More performance on changebasis_I

[hyrodium]

Before this PR

julia> using BasicBSpline, BenchmarkTools

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

julia> P′ = BSplineSpace{3}(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_I(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_I(P, P′)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  25.378 μs …   3.890 ms  ┊ GC (min … max): 0.00% … 97.68%
 Time  (median):     28.083 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   33.081 μs ± 110.248 μs  ┊ GC (mean ± σ):  9.78% ±  2.91%

   ▁▄▆██▇▆▄▃▁▂▃▄▄▄▄▃▂▁▁▁▁▁      ▁                              ▂
  ▆██████████████████████████████████▇▇▆▇▆▆▆▅▆▅▆▅▅▃▄▅▄▅▅▃▅▂▄▂▅ █
  25.4 μs       Histogram: log(frequency) by time      52.1 μs <

 Memory estimate: 40.55 KiB, allocs estimate: 508.

julia> P = BSplineSpace{2}(knotvector"3 113")
BSplineSpace{2, Int64, KnotVector{Int64}}(KnotVector([1, 1, 1, 3, 4, 5, 5, 5]))

julia> P′ = BSplineSpace{3}(knotvector"4 324")
BSplineSpace{3, Int64, KnotVector{Int64}}(KnotVector([1, 1, 1, 1, 3, 3, 3, 4, 4, 5, 5, 5, 5]))

julia> changebasis_I(P, P′)
5×9 SparseArrays.SparseMatrixCSC{Float64, Int32} with 16 stored entries:
 1.0  0.333333   ⋅         ⋅         ⋅         ⋅         ⋅         ⋅         ⋅ 
  ⋅   0.666667  0.777778  0.333333  0.111111   ⋅         ⋅         ⋅         ⋅ 
  ⋅    ⋅        0.222222  0.666667  0.888889  0.833333  0.166667   ⋅         ⋅ 
  ⋅    ⋅         ⋅         ⋅         ⋅        0.166667  0.833333  0.666667   ⋅ 
  ⋅    ⋅         ⋅         ⋅         ⋅         ⋅         ⋅        0.333333  1.0

julia> @benchmark changebasis_I(P, P′)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  15.930 μs …  4.208 ms  ┊ GC (min … max): 0.00% … 97.75%
 Time  (median):     17.473 μs              ┊ GC (median):    0.00%
 Time  (mean ± σ):   19.979 μs ± 75.837 μs  ┊ GC (mean ± σ):  7.42% ±  1.95%

     ▄▇█▆▃                                                     
  ▁▂▆██████▅▄▂▂▂▂▃▂▃▃▂▂▂▂▂▂▂▂▂▂▂▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ▂
  15.9 μs         Histogram: frequency by time        29.5 μs <

 Memory estimate: 25.95 KiB, allocs estimate: 311.

After this PR

julia> using BasicBSpline, BenchmarkTools

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

julia> P′ = BSplineSpace{3}(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_I(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_I(P, P′)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  22.683 μs …  3.696 ms  ┊ GC (min … max): 0.00% … 96.94%
 Time  (median):     24.937 μs              ┊ GC (median):    0.00%
 Time  (mean ± σ):   28.890 μs ± 95.613 μs  ┊ GC (mean ± σ):  8.57% ±  2.57%

   ▂▄▇███▇▅▄▂▂▁▁▃▃▄▄▃▃▂▂▂▂▂▁▁▁▁▁▁                             ▂
  ▆████████████████████████████████▇▇▆▇▇▇▇▆▇▅▆▇▅▅▅▅▅▆▄▂▄▃▅▂▄▄ █
  22.7 μs      Histogram: log(frequency) by time        44 μs <

 Memory estimate: 33.38 KiB, allocs estimate: 393.

julia> P = BSplineSpace{2}(knotvector"3 113")
BSplineSpace{2, Int64, KnotVector{Int64}}(KnotVector([1, 1, 1, 3, 4, 5, 5, 5]))

julia> P′ = BSplineSpace{3}(knotvector"4 324")
BSplineSpace{3, Int64, KnotVector{Int64}}(KnotVector([1, 1, 1, 1, 3, 3, 3, 4, 4, 5, 5, 5, 5]))

julia> changebasis_I(P, P′)
5×9 SparseArrays.SparseMatrixCSC{Float64, Int32} with 16 stored entries:
 1.0  0.333333   ⋅         ⋅         ⋅         ⋅         ⋅         ⋅         ⋅ 
  ⋅   0.666667  0.777778  0.333333  0.111111   ⋅         ⋅         ⋅         ⋅ 
  ⋅    ⋅        0.222222  0.666667  0.888889  0.833333  0.166667   ⋅         ⋅ 
  ⋅    ⋅         ⋅         ⋅         ⋅        0.166667  0.833333  0.666667   ⋅ 
  ⋅    ⋅         ⋅         ⋅         ⋅         ⋅         ⋅        0.333333  1.0

julia> @benchmark changebasis_I(P, P′)
BenchmarkTools.Trial: 10000 samples with 9 evaluations.
 Range (min … max):  2.528 μs … 351.001 μs  ┊ GC (min … max): 0.00% … 97.00%
 Time  (median):     2.714 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   3.137 μs ±   9.145 μs  ┊ GC (mean ± σ):  8.05% ±  2.74%

  ▁▆██▇▆▅▃▂▁          ▁▁▁▁▁▁▁▁▁▁ ▁                            ▂
  ██████████▇▆▇▆████████████████▇█▇▆▆▆▇▆▇▆▆▆▅▇▅▆▅▅▅▅▂▅▅▅▅▅▄▄▄ █
  2.53 μs      Histogram: log(frequency) by time      5.31 μs <

 Memory estimate: 4.88 KiB, allocs estimate: 52.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (6a0cb27) 96.13% compared to head (8f8c110) 96.07%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #347      +/-   ##
==========================================
- Coverage   96.13%   96.07%   -0.06%     
==========================================
  Files          14       14              
  Lines        1603     1606       +3     
==========================================
+ Hits         1541     1543       +2     
- Misses         62       63       +1     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.