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Fast calculation of pair correlation function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg98626] Fast calculation of pair correlation function
  • From: markus <markusg.phys at googlemail.com>
  • Date: Tue, 14 Apr 2009 06:19:43 -0400 (EDT)

Hi,

I have a quite large list (length ~ 10,000) of coordinates (positions
of particles from a simulation), e.g. data={{x1,y1,z1},
{x2,y2,z2},...}, and I am looking for fast way to calculate the "pair
correlation" or "radial distribution function", which tells me, for
each value of r, how many particles are separated by a distance r (+-
epsilon).
Usually, this can be calculated by something like:

Do[Do[histogr[[ Ceiling[Norm[ data[[i]]-data[[j]] ] / delta] ]], {j, i
+1, Length[data]}], {i, 1, Length[data]-1}]

where histogr is just a list whose index corresponds to the distance
r.

Unfortunately I have found that for lists of length >1,000, this way
of calculating is very slow (it can take ~minutes), compared to the
equivalent C code, which proceeds in a few seconds. I have also tried
to "Compile" the function, but the speed does not increase...

Does anybody know some fast way of calculating the pair distribution
function in Mathematica?


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