hypersphere_angle

hypersphere_angle, a MATLAB 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. In dimension 1, we have average dot product of 1, and angle 0. As the dimension increases, the average dot product rapidly decreases to 0, while the average angle goes to 90 degrees.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

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

Related Data and Programs:

hypersphere_angle_test

hypersphere, a MATLAB 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, a MATLAB 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;