TriangularIndices.jl

This small package is intended to help with iterating over the indices of triangular matrices. For example:

using TriangularIndices

z = zeros(Int, (3,3))
for (k, (i,j)) in enumerate(UpperTriangularIndices(z))
    z[i,j] = k
end

will result in

z == [ 1  2  4
       0  3  5
       0  0  6 ]

Of course, the above code could just as easily have been written

z = zeros(Int, (3,3))
k = 1
for j in 1:size(z,1)
    for i in 1:j
        z[i,j] = k
        k += 1
    end
end

which would not require the use of TriangularIndices.jl, and which might even be faster for single-threaded code. However, UpperTriangularIndices objects support length as well as partitioning using getindex, which makes them useful with macros that distribute the iterator over threads or processes, such as @distributed from Distributed, @threads from Threads, or @floop from FLoops.

For reverse indexing, there is a fast specialization of findfirst

findfirst(==((2,3)), UpperTriangularIndices(3)) # returns 5

Note: There's currently no corresponding implementation of LowerTriangularIndices. If somebody is interested in writing one, the linear-to-cartesian indexing operation could use this code.