disk01_monte_carlo

disk01_monte_carlo, a Python code which uses the Monte Carlo method to estimate the integral of a function over the interior of a disk in 2D.

Licensing:

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

Languages:

disk01_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:

disk01_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit disk in 2d.

disk01_rule, a Python code which computes quadrature rules for the unit disk in 2d, that is, the interior of the circle of radius 1 and center (0,0).

python_monte_carlo, a Python 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:

• disk01_monte_carlo.py, the source code.
• disk01_monte_carlo.sh, runs all the tests.
• disk01_monte_carlo.txt, the output file.