Re: Interpoint distances
- To: mathgroup at smc.vnet.net
- Subject: [mg41344] Re: Interpoint distances
- From: "Carl K. Woll" <carlw at u.washington.edu>
- Date: Thu, 15 May 2003 04:05:03 -0400 (EDT)
- Organization: University of Washington
- References: <b9tdnj$7r0$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi Mark,
Here is one idea:
distlist[t_]:=Block[{c={}},
Nest[
(c={c,Sqrt[Plus@@((Transpose[Rest[#]]-First[#])^2)]};Rest[#])&,
t,
Length[t]-1
];
Flatten[c]
]
This function is quite a bit faster than yours with large data sets (almost
2 orders of magnitude for your test case on my machine, a 1.9GHz Pentium),
and scales as O(n^2).
Carl Woll
Physics Dept
U of Washington
"DIAMOND Mark R." <dot at dot.dot> wrote in message
news:b9tdnj$7r0$1 at smc.vnet.net...
> I am trying to find an efficient method of calculating all the pairwise
> (Euclidean) interpoint distances in a given list of points in R^2. I am
sure
> that if my matrix algebra were any good, this would be solvable in a
better
> manner than I have done it. Ideally, I would like to count each pair of
> points only once, and not count points paired with themselves.I've
searched
> the archive, and tried the obvious combinations of words on Google, but no
> luck.
>
> My slow method (but the fastest of those I've tried) is
>
> (* Define a distance function for a pair of points *)
> distance[{{x0_, y0_}, {x1_, y1_}}] := Module[
> {
> xd = x0 - x1,
> yd = y0 - y1
> },
> Sqrt[xd^2 + yd^2]
> ]
>
> (* Create a list of random points with which to experiment *)
> t=Table[{Random[], Random[]}, {1024}]
>
> (* Union in the next line is just used to get rid of all the duplicates,
and
> to dump all but one of the 0 interpoint distances between a point and
itself
> *)
> interpointDistances = Union[Map[distance, Flatten[Outer[List, t, t, 1],
> 1]]];
>
> I would be very grateful for any suggestions for improvement.
>
> Cheers,
>
> Mark
> --
> Mark R. Diamond
>
>
>
>
>
>