# annulus_monte_carlo

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.

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
```

### Licensing:

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

### Languages:

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.

### Related Data and Programs:

annulus_rule, a C 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 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 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 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 uses the monte carlo method to estimate integrals over the interior of the general disk in 2d.

disk01_monte_carlo, a C code which uses the monte carlo method to estimate integrals 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;

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 sphere 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 integrals of a function over the surface of the unit sphere in 3d;

sphere_triangle_monte_carlo, a C 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 C 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 C code which uses the monte carlo method to estimate integrals over a tetrahedron.

tetrahedron01_monte_carlo, a C code which uses the monte carlo method to estimate integrals over the interior of the unit tetrahedron in 3d.

triangle_monte_carlo, a C code which uses the monte carlo method to estimate integrals over the interior of a triangle in 2d.

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.

### Source Code:

Last revised on 06 July 2018.