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.