# pyramid_monte_carlo

pyramid_monte_carlo, a FORTRAN90 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.

### Licensing:

The computer code and data files described and made available on this web page are 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 a Python version.

### Related Data and Programs:

annulus_monte_carlo a FORTRAN90 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 FORTRAN90 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 FORTRAN90 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 FORTRAN90 code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit cube in 3D;

DISK01_MONTE_CARLO, a FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the interior of the unit disk in 2D.

DISK01_QUARTER_MONTE_CARLO, a FORTRAN90 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 FORTRAN90 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 FORTRAN90 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 FORTRAN90 code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit hyperball in M dimensions;

HYPERBALL_VOLUME_MONTE_CARLO, a FORTRAN90 code which applies a Monte Carlo method to estimate the volume of the unit hyperball in M dimensions;

HYPERCUBE_MONTE_CARLO, a FORTRAN90 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 FORTRAN90 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 FORTRAN90 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 FORTRAN90 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 FORTRAN90 code which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.

PYRAMID_GRID, a FORTRAN90 code which computes a grid of points over the interior of the unit pyramid in 3D;

PYRAMID_INTEGRALS, a FORTRAN90 code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3D.

PYRAMID_RULE, a FORTRAN90 code which computes quadrature rules over the interior of the unit pyramid in 3D.

SIMPLEX_MONTE_CARLO, a FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.

SPHERE_MONTE_CARLO, a FORTRAN90 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 FORTRAN90 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 FORTRAN90 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 FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.

TRIANGLE_MONTE_CARLO, a FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the interior of a general triangle in 2D.

TRIANGLE01_MONTE_CARLO, a FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.

WEDGE_MONTE_CARLO, a FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.

### Source Code:

Last revised on 20 August 2020.