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mforets opened this issue Jun 12, 2021 · 1 comment · May be fixed by #3837
Open

Concrete cartesian product of zonotopes in standard form #2739

mforets opened this issue Jun 12, 2021 · 1 comment · May be fixed by #3837
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@mforets
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mforets commented Jun 12, 2021

If Z is an n-dimensional zonotope of order 2, we say that it is in standard form if its generators matrix is G = [M D] with M and D n x n matrices and D diagonal.

Create a function cartesian_product_standard(X::Vector{Zonotope}) that returns the n-fold cartesian product in standard form, assuming all the zonotopes in X are in standard form. Bonus points if it can handle zonotopes (X[i]) of different dimensions.
@schillic
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Other possibilities, ordered by effort:

  • Add a new argument normal_form::Bool (or even normal_form::FullDiagonal if we want to add more normal forms later) to cartesian_product.
  • Add a dispatch on Zonotopes whose generator matrix is given by a certain type (a block matrix [M D] where D is a Diagonal) to cartesian_product.
  • Add a new set type ZonotopeMD <: AbstractZonotope which behaves like Zonotope but preserves the normal form.

@schillic schillic added the feature ➕ A new feature label Jun 12, 2021
@schillic schillic changed the title Concrete cartesian product in standard form Concrete cartesian product of zonotopes in standard form Jun 14, 2021
alecarraro added a commit to alecarraro/LazySets.jl that referenced this issue Apr 16, 2025
@alecarraro
JuliaReach#2739: addded ZonotopeMD and support for Cartesian product …
8f8d57d 
…in normal form
alecarraro added a commit to alecarraro/LazySets.jl that referenced this issue Apr 16, 2025
@alecarraro
JuliaReach#2739: addded ZonotopeMD and support for Cartesian product …
7e8f9c4 
…in normal form
@alecarraro alecarraro linked a pull request Apr 16, 2025 that will close this issue
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alecarraro added a commit to alecarraro/LazySets.jl that referenced this issue Apr 21, 2025
@alecarraro
JuliaReach#2739: addded ZonotopeMD and support for Cartesian product …
c307663 
…in normal form
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#2739: added ZonotopeMD and support for Cartesian product in normal alecarraro/LazySets.jl
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@schillic @mforets