# 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.

### 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:

Last revised on 10 August 2023.