SIMPLEX_MONTE_CARLO
Monte Carlo Integral Estimates over the Unit Simplex in M Dimensions

SIMPLEX_MONTE_CARLO is a FORTRAN90 library which uses the Monte Carlo method to estimate the integral of a function F(X) over the interior of the unit simplex in M dimensions.

The interior of the unit simplex in M dimensions is defined by the constraints:

        0 <= X(1:M)
        sum ( 1 <= I <= M ) X(I) <= 1

The functions F(X) are monomials, having the form

        F(X) = product ( 1 <= I <= M ) X(I)^E(I)

where the exponents are nonnegative integers.

Licensing:

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

Languages:

SIMPLEX_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_MONTE_CARLO 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.

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;

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;

HYPERBALL_VOLUME_MONTE_CARLO, a FORTRAN90 program which applies a Monte Carlo method to estimate the volume 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 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 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_GM_RULE, a FORTRAN90 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_GRID, a FORTRAN90 library which generates a regular grid of points over the interior of an arbitrary simplex in M dimensions.

SIMPLEX_INTEGRALS, a FORTRAN90 library which returns the exact value of the integral of any monomial over the interior of the unit simplex in M dimensions.

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

SPHERE_TRIANGLE_MONTE_CARLO, a FORTRAN90 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 FORTRAN90 library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit square in 2D;

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

TRIANGLE_MONTE_CARLO, a FORTRAN90 library which uses the Monte Carlo method to estimate integrals over the interior of a general 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:

simplex_monte_carlo.f90, the source code.

Examples and Tests:

simplex_monte_carlo_test.f90, a sample calling program.
simplex_monte_carlo_test.txt, the output file.

List of Routines:

MONOMIAL_VALUE evaluates a monomial.
R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
SIMPLEX01_MONOMIAL_INTEGRAL: integral in unit simplex in M dimensions.
SIMPLEX01_SAMPLE samples the unit simplex in M dimensions.
SIMPLEX01_VOLUME computes the volume of the unit simplex in M dimensions.
TIMESTAMP prints the current YMDHMS date as a time stamp.

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

Last revised on 13 January 2014.