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?