#668 - Replace inout_map by low-dimensional flowpipes

[schillic]

Closes #668.

Summary:

• Add a type SparseReachSet which behaves like a ReachSet but additionally stores the dimensions in which it was computed (from now on, a ReachSet must always be high dimensional).
• Add an interface AbstractReachSet for ReachSet and AbstractReachSet with the methods set, time_start, time_end, and project. The project method just receives a projection matrix.
• Extend low-dimensional CPost operators such that they return SparseReachSet flowpipes, which consists of two steps:
  • Add a helper function compute_dimensions to compute the dimensions for SparseReachSets (currently this function resides in BFFPSV18).
  • Store SparseReachSets.
• Modify project/project_reach:
  • Projections are now computed for each AbstractReachSet individually.
  • Time as output is handled in a slightly different way: First we create the projection by ignoring the time dimension and only in the end do we create a CartesianProduct with the time interval.
• Remove inout_map from reachability algorithms (it still exists for properties, which can maybe be refactored another time).

Some of the benchmarks in https://github.com/JuliaReach/ReachabilityBenchmarks need to be updated (because we access some ReachSet fields explicitly 👎).

[mforets]

a ReachSet must always be high dimensional).

i guess you mean full dimensional

[mforets]

There's also the related issue #541 but we can do on a follow-up PR.

[schillic]

This changeset does not work with the way we implemented the hybrid algorithm. We need to discuss this.

[schillic]

The last commit solved it again. It is certainly a workaround but I think overall the state has improved 😃

[mforets]

LGTM 🎉