Transferoperator in Compressed Sparse Column format

[April-Hannah-Lena]

As mentioned in #72 this is the PR for TransferOperator using CSC format. This is also not tested yet, I will continue to update.

[April-Hannah-Lena]

good news:

• SplitOrderedCollections has been added to the julia general registry after the mandatory waiting time of 3 days.
• A working build of the CSC TransferOperator is now up. One can now run

  
  using GAIO

the Lorenz system

const σ, ρ, β = 10.0, 28.0, 0.4 v((x,y,z)) = (σ(y-x), ρx-y-xz, xy-β*z) f(x) = rk4_flow_map(v, x)

center, radius = (0,0,25), (30,30,30) P = BoxPartition(Box(center, radius), (128,128,128)) F = BoxMap(f, P, no_of_points=200)

x = (sqrt(β(ρ-1)), sqrt(β(ρ-1)), ρ-1) # equilibrium W = unstable_set!(F, P[x])

T = TransferOperator(F, W) (λ, ev) = eigs(T)

μ = ev[1] T * μ ≈ μ

I also realized that the CSC version has the advantage of being factorizable, that is, decompositions like QR are built-in to SparseArrays.jl. Of course, there are some caveats that we should probably discuss though. 

[April-Hannah-Lena]

Ok you can now run the above code, plus the extra lines:

μ = ev[1]
ν = deepcopy(μ)
ν[160228] = 1.0 # add value to some random box outside the set
η = T * ν

The invariant part remains invariant (as expected), but the new box causes the support to grow (also as expected).

[gaioguy]

Ok, the transfer operator works again, but there still seems to be a conflict that must be resolved before we can merge this.

[April-Hannah-Lena]

I'm working on resolving conflicts right now, this PR will be scratched in favor of one which more aligns with the master branch