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The Stan Math Library is a C++ template library for automatic differentiation of any order using forward, reverse, and mixed modes. It includes a range of built-in functions for probabilistic modeling, linear algebra, and equation solving.

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Readme

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.

\htmlonly

\endhtmlonlyThe Stan Math Library is licensed under the new BSD license.

The Stan Math Library depends on the Intel TBB library which is licensed under the Apache 2.0 license. This dependency implies an additional restriction as compared to the new BSD license alone. The Apache 2.0 license is incompatible with GPL-2 licensed code if distributed as a unitary binary. You may refer to the Apache 2.0 evaluation page on the Stan Math wiki.

Stan Math depends on four libraries:

- Boost (version 1.72.0): Boost Home Page
- Eigen (version 3.3.3): Eigen Home Page
- SUNDIALS (version 5.2.0): Sundials Home Page
- Intel TBB (version 2019_U8): Intel TBB Home Page

These are distributed under the

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

Documentation for Stan math is available at mc-stan.org/math

The Stan Math Library is a C++ library which depends on the Intel TBB library and requires for some functionality (ordinary differential equations and root solving) the Sundials library. The build system is the make facility, which is used to manage all dependencies.

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

#include #includeint 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/tobusiness replaced with actual paths:

> cd /path/to/foo > make -j4 -f /path/to/stan-math/make/standalone math-libs > make -f /path/to/stan-math/make/standalone foo > ./foo log normal(1 | 2, 3)=-2.07311

The first make command with the

math-libstarget ensures that all binary dependencies of Stan Math are built and ready to use. The

-j4instructs

maketo use 4 cores concurrently which should be adapted to your needs. The second make command ensures that the Stan Math sources and all of the dependencies are available to the compiler when building

foo.

An example of a real instantiation whenever the path to Stan Math is

~/stan-dev/math/:

> make -j4 -f ~/stan-dev/math/make/standalone math-libs > make -f ~/stan-dev/math/make/standalone foo

The

math-libstarget has to be called only once, and can be omitted for subsequent compilations.

The standalone makefile ensures that all the required

-Iinclude statements are given to the compiler and the necessary libraries are linked:

~/stan-dev/mathand

~/stan-dev/math/lib/eigen_3.3.3and

~/stan-dev/math/lib/boost_1.72.0and

~/stan-dev/math/lib/sundials_5.2.0/includeand

~/stan-dev/math/lib/tbb_2019_U8/include. The

~/stan-dev/math/lib/tbbdirectory is created by the

math-libsmakefile target automatically and contains the dynamically loaded Intel TBB library. The flags

-Wl,-rpath,...instruct the linker to hard-code the path to the dynamically loaded Intel TBB library inside the stan-math directory into the final binary. This way the Intel TBB is found when executing the program.

Note for Windows users: On Windows the

-rpathfeature as used by Stan Math to hardcode an absolute path to a dynamically loaded library does not work. On Windows the Intel TBB dynamic library

tbb.dllis located in the

math/lib/tbbdirectory. The user can choose to copy this file to the same directory of the executable or to add the directory

/path/to/math/lib/tbbas absolute path to the system-wide

PATHvariable.

The above example will use the default compiler of the system as determined by

make. On Linux this is usually

g++, on MacOS

clang++, and for Windows this is

g++if the RTools for Windows are used. There's nothing special about any of these and they can be changed through the

CXXvariable of

make. The recommended way to set this variable for the Stan Math library is by creating a

make/localfile within the Stan Math library directory. Defining

CXX=g++in this file will ensure that the GNU C++ compiler is always used, for example. The compiler must be able to fully support C++11 and partially the C++14 standard. The

g++4.9.3 version part of RTools for Windows currently defines the minimal C++ feature set required by the Stan Math library.

Note that whenever the compiler is changed, the user usually must clean and rebuild all binary dependencies with the commands: ```bash

make -f path/to/stan-math/make/standalone math-clean make -j4 -f path/to/stan-math/make/standalone math-libs ``` This ensures that the binary dependencies are created with the new compiler.