- Join over
**1.5M+ people** - Join over
**100K+ communities** - Free
**without limits** - Create
**your own community**

- 18:58
mforets on gh-pages

build based on ff34caaf (compare)

- 18:26
mforets on lazy_projection

- 18:26
mforets on master

Lazy projection constructor (#1… (compare)

- 18:26mforets closed #1967
- 15:30
mforets on gh-pages

build based on 8a8dcf7 (compare)

- 15:21
- 15:21sthagen starred JuliaReach/MathematicalSystems.jl
- 15:20
schillic on 678

- 15:20
schillic on master

replace Properties module by Ma… install MathematicalPredicates … Merge pull request #746 from Ju… (compare)

- 15:20schillic closed #746
- 15:20schillic closed #678
- 15:03mforets commented #160
- 14:55schillic synchronize #746
- 14:55
schillic on 678

replace Properties module by Ma… install MathematicalPredicates … (compare)

- 14:32
schillic on gh-pages

build based on cd5e146 (compare)

- 14:13schillic synchronize #746
- 14:13
schillic on 678

replace Properties module by Ma… install MathematicalPredicates … (compare)

perhaps my question is: what is the result (set type) of

`minkowski_difference(P, W)`

using LazySets

```
function maximal_RPI_set(S, 𝒲::LazySet, 𝒟::LazySet)
S_inv = inv(S)
𝒫 = 𝒟
k = 0
while true
k +=1
# concrete set operations (S_inv⋅𝒫 ⊖ 𝒲) ∩ 𝒟
𝒫⁺ = intersection(linear_map(S_inv, minkowski_difference(𝒫,𝒲)), 𝒟)
if (𝒫⁺ ⊆ 𝒫 && 𝒫 ⊆ 𝒫⁺)
break
end
𝒫 = 𝒫⁺
end
return 𝒫, k
end
n = 2
W = BallInf(zeros(n), 0.25)
D = BallInf(zeros(n), 5.0)
# Schur Matrix S
S = [0.755 0.7; 0.0 0.75]
@time maximal_RPI_set(S, W, D)
```

where $X$ is the minkowski difference

And also, I'd like to figure out, how the computational complexity of

And to do that, I first wanted to have a really performant code.

`linear_map`

growths with the number of constraints?And to do that, I first wanted to have a really performant code.

can't we use the information to quickly compute the action of the linear map to the HPOlytope

i think we had an open issue for this

@schillic this was your idea ?

For example, for the

Or does it make totally sense, that the

`minkowski_difference`

I know that I solve #constraint linear programs (therefore, it is linear in the number of constraints) and I was surprised, that the `linear_map`

does take significantly more time than the `minkowski_differnence`

and now, I try to figure out why exactly.Or does it make totally sense, that the

`linear_map`

takes more time?
they are very fast if the sets are zonotopic

since then linear maps are just the action over the generators

yes, to have an option to pass the inverted matrix

but if the output of your minkowski_difference is not zonotopic (if it is a general HPolytope) then you have to transform one by one the constraints

if the matrix is invertible then the linear map can be computed *without* passing to the vrep

it is easy, just see how it transforms each constraints

in the general case (the matrix is not invertible) you have to pass to the vertex representation and this can be expensive

`linear_map`

inverts again
there should be an option to pass

`S`

directly
and still

if we pass

`S`

to `linear_map`

there should be an option to pass S directly

maybe our messages crossed

because you just pass it to

`linear_map`

but would not use it
because you know it's invertible and the inverse is

`S`