Task. Add a new section in the LazySets manual

A>Random Zonotope

using LazySets

Z1=rand(Zonotope,dim=1,num_generators=2)
Z2=rand(Zonotope,dim=3,num_generators=5)

B>plot 2D zonotopes

using Plots
Z=rand(Zonotope,dim=2,num_generators=4)
plot(Z)

C>set membership

ZP = Zonotope([1.0, 0.0], [0.1 0.0; 0.0 0.1])

[1.0, 0.2] ∈ ZP

∈([1.0, 0.1], ZP)

D> centre, matrix of generators

Z.center
Z.generators
dim(Z)
constraints_list(Z)
ngens(Z)

E> containment check

Z = rand(Zonotope)
Z ⊆ Z
[Singleton(vi) ⊆ Z for vi in vertices_list(Z)]
Zonotope(Z.center, Z.generators/2) ⊆ Z
BallInf(zeros(2), 0.1) ⊕ Z.center ⊆ Z
BallInf(zeros(2), 1.0) ⊕ Z.center ⊆ Z

F>cartesian product of two zonotopes

Z2=rand(Zonotope,dim=1,num_generators=1)
Z1=rand(Zonotope,dim=2,num_generators=1)
CartesianProduct(Z1,Z2)

F>Random Zonotope

A1=rand(Zonotope,dim=3,num_generators=5)
A2=rand(Zonotope,dim=2,num_generators=7)
Plot(A2)

G> M-sum of zonotopes which is again a zonotope

Z1 = rand(Zonotope)
Z2 = rand(Zonotope)
minkowski_sum(Z1,Z2) isa Zonotope

scale(4,Z1)
translate(Z1,[1.,2.])

H>H-representation

convert(HPolytope,Z1)

I>affine map

 Z = rand(Zonotope)
 rand(2, 2) * Z # linear map
 rand(2, 2) * Z ⊕ rand(2) # affine map

J>enclosing axis-aligned box overapproximation

using LazySets.Approximations
Z1=Zonotpe([0.,0.],[[1.,0],[0.,1.],[1.,1.]])
plot(Z1)
C=overapproximate(Z1,Zonotope)
plot!(C)

K>example of the construction of a zonotope using line segments

Z=Zonotope([0.,0.],[[1.,0.],[0.,1.]])
plot(Z)
Z1=Zonotope([0.,0.],[[1.,0],[0.,1.],[1.,1.]]) #add line joining [-[1.,1.] ,[1.,1.]]
plot!(Z1)


L1 = LineSegment(-[1., 0.], [1.0, 0.0])
plot(L1)
L2 = LineSegment(-[0., 1.], [0., 1.])
plot!(L2)
L3 = LineSegment(-[1.,1.] ,[1.,1.])
plot!(L3)
plot!(L1 ⊕ L2 ⊕ L3, 1e-3) # Zonotope

L> linear map of a zonotope

d=rand(1,2)
d = [0. 1.; 1. 0.]
ZL=Zonotope([0.,0.],[[1.,1.],[1.,0.]])
T= linear_map(d,ZL)
plot(d)
plot!(ZL)

M>order reduction method available

S=rand(Zonotope,dim=2,num_generators=10)
reduce_order(S, 4)
plot(S)
E=reduce_order(S,3)
plot!(E)
reduce_order(S,2)

N>overapproximation of the convex hull of two zonotopes

Z=Zonotope([0.,0.],[[1.,0.],[0.,1.]])
plot(Z)
Z1=Zonotpe([0.,0.],[[1.,0],[0.,1.],[1.,1.]])
plot!(Z1)
D=CH(Z1,Z2)
plot!(D)

O>the split method

M,N=split(S,1)
plot(M)
plot!(N)
M,N=split(S,3)
plot(M)
plot!(N)
M,N=split(S,5)
plot(M)
plot!(N)