pyramid_monte_carlo


pyramid_monte_carlo, a C++ 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 C++ 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 C++ 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 C++ code which uses the Monte Carlo method to estimate integrals over the circumference of the unit circle in 2D.

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

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DISK01_MONTE_CARLO, a C++ code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit disk in 2D;

DISK01_QUARTER_MONTE_CARLO, a C++ 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 C++ code which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipse in 2D.

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

HYPERCUBE_MONTE_CARLO, a C++ 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 C++ 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 C++ code which uses the Monte Carlo method to estimate integrals over the length of the unit line in 1D.

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

pyramid_monte_carlo_test

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

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

SQUARE_MONTE_CARLO, a C++ code which uses the Monte Carlo method to estimate integrals over the interior of the unit square in 2D.

TETRAHEDRON_MONTE_CARLO, a C++ code which uses the Monte Carlo method to estimate integrals over the interior of the general tetrahedron in 3D.

TETRAHEDRON01_MONTE_CARLO, a C++ code which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.

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

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

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

Source Code:


Last revised on 02 April 2020.