**annulus_monte_carlo**,
a MATLAB code which
uses the Monte Carlo method to estimate the integral of a function
over the interior of a circular annulus in 2D.

A circular annulus with center (XC,YC), inner radius R1 and outer radius R2, is the set of points (X,Y) so that

R1^2 <= (X-XC)^2 + (Y-YC)^2 <= R2^2

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

**annulus_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_rule, a MATLAB code which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D.

ball_monte_carlo, a MATLAB 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 MATLAB 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 MATLAB 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 MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the general disk in 2D.

disk01_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the unit disk in 2D.

disk01_quarter_monte_carlo, a MATLAB 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 MATLAB 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 MATLAB 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 MATLAB 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, a MATLAB 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 MATLAB 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 MATLAB code which uses the Monte Carlo method to estimate integrals over the length of the unit line in 1D.

polygon_monte_carlo, a MATLAB 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 MATLAB 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 MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.

sphere_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate integrals of a function over the surface of the unit sphere in 3D;

sphere_triangle_monte_carlo, a MATLAB 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, a MATLAB 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 MATLAB code which uses the Monte Carlo method to estimate integrals over a tetrahedron.

triangle_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.

triangle01_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.

wedge_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.

- annulus_area.m, returns the area of an annulus.
- annulus_sample.m, uniformly samples the points in an annulus.
- disk01_monomial_integral.m, returns the exact integral of a monomial over the unit disk.
- monomial_value.m, evaluates a monomial.