simplex_monte_carlo


simplex_monte_carlo, a Fortran77 code 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 MIT license

Languages:

simplex_monte_carlo is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

simplex_monte_carlo_test

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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;

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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_GRID, a Fortran77 library which generates a regular grid of points over the interior of an arbitrary simplex in M dimensions.

SIMPLEX_INTEGRALS, a Fortran77 library which returns the exact value of the integral of any monomial over the interior of the unit simplex in M dimensions.

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SPHERE_TRIANGLE_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.

TETRAHREDRON_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 unit triangle in 2D.

WEDGE_MONTE_CARLO, a Fortran77 library which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.

Source Code:


Last revised on 20 December 2023.