More performance

[hyrodium]

This PR fixes #333

Before this PR

julia> using BasicBSpline, BenchmarkTools

julia> Pd1 = BSplineSpace{2}(knotvector" 21 3")
BSplineSpace{2, Int64, KnotVector{Int64}}(KnotVector([2, 2, 3, 5, 5, 5]))

julia> Pd2 = BSplineSpace{3}(knotvector"212 4")
BSplineSpace{3, Int64, KnotVector{Int64}}(KnotVector([1, 1, 2, 3, 3, 5, 5, 5, 5]))

julia> @benchmark BasicBSpline.changebasis_I(Pd1, Pd2)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  52.760 μs …   3.479 ms  ┊ GC (min … max):  0.00% … 95.56%
 Time  (median):     57.709 μs               ┊ GC (median):     0.00%
 Time  (mean ± σ):   65.825 μs ± 149.739 μs  ┊ GC (mean ± σ):  10.40% ±  4.48%

    ▁▃▅▆▇████▇▆▅▄▃▂▂▂▁▁▁▁▁▁ ▁                                  ▃
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  52.8 μs       Histogram: log(frequency) by time      84.5 μs <

 Memory estimate: 98.53 KiB, allocs estimate: 1285.

After this PR

julia> using BasicBSpline, BenchmarkTools

julia> Pd1 = BSplineSpace{2}(knotvector" 21 3")
BSplineSpace{2, Int64, KnotVector{Int64}}(KnotVector([2, 2, 3, 5, 5, 5]))

julia> Pd2 = BSplineSpace{3}(knotvector"212 4")
BSplineSpace{3, Int64, KnotVector{Int64}}(KnotVector([1, 1, 2, 3, 3, 5, 5, 5, 5]))

julia> @benchmark BasicBSpline.changebasis_I(Pd1, Pd2)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  11.662 μs …  3.282 ms  ┊ GC (min … max): 0.00% … 97.70%
 Time  (median):     12.975 μs              ┊ GC (median):    0.00%
 Time  (mean ± σ):   15.312 μs ± 64.766 μs  ┊ GC (mean ± σ):  8.26% ±  1.94%

     ▇██▃▁                                                     
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  11.7 μs         Histogram: frequency by time        23.8 μs <

 Memory estimate: 20.44 KiB, allocs estimate: 285.

[codecov]

Codecov Report

Merging #344 (47046aa) into main (db826f7) will decrease coverage by 0.14%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main     #344      +/-   ##
==========================================
- Coverage   96.56%   96.43%   -0.14%     
==========================================
  Files          14       14              
  Lines        1574     1571       -3     
==========================================
- Hits         1520     1515       -5     
- Misses         54       56       +2     

Files	Coverage Δ
src/_BSplineSpace.jl	93.78% <100.00%> (-0.07%)	⬇️
src/_ChangeBasis.jl	94.07% <100.00%> (-0.02%)	⬇️

... and 1 file with indirect coverage changes

[hyrodium]

Before this PR

julia> using BasicBSpline, BenchmarkTools

julia> P6 = BSplineSpace{2}(knotvector"1111 111")
BSplineSpace{2, Int64, KnotVector{Int64}}(KnotVector([1, 2, 3, 4, 6, 7, 8]))

julia> P7 = BSplineSpace{2}(knotvector"11121111")
BSplineSpace{2, Int64, KnotVector{Int64}}(KnotVector([1, 2, 3, 4, 4, 5, 6, 7, 8]))

julia> P6 ⊆ P7
true

julia> P6 ⊑ P7
true

julia> @benchmark P6 ⊆ P7
BenchmarkTools.Trial: 10000 samples with 996 evaluations.
 Range (min … max):  23.789 ns … 53.344 ns  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     24.173 ns              ┊ GC (median):    0.00%
 Time  (mean ± σ):   24.400 ns ±  1.360 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

   █▇▅▃▂▁                                                     ▂
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  23.8 ns      Histogram: log(frequency) by time      35.5 ns <

 Memory estimate: 0 bytes, allocs estimate: 0.

julia> @benchmark P6 ⊑ P7
BenchmarkTools.Trial: 10000 samples with 301 evaluations.
 Range (min … max):  291.714 ns …  12.953 μs  ┊ GC (min … max):  0.00% … 95.71%
 Time  (median):     316.198 ns               ┊ GC (median):     0.00%
 Time  (mean ± σ):   379.197 ns ± 800.701 ns  ┊ GC (mean ± σ):  14.42% ±  6.62%

      ▁▄▇█▇▄                                                     
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  292 ns           Histogram: frequency by time          478 ns <

 Memory estimate: 752 bytes, allocs estimate: 9.

