SPHERE_MONTE_CARLO
Monte Carlo Estimate of Sphere Surface Integrals

SPHERE_MONTE_CARLO is a FORTRAN90 library which estimates the integral over the surface of the unit sphere of a function F(X,Y,Z).

Licensing:

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

Languages:

SPHERE_MONTE_CARLO is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

BALL_VOLUME_MONTE_CARLO, a FORTRAN90 program which applies a Monte Carlo method to estimate the volume of the unit ball in 6D;

SPHERE_CVT, a FORTRAN90 library which creates a mesh of well-separated points on a unit sphere using Centroidal Voronoi Tessellations.

SPHERE_DELAUNAY, a MATLAB program which computes the Delaunay triangulation of points on a sphere.

SPHERE_DESIGN_RULE, a FORTRAN90 library which returns point sets on the surface of the unit sphere, known as "designs", which can be useful for estimating integrals on the surface, among other uses.

SPHERE_EXACTNESS, a FORTRAN90 program which tests the polynomial exactness of a quadrature rule for the unit sphere;

SPHERE_GRID, a dataset directory which contains grids of points, lines, triangles or quadrilaterals on a sphere;

SPHERE_LEBEDEV_RULE, a FORTRAN90 library which computes Lebedev quadrature rules for the unit sphere;

SPHERE_QUAD, a FORTRAN90 library which estimates the integral of a function over a sphere.

STROUD, a FORTRAN90 library which defines quadrature rules for various geometric shapes.

TETRAHEDRON_MONTE_CARLO, a FORTRAN90 program which uses the Monte Carlo method to estimate integrals over a tetrahedron.

TRIANGLE_MONTE_CARLO, a FORTRAN90 program which uses the Monte Carlo method to estimate integrals over a triangle.

Source Code:

• sphere_monte_carlo.f90, the source code.
• sphere_monte_carlo.sh, BASH commands to compile the source code.

Examples and Tests:

• sphere_monte_carlo_prb.f90, a sample calling program.
• sphere_monte_carlo_prb.sh, BASH commands to compile and run the sample program.
• sphere_monte_carlo_prb_output.txt, the output file.

List of Routines:

• MONOMIAL_VALUE evaluates a monomial.
• R8_GAMMA evaluates Gamma(X) for a real argument.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• R8VEC_NORMAL_01 returns a unit pseudonormal R8VEC.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• SPHERE01_MONOMIAL_INTEGRAL returns monomial integrals on the unit sphere.
• SPHERE01_SAMPLE maps uniform points onto the unit sphere.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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