[SciPy-Dev] Vector Strength function

[Todd]

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?
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