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 MIT 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.
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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;
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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;
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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.