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) <= 1
The 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.