Pairwise distances from a single column or vector

New to Julia
1

I’m a new Julia user, so this might be really obvious, but is there a straight-forward way to generate a pairwise distance matrix from a single vector or column?
In R, it’s pretty straightforward:
for the vector c(2, 4, 6, 8)

dist(c(2, 4, 6, 8))
1 2 3
2 2
3 4 2
4 6 4 2

I’ve played around with Distances.jl, but I’m having trouble getting the function pairwise to work even for simple instances, e.g.:

using Distances
cc = [2, 4, 6, 8];
mm = [1, 3, 5, 7];
pairwise(Euclidean(), cc)

ERROR: MethodError: no method matching pairwise(::Euclidean, ::Array{Int64,1})

pairwise(Euclidean(), cc, mm)

ERROR: MethodError: no method matching pairwise(::Euclidean, ::Array{Int64,1}, ::Array{Int64,1})

The non-pairwise version works. This obviously isn’t what I’m going for, but at least it demonstrates that some of the functionality of Distances.jl is up and running:
euclidean(cc, mm)
2.0

2

I don’t know enough R to know exactly what you’re expecting, but shouldn’t the distance matrix be a 4x4 matrix? If that’s what you want, then it’s easy to write a simple Julia function to do this for you using a list comprehension:

julia> using LinearAlgebra: norm

julia> c = [2, 4, 6, 8]
4-element Array{Int64,1}:
 2
 4
 6
 8
                                                                                                                                                                                                                                                                                                                                      
julia> [norm(c[i] - c[j]) for i in eachindex(c), j in eachindex(c)]
4×4 Array{Int64,2}:                                                                                                                                                                                                                                                                                                                   
 0  2  4  6                                                                                                                                                                                                                                                                                                                           
 2  0  2  4
 4  2  0  2
 6  4  2  0
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3

In Distances, a collection of points (even if the points are one dimensional) is given as a matrix, not a vector. So either create it as a matrix or use the adjoint operator ' to give it an extra dimension.

julia> pairwise(Euclidean(), cc'; dims=2)
4×4 Array{Float64,2}:
 0.0  2.0  4.0  6.0
 2.0  0.0  2.0  4.0
 4.0  2.0  0.0  2.0
 6.0  4.0  2.0  0.0
1 Like
4

Thanks very much! I’m hoping to apply this method to large numbers of large numbers, so the implementation suggested by kristoffer.carlsson below might be faster

re: output: the output in R is in the “lower triangle” format with no zeros, so it’s just:
2
4 2
6 4 2

that’s eventually the format I’ll need things in, but I can play around with converting the output of your function. I’m pretty sure there are quick and dirty tricks to convert among distance matrix types

5

Thanks very much for this response! Just to tack on for any future newbies who stumble upon this, if you want to generate a pairwise distance matrix from just one column of a 2d matrix, you can do:

julia> ccc = [2 4 6 ; 4 8 16 ; 6 12 18; 8 16 64]; 
julia> pairwise(Euclidean(), ccc[ : , 1]'; dims = 2)
4×4 Array{Float64,2}:
 0.0  2.0  4.0  6.0
 2.0  0.0  2.0  4.0
 4.0  2.0  0.0  2.0
 6.0  4.0  2.0  0.0
1 Like
6

You can still use Robin’s answer, which I actually prefer, in a more simplified way:

julia> c = [2.0, 4, 6, 8]
4-element Array{Float64,1}:
 2.0
 4.0
 6.0
 8.0

julia> [abs(i-j) for i in c, j in c]
4×4 Array{Float64,2}:
 0.0  2.0  4.0  6.0
 2.0  0.0  2.0  4.0
 4.0  2.0  0.0  2.0
 6.0  4.0  2.0  0.0
2 Likes
7

There is also Distances.jl.

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8

Yes, I know, it’s a matter of preference, I don’t like to use a package unless I’m doing serious work with it.

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