to be usable, extensive and extensible, efficient, scalable, stable, portable, and redistributable in order to facilitate the construction and utilization of algorithms that utilize derivatives.



The Stan Math Library is licensed under the new BSD license.

Required Libraries

Stan Math depends on four libraries:

These are distributed under the lib/ subdirectory. Only these versions of the dependent libraries have been tested with Stan Math.


The Stan Math Library is largely a header-only C++ library, with exceptions for the Sundials code.

A simple hello world program using Stan Math is as follows:

#include <stan/math.hpp>
#include <iostream>

int main() {
  std::cout << "log normal(1 | 2, 3)="
            << stan::math::normal_log(1, 2, 3)
            << std::endl;

If this is in the file /path/to/foo/foo.cpp, then you can compile and run this with something like this, with the path/to business replaced with actual paths:

> cd /path/to/foo
> clang++ -std=c++11 -I /path/to/stan-math -I /path/to/Eigen -I /path/to/boost -I /path/to/sundials foo.cpp
> ./a.out
log normal(1 | 2, 3)=-2.07311

The -I includes provide paths pointing to the four necessary includes:

  • Stan Math Library: path to source directory that contains stan as a subdirectory
  • Eigen C++ Matrix Library: path to source directory that contains Eigen as a subdirectory
  • Boost C++ Library: path to source directory that contains boost as a subdirectory
  • SUNDIALS: path to source directory that contains cvodes and idas as a subdirectory

Note that the paths should not include the final directories stan, Eigen, or boost on the paths. An example of a real instantiation:

clang++ -std=c++11 -I ~/stan-dev/math -I ~/stan-dev/math/lib/eigen_3.3.3/ -I ~/stan-dev/math/lib/boost_1.66.0/ -I ~/stan-dev/math/lib/sundials_3.1.0/include foo.cpp

The following directories all exist below the links given to -I: ~/stan-dev/math/stan and ~/stan-dev/math/lib/eigen_3.3.3/Eigen and ~stan-dev/math/lib/boost_1.66.0/boost and ~stan-dev/math/lib/sundials_3.1.0/include.

Other Compilers

There's nothing special about clang++ --- the g++ compiler behaves the same way. You'll need to modify the commands for other compilers, which will need to be up-to-date enough to compile the Stan Math Library.