Accept vectors in PiecewiseSpace

[jishnub]

Currently, PiecewiseSpace converts vectors to Tuples, which is intrinsically type-unstable. Since it is often used in contexts where the number of terms isn't known at compile time (e.g. roots), the way to improve type-inference is to allow vector arguments.

Along with JuliaArrays/FillArrays.jl#291, this makes the following type-inferred as a Union:

julia> s = space(abs(Fun()));

julia> @code_typed Derivative(s)
CodeInfo(
1 ─ %1 = Core.getfield(x, 1)::ContinuousSpace{Float64, Float64, PiecewiseSegment{Float64, Vector{Float64}}}
│   %2 = invoke ApproxFunBase.DefaultDerivative(%1::ContinuousSpace{Float64, Float64, PiecewiseSegment{Float64, Vector{Float64}}}, 1::Int64)::Union{ApproxFunBase.DerivativeWrapper{TimesOperator{Float64, Tuple{Int64, Int64}, Tuple{Infinities.InfiniteCardinal{0}, Infinities.InfiniteCardinal{0}}, Operator{Float64}, Tuple{Infinities.InfiniteCardinal{0}, Infinities.InfiniteCardinal{0}}, Tuple{Int64, Int64}}, ContinuousSpace{Float64, Float64, PiecewiseSegment{Float64, Vector{Float64}}}, PiecewiseSpace{Vector{Ultraspherical{Int64, Segment{Float64}, Float64}}, DomainSets.UnionDomain{Float64, Vector{Segment{Float64}}}, Float64}, Int64, Float64}, ApproxFunBase.DerivativeWrapper{TimesOperator{Float64, Tuple{Int64, Int64}, Tuple{Infinities.InfiniteCardinal{0}, Infinities.InfiniteCardinal{0}}, Operator{Float64}, Tuple{Int64, Int64}, Tuple{Int64, Int64}}, ContinuousSpace{Float64, Float64, PiecewiseSegment{Float64, Vector{Float64}}}, PiecewiseSpace{Vector{Ultraspherical{Int64, Segment{Float64}, Float64}}, DomainSets.UnionDomain{Float64, Vector{Segment{Float64}}}, Float64}, Int64, Float64}}
└──      return %2
) => Union{ApproxFunBase.DerivativeWrapper{TimesOperator{Float64, Tuple{Int64, Int64}, Tuple{Infinities.InfiniteCardinal{0}, Infinities.InfiniteCardinal{0}}, Operator{Float64}, Tuple{Infinities.InfiniteCardinal{0}, Infinities.InfiniteCardinal{0}}, Tuple{Int64, Int64}}, ContinuousSpace{Float64, Float64, PiecewiseSegment{Float64, Vector{Float64}}}, PiecewiseSpace{Vector{Ultraspherical{Int64, Segment{Float64}, Float64}}, DomainSets.UnionDomain{Float64, Vector{Segment{Float64}}}, Float64}, Int64, Float64}, ApproxFunBase.DerivativeWrapper{TimesOperator{Float64, Tuple{Int64, Int64}, Tuple{Infinities.InfiniteCardinal{0}, Infinities.InfiniteCardinal{0}}, Operator{Float64}, Tuple{Int64, Int64}, Tuple{Int64, Int64}}, ContinuousSpace{Float64, Float64, PiecewiseSegment{Float64, Vector{Float64}}}, PiecewiseSpace{Vector{Ultraspherical{Int64, Segment{Float64}, Float64}}, DomainSets.UnionDomain{Float64, Vector{Segment{Float64}}}, Float64}, Int64, Float64}}

[codecov]

Codecov Report

Attention: Patch coverage is 62.85714% with 13 lines in your changes missing coverage. Please review.

Project coverage is 27.71%. Comparing base (c31337a) to head (e80cec5).
Report is 74 commits behind head on master.

Files with missing lines	Patch %	Lines
src/Spaces/SumSpace.jl	42.85%	12 Missing ⚠️
src/ApproxFunBase.jl	88.88%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #574      +/-   ##
==========================================
+ Coverage   27.53%   27.71%   +0.18%     
==========================================
  Files          80       80              
  Lines        8379     8403      +24     
==========================================
+ Hits         2307     2329      +22     
- Misses       6072     6074       +2     

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