pyramid_monte_carlo, an Octave 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 an Octave version and a Python version.
annulus_monte_carlo an Octave 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, an Octave 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, an Octave code which applies a Monte Carlo method to estimate the integral of a function over the circumference of the unit circle in 2D.
cube_monte_carlo, an Octave 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, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the general disk in 2D.
disk01_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the unit disk in 2D.
disk01_quarter_monte_carlo, an Octave 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 an Octave code which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipse in 2D.
ellipsoid_monte_carlo an Octave 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, an Octave code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit hyperball in M dimensions;
hypercube_monte_carlo, an Octave 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, an Octave 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, an Octave code which applies a Monte Carlo method to estimate the integral of a function over the length of the unit line in 1D;
polygon_monte_carlo, an Octave code which applies a Monte Carlo method to estimate the integral of a function over the interior of a polygon in 2D.
pyramid_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3D.
simplex_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.
sphere_monte_carlo, an Octave 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, an Octave 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, an Octave 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, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.
triangle_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.
triangle01_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.
wedge_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.