Re: Interpoint distances
- To: mathgroup at smc.vnet.net
- Subject: [mg41353] Re: [mg41327] Interpoint distances
- From: jmt <jmt at dxdydz.net>
- Date: Thu, 15 May 2003 04:09:03 -0400 (EDT)
- References: <200305141220.IAA07863@smc.vnet.net>
- Reply-to: jmt at dxdydz.net
- Sender: owner-wri-mathgroup at wolfram.com
One remark first : in many applications, the euclidian distance needs
not to be computed since most of the time the square of the euclidian
distance will suffice. Computing a square root when not necessary will
burden your algorithm.
Second remark : your example suggests that you want to compute the
interpoint distance of a set of points. Depending on the size of this
set, Mathematica will or will not use PackedArray. It is then difficult
to give a universal answer.
On Wednesday 14 May 2003 14:20, DIAMOND Mark R. wrote:
> 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
- References:
- Interpoint distances
- From: "DIAMOND Mark R." <dot@dot.dot>
- Interpoint distances