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- 23:06
mforets on gh-pages

build based on 25d08115 (compare)

- 22:30
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#1207 - Concrete projection of … (compare)

- 22:30mforets closed #1959
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simplify all/any for simple una… Merge pull request #1980 from J… #1928 - Major update of concret… and 1 more (compare)

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build based on 0f2815b4 (compare)

- 20:31cqql commented #1928
- 20:25mforets opened #1990
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#1928 - Major update of concret… (compare)

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- 19:41schillic labeled #1935
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- 19:40schillic labeled #1934
- 19:40schillic labeled #1934

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

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`

hmm this is related but not the same?

we didn't speak about passing the inverse matrix there