Revise type parameters of LinearMap

[schillic]

struct LinearMap{NM, N} <: LazySet{N}

Proposal:

struct LinearMap{N, NM} <: LazySet{N}

Reason: All other set types have the numeric type as their first argument. With this change we can do this:

function foo(X::LazySet{N}) where {N<:AbstractFloat}
    ...
    zero(N)
    ...
end

(We might actually do this already.)

[schillic]

While we are at it, should we add another type parameter for the set type, as we do for the other lazy operations?

[mforets]

yes, i agree. while we are at it, we can also add the parametric type of the linear map.

[schillic]

We could also change the second type argument from the matrix numeric type NM (which should usually be identical to N anyway) to the actual matrix type:
struct LinearMap{N<:Real, MAT<:AbstractMatrix{N}, S<:LazySet{N}} <: LazySet{N}

EDIT: We can also use M for MAT, but then we need to rename the field of the same name.

[mforets]

i think we should keep MN possibly different to N. for example if you have an interval matrix the coefficients are intervals.

[schillic]

Good point. Then, would it be
struct LinearMap{N<:Real, MAT<:AbstractMatrix{MN}, S<:LazySet{N}} <: LazySet{N}
or just
struct LinearMap{N<:Real, AbstractMatrix{MN}, S<:LazySet{N}} <: LazySet{N}
as before?
Motivation: Julia can create more efficient code if it sees the matrix type in advance, but I am not completely sure if it cannot see it in the other case as well.
Or do we even need MN then?

[mforets]

i would typically write out the full one:

julia> abstract type LazySet{N} end

julia> struct LinearMap{N<:Real, MN, MAT<:AbstractMatrix{MN}, S<:LazySet{N}} <: LazySet{N}
       end

julia> struct LinearMap2{N<:Real, MAT<:AbstractMatrix{MN}, S<:LazySet{N}} <: LazySet{N}
       end
ERROR: UndefVarError: MN not defined