hypersphere_angle

hypersphere_angle, an Octave code which considers the problem of describing the typical value of the angle between a pair of points randomly selected on the unit hypersphere in M dimensions. Since by symmetry, this will be zero, we instead look at the average of the absolute value of the dot product, and the corresponding angle. This starts out at 1 for dimension 1, and rapidly decreases as the spatial dimension increases.

Licensing:

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

Languages:

hypersphere_angle is available in a MATLAB version and an Octave version.

Related Data and Programs:

hypersphere_angle_test

hypersphere, an Octave code which carries out various operations for an M-dimensional hypersphere, including converting between Cartesian and spherical coordinates, stereographic projection, sampling the surface of the sphere, and computing the surface area and volume.

hypersphere_distance, an Octave code which considers the problem of describing the typical value of the distance between a pair of points randomly selected on the unit hypersphere in M dimensions.

Source Code:

• hypersphere_angle_stats.m, estimates the mean and variance of the pairwise dot product and angle, using sampling.
• hypersphere_unit_sample.m, returns a random point on the unit hypersphere;