pyramid_monte_carlo, a FORTRAN77 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 an Octave version and a Python version.
ball_monte_carlo, a FORTRAN77 library 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 FORTRAN77 library 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, a FORTRAN77 library 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 FORTRAN77 library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit disk in 2D;
ELLIPSE_MONTE_CARLO a FORTRAN77 library which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipse in 2D.
ELLIPSOID_MONTE_CARLO a FORTRAN77 library 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 FORTRAN77 library 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 FORTRAN77 program which applies a Monte Carlo method to estimate the volume of the unit hyperball in M dimensions;
HYPERCUBE_MONTE_CARLO, a FORTRAN77 library 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 FORTRAN77 library 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 FORTRAN77 library 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, a FORTRAN77 library which applies a Monte Carlo method to estimate the integral of a function over the interior of a polygon in 2D.
PYRAMID_EXACTNESS, a FORTRAN77 program which investigates the monomial exactness of a quadrature rule over the interior of a pyramid in 3D.
PYRAMID_FELIPPA_RULE, a FORTRAN77 library which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.
PYRAMID_GRID, a FORTRAN77 library which computes a grid of points over the interior of the unit pyramid in 3D;
PYRAMID_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3D.
PYRAMID_RULE, a FORTRAN77 library which computes quadrature rules for the unit pyramid in 3D.
SIMPLEX_MONTE_CARLO, a FORTRAN77 library which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.
SPHERE_MONTE_CARLO, a FORTRAN77 library 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 FORTRAN77 library 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 FORTRAN77 library 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 FORTRAN77 library which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.
TRIANGLE_MONTE_CARLO, a FORTRAN77 library which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.
WEDGE_MONTE_CARLO, a FORTRAN77 library which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.