hypersphere_monte_carlo

hypersphere_monte_carlo, a MATLAB 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

hypersphere, a MATLAB 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 MATLAB code which defines test functions for integration over the surface of the unit hypersphere in M dimensions.

matlab_monte_carlo, a MATLAB 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:

• hypersphere01_area.m, returns the area of the unit hypersphere in M dimensions.
• hypersphere01_monomial_integral.m, integrates a monomial on the surface of the unit hypersphere in M dimensions.
• hypersphere01_sample.m, uniformly samples points from the surface of the unit hypersphere in M dimensions.
• monomial_value.m, evaluates a monomial.