pyramid_monte_carlo

pyramid_monte_carlo, an Octave 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

octave_monte_carlo, an Octave code which uses Monte Carlo sampling to estimate areas and integrals.

pyramid_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit 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.