simplex_monte_carlo, an Octave 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 an Octave version and a Python version.
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.