inconsistent axes for interpolated object as an AbstractArray

[tpapp]

With the MWE

using Interpolations
a = range(2, 7; length = 10)    # > 1
J = 1:5
W = a .+ permutedims(J)
mapslices(S -> LinearInterpolation((a, ), S), W; dims = (1, ))

it is easy to run into something like a

julia> mapslices(S -> LinearInterpolation((a, ), S), W; dims = (1, ))
ERROR: BoundsError: attempt to access 10-element extrapolate(scale(interpolate(::Array{Float64,1}, BSpline(Linear())), (2.0:0.5555555555555556:7.0,)), Throw()) with element type Float64 at index [1]
Stacktrace:
 [1] throw_boundserror(::Interpolations.Extrapolation{Float64,1,ScaledInterpolation{Float64,1,Interpolations.BSplineInterpolation{Float64,1,Array{Float64,1},BSpline{Linear},Tuple{Base.OneTo{Int64}}},BSpline{Linear},Tuple{StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}}}},BSpline{Linear},Throw{Nothing}}, ::Tuple{Int64}) at ./abstractarray.jl:493

The root cause seems to be that using getindex with interpolated calculation is not consistent with eg axes:

julia> slice1 = LinearInterpolation((a, ), W[:, 1]);

julia> slice1 isa AbstractArray
true

julia> axes(slice1)
(Base.OneTo(10),)

julia> slice1[1]                       # ouch
ERROR: BoundsError: attempt to access 10-element extrapolate(scale(interpolate(::Array{Float64,1}, BSpline(Linear())), (2.0:0.5555555555555556:7.0,)), Throw()) with element type Float64 at index [1]
Stacktrace:
 [1] throw_boundserror(::Interpolations.Extrapolation{Float64,1,ScaledInterpolation{Float64,1,Interpolations.BSplineInterpolation{Float64,1,Array{Float64,1},BSpline{Linear},Tuple{Base.OneTo{Int64}}},BSpline{Linear},Tuple{StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}}}},BSpline{Linear},Throw{Nothing}}, ::Tuple{Int64}) at ./abstractarray.jl:493
 [2] inbounds_index at /home/tamas/.julia/dev/Interpolations/src/extrapolation/extrapolation.jl:102 [inlined]
 [3] inbounds_position at /home/tamas/.julia/dev/Interpolations/src/extrapolation/extrapolation.jl:93 [inlined]
 [4] Extrapolation at /home/tamas/.julia/dev/Interpolations/src/extrapolation/extrapolation.jl:43 [inlined]
 [5] getindex(::Interpolations.Extrapolation{Float64,1,ScaledInterpolation{Float64,1,Interpolations.BSplineInterpolation{Float64,1,Array{Float64,1},BSpline{Linear},Tuple{Base.OneTo{Int64}}},BSpline{Linear},Tuple{StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}}}},BSpline{Linear},Throw{Nothing}}, ::Int64) at /home/tamas/.julia/dev/Interpolations/src/Interpolations.jl:403
 [6] top-level scope at REPL[30]:1

Suggestion: don't use getindex for this purpose.

[timholy]

We have a depwarn but it is only triggered for non-integer indexes:

julia> li = LinearInterpolation((a, ), W[:,1])
10-element extrapolate(scale(interpolate(::Array{Float64,1}, BSpline(Linear())), (2.0:0.5555555555555556:7.0,)), Throw()) with element type Float64:
 3.0              
 3.555555555555555
 4.111111111111111
 4.666666666666666
 5.222222222222222
 5.777777777777778
 6.333333333333333
 6.888888888888889
 7.444444444444445
 8.0              

julia> li.itp.itp[4.1]
┌ Warning: `getindex(itp::AbstractInterpolation{T, N}, i::Vararg{Number, N}) where {T, N}` is deprecated, use `itp(i...)` instead.
│   caller = top-level scope at none:0
└ @ Core none:0
4.722222222222221

Maybe it's time to turn it on for integers too. #242
I don't have time to tackle this in the foreseeable future, though.