HYPERSPHERE_MONTE_CARLO
Monte Carlo Estimate of Hypersphere Surface Integrals


HYPERSPHERE_MONTE_CARLO is a C++ library which estimates the integral of F(X) over the surface of the unit hypersphere in M dimensions.

Licensing:

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

Languages:

HYPERSPHERE_MONTE_CARLO is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

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

CIRCLE_MONTE_CARLO, a C++ library which applies a Monte Carlo method to estimate the integral of a function on the circumference of the unit circle in 2D.

CUBE_MONTE_CARLO, a C++ 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 C++ library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit disk in 2D;

DISK_QUARTER_MONTE_CARLO, a C++ 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 C++ 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 C++ 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 C++ library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit hyperball in M dimensions;

HYPERBALL_VOLUME_MONTE_CARLO, a C++ program which applies a Monte Carlo method to estimate the volume of the unit hyperball in M dimensions;

HYPERCUBE_MONTE_CARLO, a C++ 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_INTEGRALS, a C++ library which defines test functions for integration over the surface of the unit hypersphere in M dimensions.

HYPERSPHERE_PROPERTIES, a C++ library which carries out various operations for an M-dimensional hypersphere, including converting between Cartesian and spherical coordinates, stereographic projection, sampling the surface of the sphere, and computing the surface area and volume.

LINE_MONTE_CARLO, a C++ library which uses the Monte Carlo method to estimate integrals over the length of the unit line in 1D.

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

SPHERE_MONTE_CARLO, a C++ library which applies a Monte Carlo method to estimate integrals of a function over the surface of the unit sphere in 3D;

SPHERE_TRIANGLE_MONTE_CARLO, a C++ library which applies a Monte Carlo method to estimate the integral of a function over a spherical triangle on the surface of the unit sphere in 3D;

SQUARE_MONTE_CARLO, a C++ 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 C++ library which uses the Monte Carlo method to estimate integrals over the unit tetrahedron.

TRIANGLE_MONTE_CARLO, a C++ library which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.

WEDGE_MONTE_CARLO, a C++ 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.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the C++ source codes.


Last revised on 04 January 2014.