#1851 - Add type parameter of linear constraints

[mforets]

Closes #1851.
Closes #2035.
Closes #2036.
Closes #1771.
Closes #1802.

[mforets]

the next test that fails is a conversion: convert(HPolygon, po). to fix this properly, would require doing #2036, because the implementation just passes over that array (as it should). similarly, we may require #2035 for HPolytope and #1771 for HPolyhedron.

@schillic do you have any particular suggestion about this?

[schillic]

I do not understand the problem. If you have to do all of them in one PR, that is fine with me.

[mforets]

If you have to do all of them in one PR, that is fine with me.

okay. i'll try to make the minimal changes...

I do not understand the problem.

because HPolygon type is now concretely typed, one cannot convert back to an HPolygon with the constraints list of an HPolygonOpt.

julia> p = rand(HPolygon)
HPolygon{Float64,Array{Float64,1}}(HalfSpace{Float64,Array{Float64,1}}[HalfSpace{Float64,Array{Float64,1}}([1.0123623399683432, 0.1830447941142368], 2.8290283339025173), HalfSpace{Float
64,Array{Float64,1}}([0.6808271818788811, 0.9234031649421612], 2.9682105564317505), HalfSpace{Float64,Array{Float64,1}}([0.3046243758979319, 0.6597164293182575], 1.8242398560365105), Ha
lfSpace{Float64,Array{Float64,1}}([-1.6682351717436381, 0.6468752884603611], -0.12037797885224744), HalfSpace{Float64,Array{Float64,1}}([-0.904336674244401, -0.4010639622029236], -0.552
9601287375698), HalfSpace{Float64,Array{Float64,1}}([-0.36130622049394745, -1.1136226665645736], 0.022726211675922647), HalfSpace{Float64,Array{Float64,1}}([0.5523450116922028, -0.87508
97492045417], 1.5552533054118776), HalfSpace{Float64,Array{Float64,1}}([0.3837191570446274, -0.02326329886297751], 1.0427247616868596)])


julia> convert(HPolygonOpt, p)
HPolygonOpt{Float64}(HalfSpace{Float64,VN} where VN<:AbstractArray{Float64,1}[HalfSpace{Float64,Array{Float64,1}}([1.0123623399683432, 0.1830447941142368], 2.8290283339025173), HalfSpac
e{Float64,Array{Float64,1}}([0.6808271818788811, 0.9234031649421612], 2.9682105564317505), HalfSpace{Float64,Array{Float64,1}}([0.3046243758979319, 0.6597164293182575], 1.82423985603651
05), HalfSpace{Float64,Array{Float64,1}}([-1.6682351717436381, 0.6468752884603611], -0.12037797885224744), HalfSpace{Float64,Array{Float64,1}}([-0.904336674244401, -0.4010639622029236],
 -0.5529601287375698), HalfSpace{Float64,Array{Float64,1}}([-0.36130622049394745, -1.1136226665645736], 0.022726211675922647), HalfSpace{Float64,Array{Float64,1}}([0.5523450116922028, -
0.8750897492045417], 1.5552533054118776), HalfSpace{Float64,Array{Float64,1}}([0.3837191570446274, -0.02326329886297751], 1.0427247616868596)], 1)

julia> constraints_list(ans)
8-element Array{HalfSpace{Float64,VN} where VN<:AbstractArray{Float64,1},1}:
 HalfSpace{Float64,Array{Float64,1}}([1.0123623399683432, 0.1830447941142368], 2.8290283339025173)
 HalfSpace{Float64,Array{Float64,1}}([0.6808271818788811, 0.9234031649421612], 2.9682105564317505)
 HalfSpace{Float64,Array{Float64,1}}([0.3046243758979319, 0.6597164293182575], 1.8242398560365105)
 HalfSpace{Float64,Array{Float64,1}}([-1.6682351717436381, 0.6468752884603611], -0.12037797885224744)
 HalfSpace{Float64,Array{Float64,1}}([-0.904336674244401, -0.4010639622029236], -0.5529601287375698)
 HalfSpace{Float64,Array{Float64,1}}([-0.36130622049394745, -1.1136226665645736], 0.022726211675922647)
 HalfSpace{Float64,Array{Float64,1}}([0.5523450116922028, -0.8750897492045417], 1.5552533054118776)
 HalfSpace{Float64,Array{Float64,1}}([0.3837191570446274, -0.02326329886297751], 1.0427247616868596)

