Monte Carlo Estimate of Integrals in an Annulus

**ANNULUS_MONTE_CARLO**
is a C library 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 C library 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 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 C library 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 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 C library which uses the Monte Carlo method to estimate integrals over the interior of the general disk in 2D.

DISK01_MONTE_CARLO, a C library which uses the Monte Carlo method to estimate integrals over the interior of the unit disk in 2D.

DISK01_QUARTER_MONTE_CARLO, a C library 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 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 C 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 C library 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 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 C library 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 library which uses the Monte Carlo method to estimate integrals over the length of the unit line in 1D.

POLYGON_MONTE_CARLO, a C library 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 library 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 library which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.

SPHERE_MONTE_CARLO, a C library 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 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 C 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 C library which uses the Monte Carlo method to estimate integrals over a tetrahedron.

TETRAHEDRON01_MONTE_CARLO, a C library which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.

TRIANGLE_MONTE_CARLO, a C library which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.

TRIANGLE01_MONTE_CARLO, a C library which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.

WEDGE_MONTE_CARLO, a C library which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.

- annulus_monte_carlo.h, the include file.
- annulus_area.c, computes the area of a circular annulus in 2D.
- annulus_sample.c, samples a circular annulus.
- disk01_monomial_integral.c, returns monomial integrals in the unit disk in 2D.
- monomial_value.c, evaluates a monomial.
- .r8_gammac, evaluates Gamma(X) for a real argument.
- r8_uniform_01_new.c, returns a unit pseudorandom R8.
- r8vec_normal_01_new.c, returns a unit pseudonormal R8VEC.
- r8vec_sum.c, sums a R8VEC.
- r8vec_uniform_01_new.c, returns a unit pseudorandom R8VEC.
- .timestampc, prints the current YMDHMS date as a time stamp.

You can go up one level to the C source codes.