disk01_positive_monte_carlo

disk01_positive_monte_carlo, an Octave code which uses the Monte Carlo method to estimate the integral of a function over the interior of the unit positive disk in 2D.

The unit positive disk in 2D is the set of points (X,Y) such that 0 <= X, 0 <= Y, and X^2+Y^2 <= 1.

Licensing:

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

Languages:

disk01_positive_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:

annulus_monte_carlo an Octave 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, an Octave 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, an Octave code 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, an Octave 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, an Octave code which applies a Monte Carlo method to estimate the integral of a function over the interior of a disk of radius R centered at the origin;

disk01_monte_carlo, an Octave code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit disk in 2d;

line_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the length of the unit line in 1d.

simplex_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in m dimensions.

Reference:

• John D Cook,
  Random points in a high-dimensional orthant,
  Posted 9 August 2023,
  https://www.johndcook.com/blog/2023/08/09/random-points-hypersphere-orthant/

Source Code:

• disk01_positive_area.m, returns the area of the unit positive disk.
• disk01_positive_monomial_integral.m, returns the exact integral of a monomial over the unit positive disk
• disk01_positive_sample.m, returns uniform sample points from the unit positive disk.
• monomial_value.m, evaluates a monomial.