hypersphere_monte_carlo

hypersphere_monte_carlo, a Fortran90 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_monte_carlo_test

f90_monte_carlo, a Fortran90 code which uses Monte Carlo sampling to estimate areas and integrals.

hypersphere, a Fortran90 code which carries out various operations for an M-dimensional hypersphere, including converting between Cartesian and spherical coordinates, stereographic projection, sampling the surface of the sphere, and computing the surface area and volume.

hypersphere_integrals, a Fortran90 code which returns the exact value of the integral of any monomial over the surface of the unit hypersphere in M dimensions.

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.f90, the source code.
• hypersphere_monte_carlo.sh, compiles the source code.