triangle_monte_carlo, a C++ code which estimates the integral of a function over a general triangle using the Monte Carlo method.
The library makes it relatively easy to compare different methods of producing sample points in the triangle, and to vary the triangle over which integration is carried out.
The computer code and data files described and made available on this web page are distributed under the MIT license
triangle_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 C++ 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 C++ 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 C++ code which uses the Monte Carlo method to estimate integrals over the circumference of the unit circle in 2D.
CUBE_MONTE_CARLO, a C++ 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 C++ code which applies a Monte Carlo method to estimate the integral of a function over the interior of the general disk in 2D;
DISK01_MONTE_CARLO, a C++ code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit disk in 2D;
DISK01_QUARTER_MONTE_CARLO, a C++ 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 C++ 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 C++ 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 C++ code 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 FORTRAN90 program which applies a Monte Carlo method to estimate the volume of the unit hyperball in M dimensions;
HYPERCUBE_MONTE_CARLO, a C++ 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 C++ 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, a C++ code which uses the Monte Carlo method to estimate integrals over the length of the unit line in 1D.
POLYGON_MONTE_CARLO, a C++ code which applies a Monte Carlo method to estimate the integral of a function over the interior of a polygon in 2D.
PYRAMID_MONTE_CARLO, a C++ code which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit pyramid in 3D;
SIMPLEX_MONTE_CARLO, a C++ code which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.
SPHERE_MONTE_CARLO, a C++ 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 C++ code which uses the Monte Carlo method to estimate integrals over the interior of the unit square in 2D.
TETRAHEDRON_MONTE_CARLO, a C++ code which uses the Monte Carlo method to estimate integrals over the interior of the general tetrahedron in 3D.
TETRAHEDRON01_MONTE_CARLO, a C++ code which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.
TRIANGLE01_MONTE_CARLO, a C++ code which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.
WEDGE_MONTE_CARLO, a C++ code which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.