TMJets gives different results based on set representation of X0

[schillic]

The blue and red sets should be equivalent. The only difference is that X0 is once represented as a LineSegment and once as a Hyperrectangle. (The green set is only there for comparison.)

In one case the system starts from [-1, 1] as it should and in the other case it starts from [-2, 2]. This scaling by 2 is consistent for other choices of X0.

using ReachabilityAnalysis, Plots

@taylorize function f!(dx, x, p, t)
    dx[1] = x[2]
    dx[2] = -x[1]
end
A = [0.0 1; -1 0]

X0 = LineSegment([1.0, 0], [-1.0, 0])
X1 = Hyperrectangle([0.0, 0], [1.0, 0])
println(isequivalent(X0, X1))  # prints `true`

Tmax = 3*π

prob1 = @ivp(x' = A*x, x(0) ∈ X0)
prob2 = @ivp(x' = f!(x), x(0) ∈ X0, dim=2)
prob3 = @ivp(x' = f!(x), x(0) ∈ X1, dim=2)

alg1 = GLGM06(δ=1e-2)
alg2 = TMJets21a(orderT=10, orderQ=2, abstol=1e-15)

sol1 = solve(prob1, alg=alg1, T=Tmax)
sol2 = solve(prob2, alg=alg2, T=Tmax)
sol3 = solve(prob3, alg=alg2, T=Tmax)

fig = plot(ylim=[-2, 2], xlab="t", ylab="x(t)")
plot!(fig, sol2, vars=(0, 1), lw=0, c=:blue)
plot!(fig, sol3, vars=(0, 1), lw=0, c=:red)
plot!(fig, sol1, vars=(0, 1), lw=0, c=:green, alpha=1)