JuliaReach/Lobby

Calculating Reachable states of Dynamical Systems in Julia

Marcelo Forets

@mforets

yes, but it is computed only once in his function

it is needed to be computed only once in his function, this is what i meant

Christian Schilling

@schillic

i think we agree that there should be an option to pass the inverted matrix

Marcelo Forets

@mforets

:thumbsup:

Christian Schilling

@schillic

actually it is not needed at all

because you just pass it to linear_map but would not use it

because you know it's invertible and the inverse is S

Marcelo Forets

@mforets

indeed

Christian Schilling

@schillic

maybe there should be a new function linear_map_inverse?

Marcelo Forets

@mforets

hmm optionally passing the extra stuff to linear_map seems better imo

Christian Schilling

@schillic

@ueliwechsler: sorry that this drifted. do you still follow? :)

Marcelo Forets

@mforets

@ueliwechsler congratulations you earned an issue! :p

JuliaReach/LazySets.jl#1500

hmm this is related but not the same?

we didn't speak about passing the inverse matrix there

Christian Schilling

@schillic

true, we want to do sth even faster

where you already know the inverse

Marcelo Forets

@mforets

yup

Christian Schilling

@schillic

but it's definitely related

Marcelo Forets

@mforets

ok we may want to include the optional inverse in this issue as well

this issue was some logic (my logic) broken

Christian Schilling

@schillic

Marcelo Forets

@mforets

let me add a comment about this discussion.. then i'll head for lunch

Christian Schilling

@schillic

:+1:

Christian Schilling

@schillic

@ueliwechsler: it seems to me be that in your minkowski_difference the second argument is a (again: constant) BallInf. maybe that can be exploited, but from the code for minkowski_difference i don't see how
however, your inputs are zonotopes, minkowski_difference of two zonotopes is again a zonotope (not in our current implementation, but it should be easy to add a method for that; this is JuliaReach/LazySets.jl#586), and the linear map of a zonotope is again a zonotope. the "problematic" operation here is the intersection with a BallInf, which does not preserve "being a zonotope." if you are willing to pay the price of an overapproximation to a zonotope at this point, you would get rid of the remove_redundant_constraints and the linear_map would be cheap as well. but the intersection then becomes more complicated (i think there is no way around some bottleneck :P)

Christian Schilling

@schillic

for the minkowski_difference I know that I solve #constraint linear programs (therefore, it is linear in the number of constraints)

no, the implementation of minkowski_difference performs m support-function queries, which in your case are applied to a BallInf (which is very cheap)

so i'm not surprised that minkowski_difference is fast

ueliwechsler

@ueliwechsler

Thanks for your help guys! :D
Yes, I followed (but then my supervisor interrupted me)
For my problem, I most likely need to work with HPolytopes so even though the Zonotopes option sounds really interesting, I cannot use it for my current issue.
But enabling linear_map to pass the matrix S directly would be exactly what I was looking for since if I can get rid of the performance penalty of computing the inverse every iteration.

Christian Schilling

@schillic

but then my supervisor interrupted me

they tend to do that :)

ueliwechsler

@ueliwechsler

I see, so I have to be really careful with my conclusions since they depend heavily on the type 😅

Christian Schilling

@schillic

so the BallInfs are just examples?

yes, it is common that you can write a much more efficient algorithm if you know the type of set you are dealing with

and that's also why preserving more concrete types is beneficial

for instance in your first loop iteration you could work with zonotopes (assuming we have the efficient minkowski_difference) until the intersection "for free"

but then in the second iteration you will have an HPolytope and have to use the slower methods

but that happens automatically

ueliwechsler

@ueliwechsler

I most cases, I would use the BallInf, but in general, I'd like to know the computational complexity of the general case, which for me is HPolytope.

Christian Schilling

@schillic

ok sure

ueliwechsler

@ueliwechsler

Thanks for the clarification, I was sloppy while dealing with the concrete types

Christian Schilling

@schillic

no problem, it gave us the opportunity to help :)

i can have a look at JuliaReach/LazySets.jl#1500 (the linear map) in the next days, but if you are eager, you can just add this option yourself and see if it helps (here)

this has a nasty tail, so you have to pass the option through several helper functions :)

basically make this line optional

ueliwechsler

@ueliwechsler

👍 thanks, I will try it out. I am curious how much it will change the performance.

Marcelo Forets

@mforets

minkowski_difference for hyperrectangular sets can be specialized as well or not?

Marcelo Forets

@mforets

But it is cheap anyways give 2 ballinf as you said above..

The equality check can also be improved..? Save half the evaluations in the dual inclusion by checking approximate equality of the support functions

Christian Schilling

@schillic

minkowski_difference for hyperrectangular sets can be specialized as well or not?

maybe, but the hyperrectangle will definitely be destroyed by the linear_map
but that would be an alternative to my other suggestion: overapproximate the result of linear_map by a hyperrectangle. hyperrectangles are closed under intersection, so this would give you a "stable" loop. and all of these operations are cheap, so i would really give it a try, just to see the potential performance boost

@ueliwechsler: can you try out the variant of your algorithm with this change?

𝒫⁺ = intersection(overapproximate(linear_map(S_inv, minkowski_difference(𝒫,𝒲)), Hyperrectangle), 𝒟)

The equality check can also be improved..? Save half the evaluations in the dual inclusion by checking approximate equality of the support functions

i didn't understand this proposal. but yeah, if typically one of the two inclusions fails, it is more efficient to do that check first (because it usually avoids the second check). and again for hyperrectangles this equality check can be made very efficient

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