Memory saving for Q

[Inazuma110]

Memory saving for Q

When computing modularity using the function Q, many elements of kikj, P, and diff are useless. (Because at the end of the computation, the function takes a product with $\delta(N, L)$, a sparse matrix.)
So change the code so that the function Q works without wasted elements.

I tried to benchmark before and after the change.
Before

julia> N = convert(BipartiteNetwork, web_of_life("M_PL_015"))
666×131 (String) bipartite ecological network (L: 2933 - Bool)

julia> tmp = n_random_modules(100)(N)
(666×131 (String) bipartite ecological network (L: 2933 - Bool), Dict("Bombylius undatus
 " => 64,"Sarcopoterium spinosum" => 29,"Lasioglossum crassepunctatum" => 6,"Euodynerus
velutinus" => 16,"Leptochilus alpestris" => 71,"Nomada mavromoustakisi" => 55,"Psallus s
p1 M_PL_015" => 52,"Osmia subcornuta" => 29,"Amphicoma distincta" => 29,"Psilothrix cyan
eus " => 23…))

julia> @benchmark Q(tmp...)
BenchmarkTools.Trial:
  memory estimate:  9.86 MiB
  allocs estimate:  903
  --------------
  minimum time:     5.520 ms (0.00% GC)
  median time:      6.262 ms (0.00% GC)
  mean time:        6.672 ms (5.08% GC)
  maximum time:     11.120 ms (15.41% GC)
  --------------
  samples:          749
  evals/sample:     1

After

julia> @benchmark Q(tmp...)
BenchmarkTools.Trial:
  memory estimate:  180.19 KiB
  allocs estimate:  3636
  --------------
  minimum time:     4.190 ms (0.00% GC)
  median time:      5.002 ms (0.00% GC)
  mean time:        5.251 ms (0.16% GC)
  maximum time:     9.538 ms (32.33% GC)
  --------------
  samples:          952
  evals/sample:     1

Presumably, when the number of vertices is N, the space computation has been improved from O(N^2) to O(N).
(Perhaps the amount of time computation can be improved by a constant factor.)

Related issues

Checklist

• The code is covered by unit tests (I did not make any changes to the tests, because I did not change the function behavior.)
  • Additional cases or module in test/...
  • Relevant lines in test/runtests.jl
• The code is documented (Likewise, there are no changes to the documentation.)
• Docstrings written for every function
• If needed, additional lines in docs/src/...
• All contributors have added their name and affiliation to .zenodo.json

Pinging

Pinging @tpoisot

[tpoisot]

Really nice - I'm going to tag a new release with this, it's especially efficient now that the networks are sparse matrices!