JuliaReach/Lobby

Calculating Reachable states of Dynamical Systems in Julia

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

Benoît Legat

@blegat

@mforets The advantage of JuMP is that it will automatically add needed caching and bridges layers

Christian Schilling

@schillic

@blegat while you are here: i cannot get MOI to work with Rationals. what is wrong here?

using GLPK, MathOptInterface
const MOI = MathOptInterface
N = Rational{Int}
solver = GLPK.Optimizer(method=GLPK.EXACT)
x = MOI.add_variables(solver, 1)
MOI.set(solver, MOI.ObjectiveSense(), MOI.FEASIBILITY_SENSE)
a = MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.(N[1], x), N(0))
b = MOI.LessThan(N(0))
MOI.add_constraint(solver, a, b)

this throws an error:

ERROR: MathOptInterface.UnsupportedConstraint{MathOptInterface.ScalarAffineFunction{Rational{Int64}},MathOptInterface.LessThan{Rational{Int64}}}: `MathOptInterface.ScalarAffineFunction{Rational{Int64}}`-in-`MathOptInterface.LessThan{Rational{Int64}}` constraint is not supported by the model.

note that for N = Float64 this works

this is the LP (no objective) s.t. x <= 0

Christian Schilling

@schillic

hm, it seems that GLPK does not support adding Rational constraints at all

https://github.com/JuliaOpt/GLPK.jl/blob/master/src/MOI_wrapper.jl#L1003

this is the method for Float64, but there is no method for other types

Christian Schilling

@schillic

(to support the theory, Float32 gives the same error)

Christian Schilling

@schillic

@mforets: i think the LP solvers only support Float64 (i updated my comment JuliaReach/LazySets.jl#1701). we should discuss how to proceed. one way is to convert from N to Float64, solve the LP, then convert back to N (which obviously has soundness issues, but it may be better than crashing; maybe there should be an option to print a warning or error)

Marcelo Forets

@mforets

I recall some threads about numeric types in MOI and JuMP. IMO LazySets should not make conversions of the result; if it doesnt qorm it doesnt slen

Doesnt work

In verimag some people used PPL, a library for polyhedra with exact coordinates

Christian Schilling

@schillic

i think we get into lots of trouble if the result changes the type

but ok

but are you fine with conversion to Float64 before calling the solver?

or should we just crash and say that we only support Float64?

i'm fine with either choice because we anyway always used Float64 so far

and it is somewhat cleaner to not do conversions

I recall some threads about numeric types in MOI

yes, MOI is ready for that. it only crashes when i pass the model to a solver

Marcelo Forets

@mforets

So the best thing may be to not do anything..

Christian Schilling

@schillic

ok but then i need to remove many Rational tests

just to say

i agree with you :+1:

can you confirm?

i think the code should work if the solver supported it

should we print a warning whenever a user tries to set up an LP with non-Float64? because the error is quite cryptic. the downside is that if the user employs a solver that supports the type, then the warning is "wrong"

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