hypersphere_monte_carlo, a MATLAB code 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 MIT 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.
annulus_monte_carlo a MATLAB code 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 MATLAB code 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 code 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 code 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 code which uses the Monte Carlo method to estimate integrals over the interior of the general disk in 2D.
disk01_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the unit disk in 2D.
disk01_quarter_monte_carlo, a MATLAB code 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 code 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 code 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 code 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 code 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 code which defines test functions for integration over the surface of the unit hypersphere in M dimensions.
hypersphere_properties, a MATLAB code 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 code 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 code which uses the Monte Carlo method to estimate integrals over the length of the unit line in 1D.
polygon_monte_carlo, a MATLAB code 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 code 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 code which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.
sphere_monte_carlo, a MATLAB code 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 code 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 code 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 code which uses the Monte Carlo method to estimate integrals over a tetrahedron.
triangle_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.
triangle01_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.
wedge_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.