[Numpy-discussion] Rebinning numpy array

[Sturla Molden]

Fit a poisson distribution (radioactive decay is a Poisson process),
recompute lambda for whatever bin-size you need, and compute
the new (estimated) bin counts by maximum likehood. It basically
becomes a contrained optimization problem.

Sturla


Den 13.11.2011 17:04, skrev Johannes Bauer:
> Hi group,
>
> I have a rather simple problem, or so it would seem. However I cannot
> seem to find the right solution. Here's the problem:
>
> A Geiger counter measures counts in distinct time intervals. The time
> intervals are not of constant length. Imaging for example that the
> counter would always create a table entry when the counts reach 10. Then
> we would have the following bins (made-up data for illustration):
>
> Seconds		Counts	Len	CPS
> 0 - 44		10	44	0.23
> 44 - 120	10	76	0.13
> 120 - 140	10	20	0.5
> 140 - 200	10	60	0.16
>
> So we have n bins (in this example 4), but they're not equidistant. I
> want to rebin samples to make them equidistant. For example, I would
> like to rebin into 5 bins of 40 seconds time each. Then the rebinned
> example (I calculate by hand so this might contain errors):
>
> 0-40		9.09
> 40-80		5.65
> 80-120		5.26
> 120-160		13.33
> 160-200		6.66
>
> That means, if a destination bin completely overlaps a source bin, its
> complete value is taken. If it overlaps partially, linear interpolation
> of bin sizes should be used.
>
> It is very important that the overall count amount stays the same (in
> this case 40, so my numbers seem to be correct, I checked that). In this
> example I increased the bin size, but usually I will want to decrease
> bin size (even dramatically).
>
> Now my pathetic attempts look something like this:
>
> interpolation_points = 4000
> xpts = [ time.mktime(x.timetuple()) for x in self.getx() ]
>
> interpolatedx = numpy.linspace(xpts[0], xpts[-1], interpolation_points)
> interpolatedy = numpy.interp(interpolatedx, xpts, self.gety())
>
> self._xreformatted = [ datetime.datetime.fromtimestamp(x) for x in
> interpolatedx ]
> self._yreformatted = interpolatedy
>
> This works somewhat, however I see artifacts depending on the
> destination sample size: for example when I have a spike in the sample
> input and reduce the number of interpolation points (i.e. increase
> destination bin size) slowly, the spike will get smaller and smaller
> (expected behaviour). After some amount of increasing, the spike however
> will "magically" reappear. I believe this to be an interpolation artifact.
>
> Is there some standard way to get from a non-uniformally distributed bin
> distribution to a unifomally distributed bin distribution of arbitrary
> bin width?
>
> Best regards,
> Joe
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