PairwiseListMatrices

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This package allows you to use a pairwise list as a matrix:

mutable struct PairwiseListMatrix{T,diagonal,VT} <: AbstractArray{T, 2}
    list::VT
    diag::VT
    nelements::Int
    ...
end

PairwiseListMatrix{T, diagonal, VT} is a (squared) symmetric matrix that stores a list of type VT with values of type T for the pairwise comparison/evaluation of nelements. If diagonal is true the first element of the list is 1, 1 otherwise is 1, 2. If diagonal is false the diagonal values are stored in a vector on the diag field.

In pairwise calculations like cor() if results are saved as PairwiseListMatrix the space is N(N+1)/2 instead of N*N. This is useful to compare a large number of elements, because you are saving ~ 50% of the memory.

PairwiseListMatrix is faster than a full matrix to make operatation like sum and mean in the whole matrix, since it is cache efficient. However it is slower than a full matrix for reducing along dimensions.

• Creation benchmark
• Statistics benchmark

julia> # Pkg.add("PairwiseListMatrices")

julia> using PairwiseListMatrices

julia> plm  = PairwiseListMatrix([1,2,3], false)
3×3 PairwiseListMatrices.PairwiseListMatrix{Int64,false,Array{Int64,1}}:
 0  1  2
 1  0  3
 2  3  0

julia> nplm  = setlabels(plm, ["a","b","c"])
3×3 Named PairwiseListMatrices.PairwiseListMatrix{Int64,false,Array{Int64,1}}
A ╲ B │ a  b  c
──────┼────────
a     │ 0  1  2
b     │ 1  0  3
c     │ 2  3  0

julia> table = to_table(nplm)
6×3 Matrix{Any}:
 "a"  "a"  0
 "a"  "b"  1
 "a"  "c"  2
 "b"  "b"  0
 "b"  "c"  3
 "c"  "c"  0

julia> from_table(table, true)
3×3 Named PairwiseListMatrix{Any, true, Vector{Any}}
A ╲ B │ a  b  c
──────┼────────
a     │ 0  1  2
b     │ 1  0  3
c     │ 2  3  0