Fix inference problems in linear solvers

[mforets]

No description provided.

[mforets]

• If the algorithm is not passed directly, there is an inference problem because the default depends on the dimension and there is (in general) no such information at compile time INT for 1d and GLGM06 for ND. Of course if it's worth it we can just keep GLGM06 as default, given that it works with 1d as well.

[mforets]

for reference,

julia> versioninfo()

Julia Version 1.4.0
Commit b8e9a9ecc6 (2020-03-21 16:36 UTC)
Platform Info:
  OS: Linux (x86_64-pc-linux-gnu)
  CPU: Intel(R) Core(TM) i7-8705G CPU @ 3.10GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-8.0.1 (ORCJIT, skylake)
Environment:
  JULIA_LOAD_PATH = :/home/mforets/Tools/GMSH/gmsh-4.5.4-Linux64-sdk/lib

INT

julia> include("/home/mforets/.julia/dev/ReachabilityAnalysis/test/models/linear/exponential1D.jl")

julia> prob, tspan = exponential_1d()

julia> @inferred solve(prob, (0.0, 1.0), INT(δ=1e-3)); # OK

juila> @inferred solve(prob, (0.0, 1.0)); # fails
return type ReachabilityAnalysis.ReachSolution{Flowpipe{Float64,ReachSet{Float64,Interval{Float64,IntervalArithmetic.Interval{Float64}}}},INT{Float64,Forward}} does not match inferred return type ReachabilityAnalysis.ReachSolution

Stacktrace:
 [1] error(::String) at ./error.jl:33
 [2] top-level scope at In[35]:1

julia> @btime solve($prob, (0.0, 1.0));
  2.246 μs (18 allocations: 4.92 KiB)

julia> @btime solve($prob, (0.0, 1.0), INT(δ=0.01));
  2.150 μs (18 allocations: 4.92 KiB)

GLGM06

julia> include("/home/mforets/.julia/dev/ReachabilityAnalysis/test/models/linear/motor.jl")

julia> prob, tspan = motor_homog()

julia> @inferred solve(prob, (0.0, 1.0), GLGM06(δ=1e-3, max_order=3)); # fails but it shouldn't
return type ReachabilityAnalysis.ReachSolution{Flowpipe{Float64,ReachSet{Float64,Zonotope{Float64,Array{Float64,1},Array{Float64,2}}}},GLGM06{Float64,Forward}} does not match inferred return type ReachabilityAnalysis.ReachSolution{_A,GLGM06{Float64,Forward}} where _A<:ReachabilityAnalysis.AbstractFlowpipe

Stacktrace:
 [1] error(::String) at ./error.jl:33
 [2] top-level scope at In[28]:2

julia> @btime solve($prob, (0.0, 1.0), GLGM06(δ=1e-3, max_order=3));
  590.537 μs (4306 allocations: 1002.36 KiB)