simplex_integrals, a Fortran90 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 information on this web page is 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, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit ball in 3D.
circle_integrals, a Fortran90 code which returns the exact value of the integral of any monomial over the surface of the unit circle in 2D.
CUBE_INTEGRALS, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3D.
DISK01_INTEGRALS, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit disk in 2D.
HYPERBALL_INTEGRALS, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit hyperball in M dimensions.
HYPERCUBE_INTEGRALS, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit hypercube in M dimensions.
HYPERSPHERE_INTEGRALS, a Fortran90 code which returns the exact value of the integral of any monomial over the surface of the unit hypersphere in M dimensions.
LINE_INTEGRALS, a Fortran90 code which returns the exact value of the integral of any monomial over the length of the unit line in 1D.
POLYGON_INTEGRALS, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.
PYRAMID_INTEGRALS, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3D.
SIMPLEX_GM_RULE, a Fortran90 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 Fortran90 code which generates a regular grid of points over the interior of an arbitrary simplex in M dimensions.
SIMPLEX_MONTE_CARLO, a Fortran90 code which uses the Monte Carlo method to estimate the integral of a function over the interior of the unit simplex in M dimensions.
SPHERE_INTEGRALS, a Fortran90 code which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3D.
SQUARE_INTEGRALS, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit square in 2D.
TETRAHEDRON_INTEGRALS, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3D.
TRIANGLE_INTEGRALS, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2D.
WEDGE_INTEGRALS, a Fortran90 code which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3D.