#87 - Better error messages

[schillic]

Closes #87.

• adds error messages when trying to use an algorithm that requires to load an external library (see example below)
  • The new require function is borrowed from LazySets and is planned to be outsourced to a Base package soon.
  • For the SOS algorithm I created a new file because the existing file uses macros and these do not go so well with Requires (there may be a way to avoid that, but 🤷).
  • For the MSE algorithm we use a type from the external library in the default argument of the struct. I defined an internal variable (_default_vector_MSE) holding that default algorithm, which is then overwritten when the package is loaded.
• unexports the abstract types
• fixes the polynomial example in the docs, which was forgotten in update sdp and polynomial interface #83
• adds a plot of the example to the README
• minor polishing

julia> using RangeEnclosures


# new: error messages

julia> enclose(x -> -x^3/6 + 5x, 1 .. 4, MooreSkelboeEnclosure())
ERROR: AssertionError: package 'IntervalOptimisation' not loaded (it is required for executing `enclose`)

julia> enclose(x -> -x^3/6 + 5x, 1 .. 4, SumOfSquaresEnclosure(backend=nothing))
ERROR: AssertionError: package 'SumOfSquares' not loaded (it is required for executing `enclose`)

julia> enclose(x -> -x^3/6 + 5x, 1 .. 4, TaylorModelsEnclosure())
ERROR: AssertionError: package 'TaylorModels' not loaded (it is required for executing `enclose`)


# after loading the packages, the behavior is as before

juli> using IntervalOptimisation, SumOfSquares, SDPA, DynamicPolynomials, TaylorModels

julia> enclose(x -> -x^3/6 + 5x, 1 .. 4, MooreSkelboeEnclosure())
[4.83299, 10.5448]

julia> backend = SDPA.Optimizer;
julia> @polyvar x;
julia> enclose(-x^3/6 + 5x, 1..4, SumOfSquaresEnclosure(; backend=backend))
[4.83333, 10.541]

julia> enclose(x -> -x^3/6 + 5x, 1 .. 4, TaylorModelsEnclosure())
[4.27083, 12.7084]

[lucaferranti]

For the SOS algorithm I created a new file because the existing file uses macros and these do not go so well with Requires

what macros does it use? I think we got rid of @polyvar at some point?

[schillic]

what macros does it use?

RangeEnclosures.jl/src/sdp.jl

Lines 11 to 19 in 25aff78

	B = reduce(intersect, @set inf(domi) <= xi && xi <= sup(domi) for (xi, domi) in zip(x, dom))
	# ============
	# Upper bound
	# ============
	model = SOSModel(sose.backend, kwargs...)
	@variable(model, γ) # JuMP decision variable
	@constraint(model, p <= γ, domain=B, maxdegree=sose.order)
	@objective(model, Min, γ)

[lucaferranti]

right 😅