**hypercube_monte_carlo**,
a MATLAB code which
estimates the integral of a function
over the interior of the unit hypercube in M dimensions.

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

**hypercube_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 uses the Monte Carlo method to estimate integrals over 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_grid, a MATLAB code which computes a grid of points over the interior of a hypercube in M dimensions.

hypercube_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit hypercube in M dimensions.

hypersphere_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate the integral of a function on the surface of the unit hypersphere in M dimensions;

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 the integral of a function on 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 the interior of the unit tetrahedron in 3D.

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.

- hypercube01_volume.m, returns the volume of the unit cube in M dimensions.
- hypercube01_monomial_integral.m, integrates a monomial in the unit cube in M dimensions.
- hypercube01_sample.m, samples points from the unit cube in M dimensions.
- monomial_value.m, evaluates a monomial.