hyperball_monte_carlo

hyperball_monte_carlo, a MATLAB code which estimates the integral of F(X) over the interior of the unit hyperball in M dimensions.

Licensing:

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

Languages:

hyperball_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:

hyperball_monte_carlo_test

hyperball_integrals, a MATLAB code which defines test functions for integration over the interior of the unit hyperball 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:

• hyperball01_monomial_integral.m, returns monomial integrals in the unit hyperball.
• hyperball01_sample.m, uniformly samples points from the unit hyperball.
• hyperball01_volume.m, returns the volume of the unit hyperball.
• monomial_value.m, evaluates a monomial.