Generic function for pairwise operations


A very commonly used design pattern is to apply a function to all unique pairs of elements in a container, e.g.

f(x,y) = x*y
a = randn(5)
ret = eltype(a)[] #the example returns a vector, but in this case an UpperTriangular Matrix might be better.
for i in 1:(length(a-1))
   for j in (i+1):length(a)
      push!(ret, f(a[i], a[j]))

(see e.g. for a use of pairwise), but it could also apply to all pairwise combination of columns or rows in a Matrix or higher-dimensional arrays.
Julia provides map for elementwise operations. Is there such a function for pairwise operations? Alternatively, if someone were to implement such a function, where would it be put? It should be so relatively general that it should be close to Base, I think to be really interesting, or perhaps somewhere like Iterators.jl?
Distances.jl has a pairwise function that implements some of this functionality efficiently, but AFAICS not all of it.


I’m not aware of such functionality. My sense is that there’s a lot of useful abstractions that aren’t quite useful enough for someone to have built them, made them robust and decided to maintain them in the future.

In general, I very strongly encourage building all new functionality in a package that you both control and maintain. Base might be a good place for this, but it’s much better for everyone to start with functionality outside of Base.

On a sidenote, I’d want to know whether you want pairwise_map(f, M), which applies f to all pairs of entries in M, or whether you want map(f, pairs(x, y)), which takes two iterators and combines them into a single iterator that is mapped into a vector or other flat iterable.


Ah, yes, I had a feeling the answer might be something like that. Well I definitely would find something like this useful so I might give it a stab sometime (or @ChrisRackauckas would it belong in ?)

I think I’d want pairwise_map(f, M), perhaps with pairwise_mapslices(f, M) for multidimensional arrays. The return type is also tricky - maybe it should be an UpperTriangular (for linear containers)?


Yes, this is exactly the kind of stuff I’m gathering there if it has no other home!


This sounds like you’re assuming that the function being applied pairwise is symmetric, no?


argh, yes I was. Good point!


For cross-reference, the discussion continued here and there is now a PR here: