**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.The volume of the unit pyramid is 4/3.

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

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

annulus_monte_carlo a MATLAB code 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 MATLAB code 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 MATLAB code which applies a Monte Carlo method to estimate the integral of a function over the circumference of the unit circle in 2D.

cube_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit cube in 3D;

disk_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the general disk in 2D.

disk01_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the unit disk in 2D.

disk01_quarter_monte_carlo, a MATLAB code 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 MATLAB code which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipse in 2D.

ellipsoid_monte_carlo a MATLAB code 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 MATLAB code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit hyperball in M dimensions;

hypercube_monte_carlo, a MATLAB code 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 MATLAB code which applies a Monte Carlo method to estimate the integral of a function on the surface of the unit hypersphere in M dimensions;

line_monte_carlo, a MATLAB code 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 MATLAB code which applies a Monte Carlo method to estimate the integral of a function over the interior of a polygon in 2D.

pyramid_felippa_rule, a MATLAB code which returns Felippa's quadratures rules 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_rule, a MATLAB code which computes quadrature rules over the interior of the unit pyramid in 3D.

simplex_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.

sphere_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate the integral of a function on the surface of the unit sphere in 3D;

sphere_triangle_monte_carlo, a MATLAB code 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 MATLAB code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit square in 2D;

tetrahedron_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.

triangle_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.

triangle01_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.

wedge_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.

- 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.