**pyramid_monte_carlo**,
a Python code which
estimates the integral of a function F(X,Y,Z)
over the interior of the unit pyramid in 3D.

The unit pyramid has a square base of area 4, and a height of 1. Specifically, the integration region is:

- ( 1 - Z ) <= X <= 1 - Z - ( 1 - Z ) <= Y <= 1 - Z 0 <= Z <= 1.The volume of the unit pyramid is 4/3.

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

**pyramid_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 Python 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 python 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 python code 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 python code 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 python code which uses the monte carlo method to estimate integrals over the interior of a disk in 2d.

disk01_monte_carlo, a python code which uses the monte carlo method to estimate integrals over the interior of the unit disk in 2d.

disk01_quarter_monte_carlo, a python 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 python 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 python 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 python code which applies a monte carlo method to estimate the integral of a function over the interior of the unit ball in m dimensions;

hypercube_monte_carlo, a python 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 python code 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 python code which applies a monte carlo method to estimate the integral of a function over the length of the unit line segment in 1d;

polygon_monte_carlo, a python code which applies a monte carlo method to estimate the integral of a function over the interior of a polygon in 2d.

pyramid_grid, a python code which computes a grid of points over the interior of the unit pyramid in 3d;

pyramid_integrals, a python code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3d.

simplex_monte_carlo, a python code which uses the monte carlo method to estimate integrals over the interior of the unit simplex in m dimensions.

sphere_monte_carlo, a python code which applies a monte carlo method to estimate the integral of a function on the surface of the unit sphere in 3d;

square_monte_carlo, a python 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 python code which uses the monte carlo method to estimate integrals over the interior of the unit tetrahedron in 3d.

triangle01_monte_carlo, a python code which uses the monte carlo method to estimate integrals over the interior of the unit triangle in 2d.

wedge_monte_carlo, a python code which uses the monte carlo method to estimate integrals over the interior of the unit wedge in 3d.

- pyramid_monte_carlo.py, the source code.
- pyramid_monte_carlo.sh, runs all the tests.
- pyramid_monte_carlo.txt, the output file.