triangle01_monte_carlo


triangle01_monte_carlo, a FORTRAN90 code which uses the Monte Carlo method to estimate the integral of a function F(X,Y) over the interior of the unit triangle in 2D.

The interior of the unit triangle in 2D is defined by the constraints:

        0 <= X
        0 <= Y
             X + Y <= 1
      
The functions F(X,Y) are monomials, having the form
        F(X,Y) = X^E(1) * Y^E(2)
      
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:

triangle01_monte_carlo is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

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triangle01_monte_carlo_test

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Reference:

  1. Claudio Rocchini, Paolo Cignoni,
    Generating Random Points in a Tetrahedron,
    Journal of Graphics Tools,
    Volume 5, Number 4, 2000, pages 9-12.
  2. Reuven Rubinstein,
    Monte Carlo Optimization, Simulation and Sensitivity of Queueing Networks,
    Krieger, 1992,
    ISBN: 0894647644,
    LC: QA298.R79.
  3. Greg Turk,
    Generating Random Points in a Triangle,
    in Graphics Gems I,
    edited by Andrew Glassner,
    AP Professional, 1990,
    ISBN: 0122861663,
    LC: T385.G697

Source Code:


Last revised on 08 September 2020.