hypersphere_distance

hypersphere_distance, a Python code which estimates the expected value of the distance between a pair of points randomly selected on the unit hypersphere in M dimensions.

Licensing:

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

Languages:

hypersphere_distance is available in a MATLAB version and a Python version.

Related Data and Programs:

ball_distance, a Python code which considers the problem of describing the typical value of the distance between a pair of points randomly selected in the unit ball in 3D.

circle_distance, a Python code which considers the problem of describing the typical value of the distance between a pair of points randomly selected on the circumference of the unit circle in 2D.

cube_distance, a Python code which considers the problem of describing the typical value of the distance between a pair of points randomly selected in the unit cube in 3D.

disk_distance, a Python code which considers the problem of describing the typical value of the distance between a pair of points randomly selected in the unit disk in 2D.

hyperball_distance, a Python code which considers the problem of describing the typical value of the distance between a pair of points randomly selected in the unit hyperball in M dimensions.

line_distance, a Python code which considers the problem of describing the typical value of the distance between a pair of points randomly selected in the unit line segment.

normal01_multivariate_distance, a Python code which considers the problem of describing the typical value of the distance between a pair of points randomly selected from an isotropic standard normal distribution in M dimensions.

sphere_distance, a Python code which considers the problem of describing the typical value of the distance between a pair of points randomly selected on the unit sphere in 3D.

square_distance, a Python code which considers the problem of describing the typical value of the distance between a pair of points randomly selected in the unit square in 2D.

triangle_distance, a Python code which considers the problem of describing the typical value of the distance between a pair of points randomly selected form the interior of a triangle in 2D.

Reference:

• Panagiotis Siridopoulos,
  The N-Sphere Chord Length Distribution,
  ARXIV,
  https://arxiv.org/pdf/1411.5639.pdf

Source Code:

• hypersphere_distance.py, the source code.
• hypersphere_distance.sh, runs all the tests.
• hypersphere_distance.txt, the output file.

• hypersphere_distance_compare.png, compares observed and theoretical values of the PDF.
• hypersphere_distance_histogram.png, a histogram of the sample results.
• hypersphere_distance_pdf.png, a plot of the theoretical probability density function.