Monte Carlo Estimate of Integrals in Unit Pyramid

**PYRAMID_MONTE_CARLO**
is a MATLAB library 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 GNU LGPL 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.

BALL_MONTE_CARLO, a Python library 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 Python library which applies a Monte Carlo method to estimate the integral of a function on the circumference of the unit circle in 2D;

CUBE_MONTE_CARLO, a Python library 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 Python library which uses the Monte Carlo method to estimate integrals over the interior of a disk in 2D.

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

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

ELLIPSOID_MONTE_CARLO a Python library 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 Python library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit ball in M dimensions;

HYPERCUBE_MONTE_CARLO, a Python library 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 Python library which applies a Monte Carlo method to estimate the integral of a function on the surface of the unit sphere in M dimensions;

LINE_MONTE_CARLO, a Python library which applies a Monte Carlo method to estimate the integral of a function over the length of the unit line segment in 1D;

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

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

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

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

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

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

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

- gamma_log_values.py, returns selected values of the log(gamma) function;
- i4_uniform_ab.py, returns a scaled uniform I4 between A and B.
- i4vec_print.py, prints an I4VEC.
- i4vec_transpose_print.py, prints an I4VEC "transposed", that is, 5 entries to a line.
- i4vec_uniform_ab.py, returns an I4VEC whose entries are uniformly random between A and B.
- monomial_value.py, evaluates a monomial.
- pyramid01_integral.py, monomial integral in a unit pyramid.
- pyramid01_monte_carlo.py, monomial integral in a unit pyramid.
- pyramid01_sample.py, sample the unit pyramid.
- pyramid01_volume.py, volume of a unit pyramid with square base.
- r8_choose.py, computes the binomial coefficient C(N,K) as an R8.
- r8_gamma_log.py, returns the logarithm of the gamma function of an R8.
- r8_mop.py, returns the I-th power of -1 as an R8.
- r8mat_print.py, prints an R8MAT.
- r8mat_print_some.py, prints some of an R8MAT.
- r8mat_transpose_print.py, prints an R8MAT, transposed.
- r8mat_transpose_print_some.py, prints some of an R8MAT, transposed.
- r8mat_uniform_01.py, fills an R8MAT with unit pseudorandom numbers.
- r8mat_uniform_ab.py, returns a scaled pseudorandom R8MAT.
- timestamp.py, prints the current YMDHMS date as a time stamp.

- pyramid_monte_carlo_test.py, calls all the tests.
- pyramid_monte_carlo_test.sh, runs all the tests.
- pyramid_monte_carlo_test.txt, the output file.

You can go up one level to the Python source codes.