hypersphere_monte_carlo

hypersphere_monte_carlo, a Python code which estimates the integral of F(X) over the surface of the unit hypersphere in M dimensions.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

hypersphere_monte_carlo is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

hypersphere_integrals, a python code which defines test functions for integration over the surface of the unit hypersphere in m dimensions.

python_monte_carlo, a Python code which uses Monte Carlo sampling to estimate areas and integrals.

Reference:

1. Gerald Folland,
   How to Integrate a Polynomial Over a Sphere,
   American Mathematical Monthly,
   Volume 108, Number 5, May 2001, pages 446-448.

Source Code:

• hypersphere_monte_carlo.py, the source code.
• hypersphere_monte_carlo.sh, runs all the tests.
• hypersphere_monte_carlo.txt, the output file.