hyperball_distance

hyperball_distance, an Octave 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.

Licensing:

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

Languages:

hyperball_distance is available in a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

hyperball_distance_test

octave_distance, an Octave code which estimates the typical distance between a pair of points randomly selected from the surface or interior of a geometric object such as a circle, disk, sphere, cube.

Reference:

• John Hammersley,
  The distribution of distance in a hypersphere,
  The Annals of Mathematical Statistics,
  Volume 21, Number 3, pages 447-452, 1950.

Source Code:

• hyperball_distance_histogram.m, displays a histogram from N samples of pairwise distances.
• hyperball_distance_pdf.m, displays a plot of the exact PDF of the pairwise distances.
• hyperball_distance_stats.m, estimates the mean and variance of the pairwise distance, using sampling.
• hyperball_unit_sample.m, returns a random point in the unit hyperball.