ANNULUS_MONTE_CARLO
Monte Carlo Estimate of Integrals in an Annulus

ANNULUS_MONTE_CARLO is a FORTRAN90 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

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 FORTRAN90 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 FORTRAN90 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 FORTRAN90 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 FORTRAN90 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 FORTRAN90 library which uses the Monte Carlo method to estimate integrals over the interior of the general disk in 2D.

DISK01_MONTE_CARLO, a FORTRAN90 library which uses the Monte Carlo method to estimate integrals over the interior of the unit disk in 2D.

DISK01_QUARTER_MONTE_CARLO, a FORTRAN90 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 FORTRAN90 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 FORTRAN90 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 FORTRAN90 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 FORTRAN90 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 FORTRAN90 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 FORTRAN90 library which uses the Monte Carlo method to estimate integrals over the length of the unit line in 1D.

POLYGON_MONTE_CARLO, a FORTRAN90 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 FORTRAN90 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 FORTRAN90 library which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.

SPHERE_MONTE_CARLO, a FORTRAN90 library which applies a Monte Carlo method to estimate integrals of a function over the surface of the unit sphere in 3D;

SQUARE_MONTE_CARLO, a FORTRAN90 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 FORTRAN90 library which uses the Monte Carlo method to estimate integrals over a tetrahedron.

TRIANGLE_MONTE_CARLO, a FORTRAN90 library which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.

TRIANGLE01_MONTE_CARLO, a FORTRAN90 library which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.

WEDGE_MONTE_CARLO, a FORTRAN90 library which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.

Source Code:

• annulus_monte_carlo.f90, the source code.

Examples and Tests:

• annulus_monte_carlo_test.f90, a sample calling program.
• annulus_monte_carlo_test.txt, the output file.

List of Routines:

• ANNULUS_AREA computes the area of a circular annulus in 2D.
• ANNULUS_SAMPLE samples a circular annulus.
• DISK01_MONOMIAL_INTEGRAL returns monomial integrals in the unit disk in 2D.
• MONOMIAL_VALUE evaluates a monomial.
• R8_GAMMA evaluates Gamma(X) for a real argument.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.