Re: Euclidean distance of all pairwise combinations (redundants)

• To: mathgroup at smc.vnet.net
• Subject: [mg128671] Re: Euclidean distance of all pairwise combinations (redundants)
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Thu, 15 Nov 2012 03:59:35 -0500 (EST)
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• References: <20121114062906.D261769B8@smc.vnet.net>

You want to use Tuples rather than Subsets

list = {{1, 1}, {2, 2}, {3, 3}};

EuclideanDistance @@@ Tuples[list, 2]

{0, Sqrt[2], 2 Sqrt[2], Sqrt[2], 0, Sqrt[2], 2 Sqrt[2], Sqrt[2], 0}

Norm /@ Subtract @@@ Tuples[list, 2]

{0, Sqrt[2], 2 Sqrt[2], Sqrt[2], 0, Sqrt[2], 2 Sqrt[2], Sqrt[2], 0}

Norm[Subtract[##]] & @@@ Tuples[list, 2]

{0, Sqrt[2], 2 Sqrt[2], Sqrt[2], 0, Sqrt[2], 2 Sqrt[2], Sqrt[2], 0}

Norm[#[[1]] - #[[2]]] & /@ Tuples[list, 2]

{0, Sqrt[2], 2 Sqrt[2], Sqrt[2], 0, Sqrt[2], 2 Sqrt[2], Sqrt[2], 0}

Outer[Norm[#1 - #2] &, list, list, 1] // Flatten

{0, Sqrt[2], 2 Sqrt[2], Sqrt[2], 0, Sqrt[2], 2 Sqrt[2], Sqrt[2], 0}

Bob Hanlon

On Wed, Nov 14, 2012 at 1:29 AM, Jesse Pisel <jessepisel at gmail.com> wrote:
> I have been having a tough time trying to figure out how to include all red undant pairwise combinations in my results for the euclidean distance between a set of points. I have a set of points with xy coordinates and want the euclidean distance between each point including the point and itself. So if my points in xy space are list = {{1, 1}, {2, 2}, {3, 3}} for example, I want the distance from {1, 1} to {1, 1}, {1, 1} to {2, 2}, and {2, 2} to {3, 3} etc. for each point for a total of 9 distances all together. The EuclideanDistance function removes the redundant distances that I want retained in the results. I have been using this code just to play with data but would like to be able to expand up to 500+ points:
>
> list = {{1, 1}, {2, 2}, {3, 3}}
> EuclideanDistance @@@ Subsets[list, {2}]
>
> Any ideas on how to get the euclidean distance between all the points including redundants and self references?
>
>

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