Convert TM to zonotop

TM_to_Zonotope.jl

using LazySets, TaylorModels
import IntervalArithmetic
const IA = IntervalArithmetic

const zeroI = IA.Interval(0.0) # [0.0, 0.0]
const oneI = IA.Interval(1.0) # [1.0, 1.0]
const symI = IA.Interval(-1.0, 1.0)
@inline zeroBox(m) = IntervalBox(zeroI, m)
@inline symBox(m) = IntervalBox(symI, m)

# cuts the Δt into NΔt pieces, returning a vector of zonotopes
function TM_Zono(tTM, vTM, n, NΔt)
    N = length(tTM)
    Rsets = Vector{Zonotope{Float64}}(undef, NΔt)

    X = vTM[:, i]
  
    # pick the time domain of the given TM (same in all dimensions)
    Δt = TaylorModels.domain(X[1])

    if NΔt > 1
        Δt_div = range(IA.inf(Δt), stop=IA.sup(Δt), length=NΔt+1)
    else
        Δt_div = Δt
    end

    for k in 1:(length(Δt_div)-1)
        # evaluate the Taylor model in time, the coefficents are now intervals
        X_Δt = evaluate(X, IA.Interval(Δt_div[k], Δt_div[k+1]))

        # builds the associated taylor model for each coordinate j = 1...n
        X̂ = [TaylorModelN(X_Δt[j], X[j].rem, zeroBox(n), symBox(n)) for j in 1:n]

        # floating point rigorous polynomial approximation
        fX̂ = TaylorModels.fp_rpa.(X̂)

        # LazySets can overapproximate a Taylor model with a Zonotope
        Zi = overapproximate(fX̂, Zonotope)
        t0 = Δt_div[k]
        t1 = Δt_div[k+1]

        Rsets[NΔt * (i - 1) + k] = Zi
    end
  
    return Rsets
end