Key 0 returned by AttractrosViaRecurrences

[Datseris]

Describe the bug

If my understanding is correct, the output of basins_fractions or basins_of_attraction with AttractorsViaRecurrences should never contain 0 as an attractor ID. Only -1 and the positive integers. Yet, here is an example where 0 is a key in the found basins!

Minimal Working Example

using Attractors

function dissipative_standard_map_rule(u, p, n)
    x, y = u
    ν, f₀ = p
    s = x + y
    xn = mod2pi(s)
    yn = (1 - ν)*y + f₀*(sin(s))
    return SVector(xn, yn)
end

p0 = (ν = 0.02, f0 = 4.0)
u0 = [0.1, 0.1]
ds = DeterministicIteratedMap(dissipative_standard_map_rule, u0, p0)
density = 2000
xg = range(0, 2π; length = density+1)[1:end-1]
yg = range(-ymax, ymax; length = density)
grid = (xg, yg)

mapper_kwargs = (
    mx_chk_att = 3,       # attractors are well-separated in the state space: so this is small
    mx_chk_fnd_att = 200, # attractors are low period orbits, so this is small
    mx_chk_loc_att = 200, # very high multistability means this should be high
    mx_chk_hit_bas = 10,  # for more accuracy, but in any case basins are so riddled
                          # that it is unlikely that this clause will even be hit...
    sparse = false, # we want to compute full basins
    Ttr = 10,
)

mapper = AttractorsViaRecurrences(ds, grid; mapper_kwargs...)

basins, attractors = basins_of_attraction(mapper)
ids = sort!(unique(basins))

142-element Vector{Int32}:
  -1
   0
   1
   2
   3
   4
   5
   6
   7
   8
   ⋮

Package versions

Latest stable.

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This issue also highlights that a logging system is useful (discussed in #70 )

[awage]

Using sparse = true gives the correct answer. That's a problem with the matrix in bsn_nfo. I'll check this

[Datseris]

This means that there are some cells whose initial conditions are not used (because by defualt teh grid isinitialized with 0s everywhere when sparse = false). But why would this be? Why would some cells be skipped?

[awage]

Shouldn't happen. The key 0 is not present in attractors. Some cells are not initialized or they are skipped for some reason.