julia> HPolygon(ans)
ERROR: MethodError: no method matching HPolygon(::Array{HalfSpace{Float64,VN} where VN<:AbstractArray{Float64,1},1})
Closest candidates are:
  HPolygon() where N<:Real at /home/mforets/.julia/dev/LazySets/src/Sets/HPolygon.jl:78
  HPolygon(::Array{HalfSpace{N<:Real,VN<:AbstractArray{N<:Real,1}},1}; sort_constraints, check_boundedness, prune) where {N<:Real, VN<:AbstractArray{N,1}} at /home/mforets/.julia/dev/La
zySets/src/Sets/HPolygon.jl:52
  HPolygon(::AbstractArray{N<:Real,2}, ::AbstractArray{N<:Real,1}; sort_constraints, check_boundedness, prune) where N<:Real at /home/mforets/.julia/dev/LazySets/src/Sets/HPolygon.jl:86
Stacktrace:
 [1] top-level scope at REPL[5]:1

[mforets]

though if it's only this issue, i think i prefer to comment out those tests for a while, and put them back once the types are ready..

[schillic]

though if it's only this issue, i think i prefer to comment out those tests for a while, and put them back once the types are ready..

I changed my mind. It is not good to break code. It also ultimately requires more work to comment out the tests.

[mforets]

the following error is similar with conversion, but with HPolytope

julia> H = rand(Hyperrectangle)
Hyperrectangle{Float64,Array{Float64,1},Array{Float64,1}}([-0.5488471214626174, 1.6132145460478071], [0.9929214238936357, 0.8834733482003816])

julia> convert(HPolytope, H)

HPolytope{Float64}(HalfSpace{Float64,VN} where VN<:AbstractArray{Float64,1}[HalfSpace{Float64,LazySets.Arrays.SingleEntryVector{Float64}}([1.0, 0.0], 0.4440743024310183), HalfSpace{Fl
oat64,LazySets.Arrays.SingleEntryVector{Float64}}([0.0, 1.0], 2.496687894248189), HalfSpace{Float64,LazySets.Arrays.SingleEntryVector{Float64}}([-1.0, 0.0], 1.541768545356253), HalfSp
ace{Float64,LazySets.Arrays.SingleEntryVector{Float64}}([0.0, -1.0], -0.7297411978474255)])

julia> HPolygon(constraints_list(ans))
ERROR: MethodError: no method matching HPolygon(::Array{HalfSpace{Float64,VN} where VN<:AbstractArray{Float64,1},1})
Closest candidates are:
  HPolygon() where N<:Real at /home/mforets/.julia/dev/LazySets/src/Sets/HPolygon.jl:78
  HPolygon(::Array{HalfSpace{N<:Real,VN<:AbstractArray{N<:Real,1}},1}; sort_constraints, check_boundedness, prune) where {N<:Real, VN<:AbstractArray{N,1}} at /home/mforets/.julia/dev/
LazySets/src/Sets/HPolygon.jl:52
  HPolygon(::AbstractArray{N<:Real,2}, ::AbstractArray{N<:Real,1}; sort_constraints, check_boundedness, prune) where N<:Real at /home/mforets/.julia/dev/LazySets/src/Sets/HPolygon.jl:
83
Stacktrace:
 [1] top-level scope at REPL[97]:1

[mforets]

I changed my mind. It is not good to break code. It also ultimately requires more work to comment out the tests.

ok, i will then make the changes related to sets with constraints here.. unfortunately it is not only the tests that i pasted above that fail; there are others, because in many places the output of a function can return either HPolygon/HPolytope/HPolyhedron depending on the dimension etc.

[mforets]

The PR now passes tests locally, it is ready to go from my side if CI doesn't complain!

Most (if not all) of the issues in #1802 are solved, so that issue can also be considered closed, in the sense that concretely typed array containers are now used.

I left some TODOs for my continuation of this work in a follow up PR that will begin to narrow the specialization for the normal direction types, such that they are more predictable and better match those from their input types.

[schillic]

There are still some problems in the documentation build.