disk_monte_carlo

disk_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate the integral of a function over the interior of the general disk in 2D.

Licensing:

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

Languages:

disk_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:

disk_monte_carlo_test

disk_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of a disk of radius R centered at the origin.

disk_rule, a MATLAB code which computes quadrature rules over the interior of the general disk in 2D;

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:

• disk_area.m, returns the area of a disk.
• disk_sample.m, returns uniform sample points from a disk.
• disk01_monomial_integral.m, returns the exact integral of a monomial over the unit disk
• monomial_value.m, evaluates a monomial.