ball_monte_carlo

ball_monte_carlo, an Octave code which estimates the integral of F(X,Y,Z) over the interior of the unit ball in 3D.

Licensing:

The computer code and data files made available on this web page are distributed under the MIT license

Languages:

ball_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:

ball_monte_carlo_test

annulus_monte_carlo, an Octave code which uses the Monte Carlo method to estimate the integral of a function over the interior of a circular annulus in 2D.

ball_integrals, an Octave code which defines test functions for integration over the interior of the unit ball in 3D.

circle_monte_carlo, an Octave code which applies a Monte Carlo method to estimate the integral of a function on the circumference of the unit circle in 2D;

line_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the length of the unit line in 1D.

simplex_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex 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:

• ball01_monomial_integral.m, returns monomial integrals in the unit ball.
• ball01_sample.m, uniformly samples points from the unit ball.
• ball01_volume.m, returns the volume of the unit ball.
• monomial_value.m, evaluates a monomial.