**simplex_monte_carlo**,
a MATLAB code which
uses the Monte Carlo method to estimate the integral of a function F(X)
over the interior of the unit simplex in M dimensions.

The interior of the unit simplex in M dimensions is defined by the constraints:

0 <= X(1:M) sum ( 1 <= I <= M ) X(I) <= 1The functions F(X) are monomials, having the form

F(X) = product ( 1 <= I <= M ) X(I)^E(I)where the exponents are nonnegative integers.

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

**simplex_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_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 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_gm_rule, a MATLAB code which defines grundmann-moeller quadrature rules over the interior of a triangle in 2d, a tetrahedron in 3d, or over the interior of the simplex in m dimensions.

simplex_grid, a MATLAB code which generates a regular grid of points over the interior of an arbitrary simplex in m dimensions.

simplex_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit simplex in m dimensions.

sphere_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals 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.

tetrahredron_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.

- monomial_value.m, evaluates a monomial.
- simplexn01_monomial.m, monomial integrals in the interior of the unit simplex in M dimensions.
- simplex01_sample.m samples points from the interior of the unit simplex in M dimensions.
- simplex01_volume.m computes the volume of the unit simplex in M dimensions.