After this PR

julia> using BasicBSpline, BenchmarkTools

julia> P6 = BSplineSpace{2}(knotvector"1111 111")
BSplineSpace{2, Int64, KnotVector{Int64}}(KnotVector([1, 2, 3, 4, 6, 7, 8]))

julia> P7 = BSplineSpace{2}(knotvector"11121111")
BSplineSpace{2, Int64, KnotVector{Int64}}(KnotVector([1, 2, 3, 4, 4, 5, 6, 7, 8]))

julia> P6 ⊆ P7
true

julia> P6 ⊑ P7
true

julia> @benchmark P6 ⊆ P7
BenchmarkTools.Trial: 10000 samples with 996 evaluations.
 Range (min … max):  23.126 ns … 47.963 ns  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     23.660 ns              ┊ GC (median):    0.00%
 Time  (mean ± σ):   24.191 ns ±  2.216 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▄▆█▇▃▂▂                                                  ▂  ▂
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  23.1 ns      Histogram: log(frequency) by time      35.1 ns <

 Memory estimate: 0 bytes, allocs estimate: 0.

julia> @benchmark P6 ⊑ P7
BenchmarkTools.Trial: 10000 samples with 996 evaluations.
 Range (min … max):  23.187 ns … 41.766 ns  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     23.670 ns              ┊ GC (median):    0.00%
 Time  (mean ± σ):   24.101 ns ±  1.958 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▃▇██▃▁                                                  ▂▁▁ ▂
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  23.2 ns      Histogram: log(frequency) by time      33.1 ns <

 Memory estimate: 0 bytes, allocs estimate: 0.

[hyrodium]

#323 (comment)

Still can be improved, but getting better.

Before this PR

julia> using BasicBSpline, BenchmarkTools

julia> p = 3
3

julia> P = BSplineSpace{p}(KnotVector(1:10))
BSplineSpace{3, Int64, KnotVector{Int64}}(KnotVector([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))

julia> P′ = BSplineSpace{p}(KnotVector([1,2,3,4,4.5,5,6,7,8.1,9.1,10.5]))
BSplineSpace{3, Float64, KnotVector{Float64}}(KnotVector([1.0, 2.0, 3.0, 4.0, 4.5, 5.0, 6.0, 7.0, 8.1, 9.1, 10.5]))

julia> changebasis(P,P′)
6×7 SparseArrays.SparseMatrixCSC{Float64, Int32} with 13 stored entries:
 1.0  0.166667   ⋅    ⋅         ⋅     ⋅           ⋅ 
  ⋅   0.833333  0.5   ⋅         ⋅     ⋅           ⋅ 
  ⋅    ⋅        0.5  0.833333   ⋅     ⋅           ⋅ 
  ⋅    ⋅         ⋅   0.166667  1.0  -0.0333333   0.0183333
  ⋅    ⋅         ⋅    ⋅         ⋅    1.03333    -0.103333
  ⋅    ⋅         ⋅    ⋅         ⋅     ⋅          1.085

julia> @benchmark changebasis(P,P′)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  214.406 μs …   3.984 ms  ┊ GC (min … max):  0.00% … 92.05%
 Time  (median):     222.922 μs               ┊ GC (median):     0.00%
 Time  (mean ± σ):   254.091 μs ± 320.269 μs  ┊ GC (mean ± σ):  11.10% ±  8.23%

   ▁▃▅▇██▇▆▄▃▃▃▃▂▂▂▁                                            ▂
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  214 μs        Histogram: log(frequency) by time        295 μs <

 Memory estimate: 363.89 KiB, allocs estimate: 4150.

After this PR

julia> using BasicBSpline, BenchmarkTools

julia> p = 3
3

julia> P = BSplineSpace{p}(KnotVector(1:10))
BSplineSpace{3, Int64, KnotVector{Int64}}(KnotVector([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))

julia> P′ = BSplineSpace{p}(KnotVector([1,2,3,4,4.5,5,6,7,8.1,9.1,10.5]))
BSplineSpace{3, Float64, KnotVector{Float64}}(KnotVector([1.0, 2.0, 3.0, 4.0, 4.5, 5.0, 6.0, 7.0, 8.1, 9.1, 10.5]))

julia> changebasis(P,P′)
6×7 SparseArrays.SparseMatrixCSC{Float64, Int32} with 13 stored entries:
 1.0  0.166667   ⋅    ⋅         ⋅     ⋅           ⋅ 
  ⋅   0.833333  0.5   ⋅         ⋅     ⋅           ⋅ 
  ⋅    ⋅        0.5  0.833333   ⋅     ⋅           ⋅ 
  ⋅    ⋅         ⋅   0.166667  1.0  -0.0333333   0.0183333
  ⋅    ⋅         ⋅    ⋅         ⋅    1.03333    -0.103333
  ⋅    ⋅         ⋅    ⋅         ⋅     ⋅          1.085

julia> @benchmark changebasis(P,P′)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  26.300 μs …   4.336 ms  ┊ GC (min … max):  0.00% … 97.00%
 Time  (median):     28.945 μs               ┊ GC (median):     0.00%
 Time  (mean ± σ):   34.048 μs ± 118.740 μs  ┊ GC (mean ± σ):  10.23% ±  2.92%

      ▄██▅▃                                                     
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  26.3 μs         Histogram: frequency by time         45.3 μs <

 Memory estimate: 40.86 KiB, allocs estimate: 508.