**cube_monte_carlo**,
a FORTRAN90 code which
estimates the integral of a function
over the interior of the unit cube in 3D.

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

**cube_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 FORTRAN90 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 FORTRAN90 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 FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the circumference of the unit circle in 2D.

CUBE_ARBQ_RULE, a FORTRAN90 code which returns quadrature rules, with exactness up to total degree 15, over the interior of the symmetric cube in 3D, by Hong Xiao and Zydrunas Gimbutas.

CUBE_EXACTNESS, a FORTRAN90 code which investigates the polynomial exactness of quadrature rules over the interior of a cube in 3D.

CUBE_FELIPPA_RULE, a FORTRAN90 code which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.

CUBE_GRID, a FORTRAN90 code which computes a grid of points over the interior of a cube in 3D.

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_MONTE_CARLO, a FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the interior of the unit disk in 2D.

DISK01_QUARTER_MONTE_CARLO, a FORTRAN90 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 FORTRAN90 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 FORTRAN90 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 FORTRAN90 code 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 FORTRAN90 code which applies a Monte Carlo method to estimate the volume of the unit hyperball in M dimensions;

HYPERCUBE_MONTE_CARLO, a FORTRAN90 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 FORTRAN90 code which applies a Monte Carlo method to estimate the integral of a function on the surface of the unit hypersphere in M dimensions;

LINE_MONTE_CARLO, a FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the length of the unit line in 1D.

POLYGON_MONTE_CARLO, a FORTRAN90 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 FORTRAN90 code 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 FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.

SPHERE_MONTE_CARLO, a FORTRAN90 code which applies a Monte Carlo method to estimate the integral of a function on the surface of the unit sphere in 3D;

SPHERE_TRIANGLE_MONTE_CARLO, a FORTRAN90 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 FORTRAN90 code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit square in 2D.

TETRAHEDRON_MONTE_CARLO, a FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the unit tetrahedron.

TRIANGLE_MONTE_CARLO, a FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the interior of the triangle in 2D.

TRIANGLE01_MONTE_CARLO, a FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.

WEDGE_MONTE_CARLO, a FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.

- cube_monte_carlo.f90, the source code.
- cube_monte_carlo.sh, the source code.