Sensitivity branch has a major bug for power mean proximity

[rafaqz]

ConScape.jl/src/gridrsp.jl

Line 765 in 355c182

S_e_aff, S_e_cost = PM_sensitivity(grsp.g.affinities, nothing, grsp.θ, grsp.W, grsp.Z, grsp.Z, qˢ, qᵗ, targetnodes)

Here you can see that grsp.Z is passed in for both Z and K arguments. But K is written into in PM_sensitivity here with ./=:

ConScape.jl/src/randomizedshortestpath.jl

Line 504 in 355c182

K ./= [Z[lmarks[i],i] for i in 1:length(lmarks)]'

This also alters Z, as they are the same matrix. Z is later passed to betweenness functions despite being altered:

ConScape.jl/src/randomizedshortestpath.jl

Line 509 in 355c182

bet_edge_k = ConScape.RSP_edge_betweenness_kweighted(W, Z, qˢ, qᵗ, K, lmarks)

@ninbrm I assume this is not intended, and will remove for testing the new version. Please confirm!

[ninbrm]

I wouldn't assume this is unintended, as it seems to produce the right results. In the context of the power mean K is defined as Z.

[rafaqz]

Only produces the right result when theta = 1.0 ?

The comment also says that K is a copy of Z, which makes sense. It just isnt actually a copy, its the same matrix.

[ninbrm]

I recall that we had at some point a bug where we needed to divide with theta instead of multiply -- or the other way round, I am not sure. The result was that it worked for theta = 1 and I only picked up the bug when using theta \neq 1. Looking at the code and the algorithm in the appendix, it seems that bug didn't get fixed: S_e_aff = (bet_edge_k.*Aⁱ .- (bet_node_k./rowsums).*Idx).*θ -- whereas line 15 of algorithm 2 has a division with theta. I am a bit puzzled as I cannot find the file that has this corrected. Does changing this fix the bug?
RE: K=copy(Z), I guess if later computations are changing Z, this is probably undesirable... This is not handled by the "scope" of the variable within the function -- I am far out of my zone of comfort here?