circle_monte_carlo

circle_monte_carlo, an Octave code which estimates the integral of F(X,Y) along the circumference of the unit circle in 2D.

Licensing:

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

Languages:

circle_monte_carlo is available in a C version and a C++ version and and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

circle_monte_carlo_test

line_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the length of the unit line in 1d.

simplex_monte_carlo, a MATLAB 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:

• circle01_length.m, returns the length of the circumference of the unit circle in 2D.
• circle01_monomial_integral.m, integrates a monomial on the circumference of the unit circle in 2D.
• circle01_sample_ergodic.m, ergodically samples points from the circumference of the unit circle in 2D.
• circle01_sample_random.m, randomly samples points from the circumference of the unit circle in 2D.
• monomial_value.m, evaluates a monomial.