Faster changebasis

[hyrodium]

Before this PR

julia> using BasicBSpline, BenchmarkTools

julia> P1 = BSplineSpace{1}(KnotVector([1, 3, 5, 8]))
BSplineSpace{1, Int64, KnotVector{Int64}}(KnotVector([1, 3, 5, 8]))

julia> P2 = BSplineSpace{1}(KnotVector([1, 3, 5, 6, 8, 9]))
BSplineSpace{1, Int64, KnotVector{Int64}}(KnotVector([1, 3, 5, 6, 8, 9]))

julia> @benchmark changebasis(P1, P2)
BenchmarkTools.Trial: 10000 samples with 10 evaluations.
 Range (min … max):  1.898 μs … 350.734 μs  ┊ GC (min … max):  0.00% … 99.22%
 Time  (median):     2.059 μs               ┊ GC (median):     0.00%
 Time  (mean ± σ):   2.501 μs ±  10.480 μs  ┊ GC (mean ± σ):  13.18% ±  3.12%

   ▄▆▇███▇▆▅▃▃▁▁▂▂▃▂▃▂▂▂▁▁▁▁                                  ▂
  ███████████████████████████████▇███▇███▇████████▇▆▇▆▇▇▆▆▆▆▄ █
  1.9 μs       Histogram: log(frequency) by time      3.47 μs <

 Memory estimate: 4.59 KiB, allocs estimate: 51.

After this PR

julia> using BasicBSpline, BenchmarkTools

julia> P1 = BSplineSpace{1}(KnotVector([1, 3, 5, 8]))
BSplineSpace{1, Int64, KnotVector{Int64}}(KnotVector([1, 3, 5, 8]))

julia> P2 = BSplineSpace{1}(KnotVector([1, 3, 5, 6, 8, 9]))
BSplineSpace{1, Int64, KnotVector{Int64}}(KnotVector([1, 3, 5, 6, 8, 9]))

julia> @benchmark changebasis(P1, P2)
BenchmarkTools.Trial: 10000 samples with 78 evaluations.
 Range (min … max):  829.256 ns … 39.370 μs  ┊ GC (min … max):  0.00% … 96.59%
 Time  (median):     865.090 ns              ┊ GC (median):     0.00%
 Time  (mean ± σ):   993.385 ns ±  1.955 μs  ┊ GC (mean ± σ):  10.73% ±  5.31%

   ▄▇██▇▆▄▃▂▁▁                                                 ▂
  ███████████████▇▇▇▇▇▇▇███▇█▇▆▆▆▆▄▄▄▃▅▅▅▆▇▆▅▆▇▇▇▆▇▇▇▆▆▅▄▆▅▆▆▆ █
  829 ns        Histogram: log(frequency) by time      1.29 μs <

 Memory estimate: 1.81 KiB, allocs estimate: 18.

[codecov]

Codecov Report

Merging #308 (aa47ad1) into main (068fedd) will decrease coverage by 0.06%.
The diff coverage is 98.59%.

@@            Coverage Diff             @@
##             main     #308      +/-   ##
==========================================
- Coverage   98.46%   98.41%   -0.06%     
==========================================
  Files          13       12       -1     
  Lines        1241     1263      +22     
==========================================
+ Hits         1222     1243      +21     
- Misses         19       20       +1     

Impacted Files	Coverage Δ
src/_ChangeBasis.jl	97.70% <98.59%> (-0.25%)	⬇️
src/BasicBSpline.jl

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[hyrodium]

Now the performance is much better:

julia> using BasicBSpline, BenchmarkTools

julia> P1 = BSplineSpace{1}(KnotVector([1, 3, 5, 8]))
BSplineSpace{1, Int64, KnotVector{Int64}}(KnotVector([1, 3, 5, 8]))

julia> P2 = BSplineSpace{1}(KnotVector([1, 3, 5, 6, 8, 9]))
BSplineSpace{1, Int64, KnotVector{Int64}}(KnotVector([1, 3, 5, 6, 8, 9]))

julia> @benchmark changebasis(P1, P2)
BenchmarkTools.Trial: 10000 samples with 173 evaluations.
 Range (min … max):  616.832 ns … 23.942 μs  ┊ GC (min … max):  0.00% … 96.58%
 Time  (median):     651.231 ns              ┊ GC (median):     0.00%
 Time  (mean ± σ):   778.790 ns ±  1.384 μs  ┊ GC (mean ± σ):  12.35% ±  6.72%

   ▅██▇▅▄▃▃▂▁▁▂▃▃▂▁                                            ▂
  █████████████████████████▇██▇▇▆▇▆▆▆▆▆▆▅▆▆▄▇▆▇▆▆▅▄▆▄▅▅▅▄▃▃▄▄▃ █
  617 ns        Histogram: log(frequency) by time      1.18 μs <

 Memory estimate: 1.28 KiB, allocs estimate: 14.