add 'setops' option to 'FirstOrder'

Author: schillic

src/Discretization/FirstOrderModule.jl

@@ -4,7 +4,8 @@
 module FirstOrderModule
 
 using ..DiscretizationModule
-using ..Exponentiation: _exp, BaseExp
+using ..Exponentiation: _exp, _alias, BaseExp
+using ..ApplySetops: _apply_setops
 using LinearAlgebra
 using MathematicalSystems
 using LazySets
@@ -35,18 +36,20 @@ The transformations are [LeGuernicG10](@cite):
 
 where ``B_ε`` is the input ball of radius ``ε`` centered in the origin.
 """
-struct FirstOrder{EM} <: AbstractApproximationModel
+struct FirstOrder{EM,SO} <: AbstractApproximationModel
     exp::EM
+    setops::SO
 end
 
 # convenience constructor
-function FirstOrder(; exp=BaseExp)
-    return FirstOrder(exp)
+function FirstOrder(; exp=BaseExp, setops=:lazy)
+    return FirstOrder(_alias(exp), _alias(setops))
 end
 
 function Base.show(io::IO, alg::FirstOrder)
     print(io, "`FirstOrder` approximation model with:\n")
     print(io, "    - exponentiation method: $(alg.exp)\n")
+    print(io, "    - set operations method: $(alg.setops)\n")
     return nothing
 end
 
@@ -69,6 +72,7 @@ function discretize(ivp::IVP{<:CLCS,<:AbstractZonotope}, δ, alg::FirstOrder)
     Xδ = Φ * X0
     α = (exp(norm_A * δ) - 1 - norm_A * δ) * norm(X0, Inf)
     Ω0 = ConvexHull(X0, Xδ + BallInf(zeros(n), α))
+    Ω0 = _apply_setops(Ω0, alg.setops)
 
     # create result
     X = stateset(ivp)
@@ -96,10 +100,12 @@ function discretize(ivp::IVP{<:CLCCS,<:AbstractZonotope}, δ, alg::FirstOrder)
     norm_U_over_A = norm(U, Inf) / norm_A
     α = factor * (norm(X0, Inf) + norm_U_over_A)
     Ω0 = ConvexHull(X0, Xδ + δ * U + BallInf(zeros(n), α))
+    Ω0 = _apply_setops(Ω0, alg.setops)
 
     # discretize inputs
     β = factor * norm_U_over_A
     V = δ * U + BallInf(zeros(n), β)
+    V = _apply_setops(V, alg.setops)
 
     # create result
     B = IdentityMultiple(one(eltype(A)), size(A, 1))