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- RunPersistence(InputData)
- Finds extrema and their persistence in one-dimensional data.
Local minima and local maxima are extracted, paired,
and returned together with their persistence.
The global minimum is extracted as well.
We assume a connected one-dimensional domain.
Think of "data on a line", or a function f(x) over some domain xmin <= x <= xmax.
We are only concerned with the data values f(x)
and do not care to know the x positions of these values,
since this would not change which point is a minimum or maximum.
This function returns a list of extrema together with their persistence.
The list is NOT sorted, but the paired extrema can be identified, i.e.,
which minimum and maximum were removed together at a particular
persistence level. As follows:
The odd entries are minima, the even entries are maxima.
The minimum at 2*i is paired with the maximum at 2*i+1.
The last entry of the list is the global minimum.
It is not paired with a maximum.
Hence, the list has an odd number of entries.
Author: Tino Weinkauf
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