Add SubKnotVector

[hyrodium]

This PR adds SubKnotVector and methods of Base.view for performance.

[codecov]

Codecov Report

Merging #320 (5c1ef01) into main (b472612) will increase coverage by 2.15%.
The diff coverage is 97.56%.

@@            Coverage Diff             @@
##             main     #320      +/-   ##
==========================================
+ Coverage   96.00%   98.15%   +2.15%     
==========================================
  Files          13       13              
  Lines        1300     1300              
==========================================
+ Hits         1248     1276      +28     
+ Misses         52       24      -28     

Impacted Files	Coverage Δ
src/BasicBSpline.jl	100.00% <ø> (ø)
src/_KnotVector.jl	95.33% <93.75%> (-0.42%)	⬇️
src/_BSplineSpace.jl	97.84% <100.00%> (+0.36%)	⬆️
src/_ChangeBasis.jl	97.30% <100.00%> (+11.19%)	⬆️

[hyrodium]

The performance regression (#317) problem is partially resolved but is still insufficient.

julia> using BasicBSpline, BenchmarkTools

julia> P1 = BSplineSpace{2}(KnotVector(0:8));

julia> P2 = BSplineSpace{2}(KnotVector(0:0.5:8));

julia> changebasis(P1, P2)
6×14 SparseArrays.SparseMatrixCSC{Float64, Int64} with 24 stored entries:
 0.25  0.75  0.75  0.25   ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅ 
  ⋅     ⋅    0.25  0.75  0.75  0.25   ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅ 
  ⋅     ⋅     ⋅     ⋅    0.25  0.75  0.75  0.25   ⋅     ⋅     ⋅     ⋅     ⋅     ⋅ 
  ⋅     ⋅     ⋅     ⋅     ⋅     ⋅    0.25  0.75  0.75  0.25   ⋅     ⋅     ⋅     ⋅ 
  ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅    0.25  0.75  0.75  0.25   ⋅     ⋅ 
  ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅    0.25  0.75  0.75  0.25

julia> @benchmark changebasis(P1, P2)
BenchmarkTools.Trial: 10000 samples with 4 evaluations.
 Range (min … max):  7.580 μs … 761.908 μs  ┊ GC (min … max): 0.00% … 96.26%
 Time  (median):     7.925 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   9.771 μs ±  12.493 μs  ┊ GC (mean ± σ):  2.40% ±  1.92%

  ██▄    ▂▅▃▁▁▂▃▃▃▂▂▂▁▁▁▂▂▂▂▂▂▂▁▁▁▁                           ▂
  ███▇▆█▇███████████████████████████▇█▇▇▇▇▆▆▅▆▄▅▅▅▆▅▃▄▅▆▄▅▅▄▅ █
  7.58 μs      Histogram: log(frequency) by time      20.8 μs <

 Memory estimate: 4.86 KiB, allocs estimate: 34.

julia> P1 = BSplineSpace{2}(KnotVector(0:80));

julia> P2 = BSplineSpace{2}(KnotVector(0:0.5:80));

julia> changebasis(P1, P2)
78×158 SparseArrays.SparseMatrixCSC{Float64, Int64} with 312 stored entries:
⎡⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎤
⎢⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⎥
⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⎥
⎣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⎦

julia> @benchmark changebasis(P1, P2)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  219.837 μs …  1.466 ms  ┊ GC (min … max): 0.00% … 81.20%
 Time  (median):     225.216 μs              ┊ GC (median):    0.00%
 Time  (mean ± σ):   227.603 μs ± 37.103 μs  ┊ GC (mean ± σ):  0.48% ±  2.55%

           ▂█▂                                                  
  ▁▃▅▅▄▃▃▃▅███▅▃▃▃▃▃▃▃▂▂▂▂▂▂▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ▂
  220 μs          Histogram: frequency by time          250 μs <

 Memory estimate: 49.92 KiB, allocs estimate: 42.

[hyrodium]

The performance on issubset is much imprroved.

Before this PR

julia> using BasicBSpline, BenchmarkTools

julia> P = BSplineSpace{0}(knotvector"  1 2 1 1")
BSplineSpace{0, Int64, KnotVector{Int64}}(KnotVector([3, 5, 5, 7, 9]))

julia> P′= BSplineSpace{2}(knotvector"1 3 4 3 3 1")
BSplineSpace{2, Int64, KnotVector{Int64}}(KnotVector([1, 3, 3, 3, 5, 5, 5, 5, 7, 7, 7, 9, 9, 9, 11]))

julia> P ⊆ P′
true

julia> @benchmark P ⊆ P′
BenchmarkTools.Trial: 10000 samples with 201 evaluations.
 Range (min … max):  384.657 ns …  14.072 μs  ┊ GC (min … max): 0.00% … 93.94%
 Time  (median):     420.149 ns               ┊ GC (median):    0.00%
 Time  (mean ± σ):   481.209 ns ± 732.955 ns  ┊ GC (mean ± σ):  8.62% ±  5.50%

     ▂▄▆▇██▇▆▅▄▃▂▂▁▁▁ ▂▃▄▅▅▅▄▃▂▁                                ▃
  ▂▅▇█████████████████████████████▇▇▇▇▇██████▇▇▇▆▅▇▆▆▆▆▇▆▅▄▅▆▄▅ █
  385 ns        Histogram: log(frequency) by time        625 ns <

 Memory estimate: 832 bytes, allocs estimate: 8.

After this PR

julia> using BasicBSpline, BenchmarkTools

julia> P = BSplineSpace{0}(knotvector"  1 2 1 1")
BSplineSpace{0, Int64, KnotVector{Int64}}(KnotVector([3, 5, 5, 7, 9]))

julia> P′= BSplineSpace{2}(knotvector"1 3 4 3 3 1")
BSplineSpace{2, Int64, KnotVector{Int64}}(KnotVector([1, 3, 3, 3, 5, 5, 5, 5, 7, 7, 7, 9, 9, 9, 11]))

julia> P ⊆ P′
true

julia> @benchmark P ⊆ P′
BenchmarkTools.Trial: 10000 samples with 994 evaluations.
 Range (min … max):  31.729 ns … 175.514 ns  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     33.020 ns               ┊ GC (median):    0.00%
 Time  (mean ± σ):   36.166 ns ±   7.525 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▂█▇▁ ▄▇ ▁▂▂▄▁                  ▁▂▁                           ▂
  ████▄██▆█████▇▆▇▆▅▆▆▅▅▃▄▄▄▄▅▅▅▆████▆▆▇▇▇▇▇▇▇▇▇▇█▇▅▇▇▇▆▅▆▆▅▆▅ █
  31.7 ns       Histogram: log(frequency) by time      63.8 ns <

 Memory estimate: 0 bytes, allocs estimate: 0.