Christian Schilling

Closes #1712. Requires: * [x] #1696 * [x] potentially a new release of `SetProg` (double-check) Remaining things * [ ] finish documentation * [ ] conversion of result to `LazySets.Ellipsoid`...

https://github.com/JuliaReach/LazySets.jl/blob/f62bd86c9f9491a400eb52da5b1c9f2df4a9b7da/src/Approximations/overapproximate.jl#L1612-L1615 The above method can be called with a `PolarDirections` object. Then it calls another method with just the type `PolarDirections`. https://github.com/JuliaReach/LazySets.jl/blob/f62bd86c9f9491a400eb52da5b1c9f2df4a9b7da/src/Approximations/overapproximate.jl#L1586-L1591 In the last line a new directions object...

In 2D we intersect with the plot limits. The same should be possible in 3D.

Let `Y = Bloating(X, ε, p)` where `ε > 0` and `X` is a polytope. The vertices of `Y` are the vertices of the convex hull of the `p`-balls around...

```julia julia> methods(scale) # 3 methods for generic function "scale": [1] scale(α::Real, x::Interval) in LazySets at .julia/dev/LazySets/src/Sets/Interval.jl:587 [2] scale(α::Real, Z::Zonotope) in LazySets at .julia/dev/LazySets/src/Sets/Zonotope.jl:303 [3] scale(α::Number, pz::PolynomialZonotope) in LazySets at...

Implement sobol sampler

1

To sample from `BallInf`'s, this package could be applied: https://github.com/stevengj/Sobol.jl _Originally posted by @mforets in https://github.com/JuliaReach/LazySets.jl/issues/917#issuecomment-543384333_

[`XUnit.jl`](https://github.com/RelationalAI-oss/XUnit.jl) can do that.

Plotting of lazy intersection with "min" heuristics is too coarse

2

The following code does *not* show the box approximation of the intersection (as I would have expected) but instead shows the set `X`: ```julia julia> LazySets.use_precise_ρ(::Intersection) = false # use...

Support function of lazy intersection with Optim depends on the order of the operands

2

The box approximation with `Optim` is too coarse. ```julia julia> X = BallInf([1.0, 2.0], 0.5); julia> Y = linear_map([1 0; -1 1], BallInf([2.0, 2.0], 1.0)); julia> Z = box_approximation(X ∩...

https://github.com/JuliaReach/LazySets.jl/blob/0a220f74437b6ee917325ffe68ddd3ccddda2ac4/src/Approximations/symmetric_interval_hull.jl#L27-L34 https://github.com/JuliaReach/LazySets.jl/blob/0a220f74437b6ee917325ffe68ddd3ccddda2ac4/src/Approximations/symmetric_interval_hull.jl#L62-L74 One of them is probably faster. Both methods should use that same code (add a new helper function with arguments `c` and `r`). We should also try out...