simplex_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit simplex in M dimensions.
The interior of the unit simplex in M dimensions is defined by
0 <= X(1:M)
sum ( 1 <= I <= M ) X(I) <= 1
The integrands are all of 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_integrals 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.
ball_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit ball in 3d.
cube_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3d.
simplex_gm_rule, an Octave 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, an Octave code which generates a regular grid of points over the interior of an arbitrary simplex in m dimensions.
simplex_monte_carlo, an Octave code which uses the monte carlo method to estimate the integral of a function over the interior of the unit simplex in m dimensions.