WEDGE_MONTE_CARLO
Monte Carlo Integral Estimates over the Unit Wedge in 3D

WEDGE_MONTE_CARLO is a FORTRAN77 library which uses the Monte Carlo method to estimate the integral of a function over the interior of the unit wedge in 3D

The interior of the unit wedge in 3D is defined by the constraints:

        0 <= X
        0 <= Y
             X + Y <= 1
       -1 <= Z <= +1
      

Licensing:

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

Languages:

WEDGE_MONTE_CARLO is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

BALL_MONTE_CARLO, a FORTRAN77 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 FORTRAN77 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 FORTRAN77 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 FORTRAN77 library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit disk in 2D;

ELLIPSE_MONTE_CARLO a FORTRAN77 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 FORTRAN77 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 FORTRAN77 library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit hyperball in M dimensions;

HYPERBALL_VOLUME_MONTE_CARLO, a FORTRAN77 program which applies a Monte Carlo method to estimate the volume of the unit hyperball in M dimensions;

HYPERCUBE_MONTE_CARLO, a FORTRAN77 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 FORTRAN77 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 FORTRAN77 library which applies a Monte Carlo method to estimate the integral of a function over the length of the unit line in 1D;

POLYGON_MONTE_CARLO, a FORTRAN77 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 FORTRAN77 library which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit pyramid in 3D;

SIMPLEX_GM_RULE, a FORTRAN77 library which defines Grundmann-Moeller quadrature rules over the interior of a triangle in 2D, a tetrahedron in 3D, or over the interior of the simplex in M dimensions.

SIMPLEX_MONTE_CARLO, a FORTRAN77 library which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.

SPHERE_MONTE_CARLO, a FORTRAN77 library which uses the Monte Carlo method to estimate integrals over the surface of the unit sphere in 3D.

SPHERE_WEDGE_MONTE_CARLO, a FORTRAN77 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 FORTRAN77 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 FORTRAN77 library which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.

TRIANGLE_MONTE_CARLO, a FORTRAN77 library which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.

WEDGE_EXACTNESS, a FORTRAN77 program which investigates the monomial exactness of a quadrature rule over the interior of the unit wedge in 3D.

WEDGE_FELIPPA_RULE, a FORTRAN77 library which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.

WEDGE_GRID, a FORTRAN77 library which computes a grid of points over the interior of the unit wedge in 3D.

WEDGE_INTEGRALS, a FORTRAN77 library which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3D.

Reference:

1. Carlos Felippa,
   A compendium of FEM integration formulas for symbolic work,
   Engineering Computation,
   Volume 21, Number 8, 2004, pages 867-890.

Source Code:

• wedge_monte_carlo.f, the source code.
• wedge_monte_carlo.sh, commands to compile the source code.

Examples and Tests:

• wedge_monte_carlo_prb.f, a sample calling program.
• wedge_monte_carlo_prb.sh, commands to compile and run the sample program.
• wedge_monte_carlo_prb_output.txt, the output file.

List of Routines:

• MONOMIAL_VALUE evaluates a monomial.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• WEDGE01_VOLUME returns the volume of the unit wedge in 3D.
• WEDGE01_INTEGRAL returns the integral of a monomial in the unit wedge in 3D.
• WEDGE01_SAMPLE samples points uniformly from the unit wedge in 3D.

You can go up one level to the FORTRAN77 source codes.