On Wed, Jan 9, 2013 at 12:32 PM, Todd <toddrjen@gmail.com> wrote:
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?
Is this the same as a mean resultant in circular statistics? def circular_resultant(rads, axis=0): mp = np.sum(np.exp(1j*rads), axis=axis) rho = np.abs(mp) mu = np.angle(mp) return mp, rho, mu Josef
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