find_roots_midpoint should gracefully handle cases with no roots

[pkofod]

julia> using IntervalRootFinding

julia> f(x)=x^0
f (generic function with 1 method)

julia> IntervalRootFinding.find_roots_midpoint(f, -5, 5)
ERROR: BoundsError: attempt to access 0-element Array{IntervalRootFinding.Root{IntervalArithmetic.Interval{Float64}},1} at index [1]
Stacktrace:
 [1] getindex(::Array{IntervalRootFinding.Root{IntervalArithmetic.Interval{Float64}},1}, ::Int64) at ./array.jl:520
 [2] #find_roots_midpoint#61(::Float64, ::Bool, ::Int64, ::Int64, ::Function, ::Function, ::Int64, ::Int64, ::IntervalRootFinding.#newton) at /home/pkm/.julia/v0.6/IntervalRootFinding/src/IntervalRootFinding.jl:107
 [3] find_roots_midpoint(::Function, ::Int64, ::Int64) at /home/pkm/.julia/v0.6/IntervalRootFinding/src/IntervalRootFinding.jl:105

julia> IntervalRootFinding.find_roots(f, -5, 5)
0-element Array{IntervalRootFinding.Root{IntervalArithmetic.Interval{Float64}},1}

It shouldn't throw an error, but return an empty result. Or error with a better error :)

[dpsanders]

Thanks for the report. find_roots_midpoint is part of the old API and will probably disappear. For the moment you can use

rts = roots(f, -5..5)
mid.([rt.interval for rt in rts])   # edited for correct syntax

Later you will be able to do

mid.(interval.(rts))

Nonetheless, the original idea of find_roots_midpoint was to have an API in which the user did not need to know anything at all about intervals. Probably we should strive to maintain such an API available?

[pkofod]

Either way is fine to me!

Later you will be able to do

does that mean "on master" or "yet to be implemented" ? :)

[dpsanders]

I thought it was a PR, but actually it works on master!

julia> using IntervalRootFinding
INFO: Precompiling module IntervalRootFinding.

julia> rts = roots(x->x^2 - 2, -5..5)
mi2-element Array{IntervalRootFinding.Root{IntervalArithmetic.Interval{Float64}},1}:
d. Root([1.41421, 1.41422], :unique)
 Root([-1.41422, -1.41421], :unique)

julia> mid.(interval.(rts))
2-element Array{Float64,1}:
  1.41421
 -1.41421

[pkofod]

Great! Will continue my interval endeavors then!

[dpsanders]

This part of the API is no longer in use.