I am interested in implementing a function for scipy. The function is called "vector strength". It is basically a measure of how reliably a set of events occur at a particular phase.

It was originally developed for neuroscience research, to determine how well a set of neural events sync up with a periodic stimulus like a sound waveform.

However, it is useful for determining how periodic a supposedly periodic set of events really are, for example:

1. Determining whether crime is really more common during a full moon and by how much

2. Determining how concentrated visitors to a coffee shop are during rush hour

3. Determining exactly how concentrated hurricanes are during hurricane season

My thinking is that this could be implemented in stages:

First would be a Numpy function that would add a set of vectors in polar coordinates. Given a number of magnitude/angle pairs it would provide a summed magnitude/angle pair. This would probably be combined with a cartesian<->polar conversion functions.

Making use of this function would be a scipy function that would actually implement the vector strength calculation. This is done by treating each event as a unit vector with a phase, then taking the average of the vectors. If all events have the same phase, the result will have an amplitude of 1. If they all have a different phases, the result will have an amplitude of 0.

It may even be worth having a dedicated polar dtype, although that may be too much.

What does everyone think of this proposal?