Extra bin when using `probabilities` vs `invariantmeasure`

[kahaaga]

CC @rusandris (moved your comment into a separate issue)

          This might be a separate issue, but since it is related, I'll mention it here.

Why one get different number of states in the outcome space when using probabilities vs. invariantmeasure?

using DynamicalSystems

henon_rule(x, p, n) = SVector{2}(1.0 - p[1]*x[1]^2 + x[2], p[2]*x[1])
henon = DeterministicIteratedMap(henon_rule, zeros(2), [1.4, 0.3])
orbit, t = trajectory(henon, 20_000; Ttr = 500)

using ComplexityMeasures
grid_size = 20
binning = RectangularBinning(grid_size)
p_cm = probabilities(ValueBinning(binning),orbit) #100 states

which gives a 100 states.

iv = invariantmeasure(orbit,binning)
P_cm,symbols = transfermatrix(iv) #101 states?? 

which in contrast gives 101 states, despite using the same binning.

Originally posted by @rusandris in https://github.com/JuliaDynamics/ComplexityMeasures.jl/issues/337#issuecomment-1847166764

[kahaaga]

I thought this had to do with #328, but it seems that the problem is not that, because I can still reproduce this issue on main.

[rusandris]

because I can still reproduce this issue on main

Yes, it's still there in the 3.0 release as well

[Datseris]

is this solved? wasn't this about the usage of precise?

[kahaaga]

This isn't solved. The issue was unrelated to the use of precise, or at least not entirely solved by utilizing precise.