CIRCLE_MONTE_CARLO
Monte Carlo Estimate of Circle Circumference Integrals

CIRCLE_MONTE_CARLO is a Python library 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 GNU LGPL license.

Languages:

CIRCLE_MONTE_CARLO is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

ANNULUS_MONTE_CARLO a Python library which uses the Monte Carlo method to estimate the integral of a function over the interior of a circular annulus in 2D.

BALL_MONTE_CARLO, a Python library which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit ball in 3D;

CIRCLE_INTEGRALS, a Python library which defines test functions for integration over the circumference of the unit circle in 2D.

CUBE_MONTE_CARLO, a Python library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit cube in 3D.

DISK_MONTE_CARLO, a Python library which uses the Monte Carlo method to estimate integrals over the interior of a disk in 2D.

DISK01_MONTE_CARLO, a Python library which uses the Monte Carlo method to estimate integrals over the interior of the unit disk in 2D.

DISK01_QUARTER_MONTE_CARLO, a Python library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit quarter disk in 2D;

ELLIPSE_MONTE_CARLO a Python library which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipse in 2D.

ELLIPSOID_MONTE_CARLO a Python library which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipsoid in M dimensions.

HYPERBALL_MONTE_CARLO, a Python library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit ball in M dimensions;

HYPERCUBE_MONTE_CARLO, a Python library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit hypercube in M dimensions;

HYPERSPHERE_MONTE_CARLO, a Python library which applies a Monte Carlo method to estimate the integral of a function on the surface of the unit sphere in M dimensions;

LINE_MONTE_CARLO, a Python library which applies a Monte Carlo method to estimate the integral of a function over the length of the unit line segment in 1D;

POLYGON_MONTE_CARLO, a Python library which applies a Monte Carlo method to estimate the integral of a function over the interior of a polygon in 2D.

PYRAMID_MONTE_CARLO, a Python library which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit pyramid in 3D;

SIMPLEX_MONTE_CARLO, a Python library which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.

SPHERE_MONTE_CARLO, a Python library which applies a Monte Carlo method to estimate the integral of a function on the surface of the unit sphere in 3D;

SQUARE_MONTE_CARLO, a Python library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit square in 2D;

TETRAHEDRON_MONTE_CARLO, a Python library which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.

TRIANGLE01_MONTE_CARLO, a Python library which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.

WEDGE_MONTE_CARLO, a Python library which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.

Reference:

1. Gerald Folland,
   How to Integrate a Polynomial Over a Sphere,
   American Mathematical Monthly,
   Volume 108, Number 5, May 2001, pages 446-448.

Examples and Tests:

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

You can go up one level to the Python source codes.