sampling

[ga72kud]

How does the sampling work for a LazySet. I used Projections and intersections to process the sets. Is there a method for flowpipes

[schillic]

Flowpipes live in ReachabilityAnalysis (RA). I transferred the issue there. In RA there is no sample method, but you can easily define it. Here is one proposal:

LazySets.sample(fp::ReachabilityAnalysis.ReachSolution, m) = vcat([sample(set(R), m) for R in array(flowpipe(fp))]...)

Example:

using ReachabilityAnalysis, Polyhedra, Plots

# sample model (here: Motor)

using SparseArrays

function motor_homog()
    I = [1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 6, 7, 7, 7, 7, 8]
    J = [2, 3, 2, 1, 2, 3, 4, 1, 6, 7, 6, 5, 6, 7, 8, 5]
    V = [1, 8487.2, -1.0865, -2592.1, -21.119, -698.91, -141399.0, 1.0, 1.0,
         8487.2, -1.0865, -2592.1, -21.119, -698.91, -141399.0, 1.0]
    A = sparse(I, J, V)
    X0 = Hyperrectangle(low=[0.002, 0.0, 0.0, 0.0, 0.001, 0.0, 0.0, 0.0],
                        high=[0.0025, 0.0, 0.0, 0.0, 0.0015, 0.0, 0.0, 0.0])
    return @ivp(x' = Ax, x(0) ∈ X0)
end

P = motor_homog();

# compute the flowpipe

F = solve(P, T=0.02, δ = 1e-3);

# sample 30 elements from each reach set

julia> V = sample(F, 30);

# plot the reach sets and the samples (here I plot dimensions 1 and 2)

julia> plot(F, vars=(1, 2))
julia> plot!([Singleton(p[1:2]) for p in V])

[ga72kud]

@schillic, thank you, this helped. I did not understand all the details of the example. This is what I got:

function sample_flowpipe(fp, m)
	return [LazySets.sample(set(R), m) for R in fp]
end

 sample_flowpipe(𝒫ℛ, 3)