TETRAHEDRON_MONTE_CARLO is a MATLAB library which uses the Monte Carlo method to estimate the integral of a function F(X,Y,Z) over the interior of the unit tetrahedron in 3D.
The interior of the unit tetrahedron in 3D is defined by the constraints:
0 <= X 0 <= Y 0 <= Z X + Y + Z <= 1The functions F(X,Y,Z) are monomials, having the form
F(X,Y,Z) = X^E(1) * Y^E(2) * Z^E(3)where the exponents are nonnegative integers.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
TETRAHEDRON_MONTE_CARLO is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.
BALL_MONTE_CARLO, a MATLAB library 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 library 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 library 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 library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit disk in 2D;
DISK_QUARTER_MONTE_CARLO, a MATLAB library 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 library 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 library 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 library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit hyperball in M dimensions;
HYPERBALL_VOLUME_MONTE_CARLO, a MATLAB program which applies a Monte Carlo method to estimate the volume of the unit hyperball in M dimensions;
HYPERCUBE_MONTE_CARLO, a MATLAB library 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 library 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 library which uses the Monte Carlo method to estimate integrals over the length of the unit line in 1D.
POLYGON_MONTE_CARLO, a MATLAB library 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 library which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit pyramid in 3D;
SIMPLEX_MONTE_CARLO, a MATLAB library which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.
SPHERE_MONTE_CARLO, a MATLAB library which uses the Monte Carlo method to estimate integrals over the surface of the unit sphere in 3D.
SPHERE_TRIANGLE_MONTE_CARLO, a MATLAB library 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 library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit square in 2D.
TETRAHEDRON_ARBQ_RULE, a MATLAB library which returns quadrature rules, with exactness up to total degree 15, over the interior of a tetrahedron in 3D, by Hong Xiao and Zydrunas Gimbutas.
TETRAHEDRON_EXACTNESS, a MATLAB program which investigates the monomial exactness of a quadrature rule over the interior of a tetrahedron in 3D.
TETRAHEDRON_FELIPPA_RULE, a MATLAB library which returns Felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.
TETRAHEDRON_INTEGRALS, a MATLAB library which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3D.
TETRAHEDRON_KEAST_RULE, a MATLAB library which defines ten quadrature rules, with exactness degrees 0 through 8, over the interior of a tetrahedron in 3D.
TETRAHEDRON_NCC_RULE, a MATLAB library which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a tetrahedron in 3D.
TETRAHEDRON_NCO_RULE, a MATLAB library which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a tetrahedron in 3D.
TRIANGLE_MONTE_CARLO, a MATLAB library which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.
WEDGE_MONTE_CARLO, a MATLAB library which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.
You can go up one level to the MATLAB source codes.