HYPERSPHERE_MONTE_CARLO, a MATLAB library which estimates the integral of F(X) over the surface of the unit hypersphere in M dimensions.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
HYPERSPHERE_MONTE_CARLO is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.
BALL_MONTE_CARLO, a MATLAB 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 MATLAB 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 MATLAB 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 MATLAB library which uses the Monte Carlo method to estimate integrals over the interior of the general disk in 2D.
DISK01_MONTE_CARLO, a MATLAB library which uses the Monte Carlo method to estimate integrals over the interior of the unit disk in 2D.
DISK01_QUARTER_MONTE_CARLO, a MATLAB 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 MATLAB 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 MATLAB 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 MATLAB library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit hyperball in M dimensions;
HYPERCUBE_MONTE_CARLO, a MATLAB 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 MATLAB library which defines test functions for integration over the surface of the unit hypersphere in M dimensions.
HYPERSPHERE_PROPERTIES, a MATLAB 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.
HYPERSPHERE_SURFACE, a MATLAB library which illustrates a procedure for estimating the location of a hypersurface defined by a characteristic function or a signed function.
LINE_MONTE_CARLO, a MATLAB library which uses the Monte Carlo method to estimate integrals over the length of the unit line in 1D.
POLYGON_MONTE_CARLO, a MATLAB 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 MATLAB 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 MATLAB library which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.
SPHERE_MONTE_CARLO, a MATLAB 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 MATLAB 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 MATLAB 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 MATLAB library which uses the Monte Carlo method to estimate integrals over a tetrahedron.
TRIANGLE_MONTE_CARLO, a MATLAB library which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.
TRIANGLE01_MONTE_CARLO, a MATLAB library which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.
WEDGE_MONTE_CARLO, a MATLAB library which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.