pyramid_monte_carlo

pyramid_monte_carlo, a MATLAB code which estimates the integral of a function F(X,Y,Z) over the interior of the unit pyramid in 3D.

The unit pyramid has a square base of area 4, and a height of 1. Specifically, the integration region is:

        - ( 1 - Z ) <= X <= 1 - Z
        - ( 1 - Z ) <= Y <= 1 - Z
                  0 <= Z <= 1.
      

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

pyramid_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:

pyramid_monte_carlo_test

matlab_monte_carlo, a MATLAB code which uses Monte Carlo sampling to estimate areas and integrals.

pyramid_exactness, a MATLAB code which investigates the monomial exactness of a quadrature rule over the interior of the unit pyramid in 3d.

pyramid_felippa_rule, a MATLAB code which returns a Felippa quadrature rule for approximating integrals over the interior of a pyramid in 3D.

pyramid_grid, a MATLAB code which computes a grid of points over the interior of the unit pyramid in 3D;

pyramid_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3D.

pyramid_jaskowiec_rule, a MATLAB code which returns quadrature rules, with exactness up to total degree 20, over the interior of a pyramid in 3D, by Jan Jaskowiec, Natarajan Sukumar.

pyramid_rule, a MATLAB code which computes quadrature rules over the interior of the unit pyramid in 3D.

pyramid_witherden_rule, a MATLAB code which returns a Witherden quadrature rule, with exactness up to total degree 10, over the interior of a pyramid in 3D.

Source Code:

• monomial_value.m, evaluates a monomial.
• pyramid01_integral.m, monomial integral in a unit pyramid.
• pyramid01_sample.m, sample the unit pyramid.
• pyramid01_volume.m, volume of a unit pyramid with square base.
• r8_mop.m, returns the I-th power of -1 as an R8.
• r8mat_transpose_print.m, prints an R8MAT, transposed.
• r8mat_transpose_print_some.m, prints some of an R8MAT, transposed.