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perf(solve): reduce memory allocations in solve system hot paths#85

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perf/reduce-allocations-solve-hotpaths
Feb 17, 2026
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perf(solve): reduce memory allocations in solve system hot paths#85
kylebeggs merged 3 commits intomainfrom
perf/reduce-allocations-solve-hotpaths

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@kylebeggs kylebeggs commented Feb 17, 2026 •
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Summary

  • forward_cache.jl: Pre-allocate A_full and b workspace outside the loop, reuse with fill!; replace [data[i] for i in neighbors] array comprehension with view(data, neighbors); replace manual lower-triangle copy with copytri!; eliminate intermediate w = λ[1:k, :] slice
  • assembly.jl: Add in-place _build_stencil!(λ, A, b, ...) variant using ldiv!/bunchkaufman! to write solution into pre-allocated buffer and return a view instead of allocating a new array + slice
  • execution.jl: Pre-allocate λ solve buffer alongside A and b in weight_kernel; explicitly reset A_full and b per stencil iteration; call new in-place _build_stencil! variant
  • interpolation.jl: Replace scalar accumulation loop with dot() for polynomial evaluation; add @inbounds to RBF accumulation loop

Closes #73

Test plan

  • Full test suite passes (julia --project=. -e "using Pkg; Pkg.test()")
  • AD extension tests pass (Enzyme + Mooncake) since _forward_with_cache output format is preserved
  • Benchmark with @benchmark update_weights!(lap) shows reduced allocations
  • Benchmark Interpolator evaluation shows reduced allocations

Benchmark results (10k points, 2D, PHS3 poly_deg=2)

update_weights! (Laplacian)

Metric main this PR Change
Allocations 358,703 300,703 -16.2%
Memory 139.37 MiB 110.48 MiB -20.7%

Interpolator evaluation (500 pts)

Metric main this PR Notes
Single-point allocs 2 2 Already minimal; dot() + @inbounds improve speed
Multi-point allocs 202 202 Already minimal

@kylebeggs
perf(solve): reduce memory allocations in solve system hot paths
571e263 
- Pre-allocate λ buffer and use in-place _build_stencil! with ldiv!/bunchkaufman!
- Use view() for local_data instead of allocating new vectors
- Replace polynomial evaluation allocation with dot() in Interpolator
- Add copytri! for efficient symmetric matrix caching in forward_cache
- Add _weight_view dispatch for Vector vs Matrix result slicing
@kylebeggs kylebeggs force-pushed the perf/reduce-allocations-solve-hotpaths branch from 5548b87 to 571e263 Compare February 17, 2026 15:11
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codecov bot commented Feb 17, 2026 •
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Codecov Report

✅ All modified and coverable lines are covered by tests.

Files with missing lines Coverage Δ
src/interpolation.jl 100.00% <100.00%> (ø)
src/solve/assembly.jl 97.38% <100.00%> (-2.62%) ⬇️
src/solve/execution.jl 99.03% <100.00%> (+0.03%) ⬆️
src/solve/forward_cache.jl 100.00% <100.00%> (ø)
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github-actions bot commented Feb 17, 2026 •
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Benchmark Results

main 7a8035d... main / 7a8035d...
Directional 2.46 ± 0.14 ms 2.45 ± 0.14 ms 1 ± 0.082
Directional (per point) 2.4 ± 0.13 ms 2.49 ± 0.14 ms 0.964 ± 0.075
Gradient 8.33 ± 0.38 ms 8.29 ± 0.39 ms 1 ± 0.066
MonomialBasis/dim=1/deg=0 0.0356 ± 0.014 μs 0.0463 ± 0.013 μs 0.77 ± 0.37
MonomialBasis/dim=1/deg=1 0.0753 ± 0.022 μs 0.0767 ± 0.022 μs 0.981 ± 0.4
MonomialBasis/dim=1/deg=2 0.0693 ± 0.022 μs 0.0878 ± 0.024 μs 0.789 ± 0.33
MonomialBasis/dim=2/deg=0 0.0351 ± 0.013 μs 0.0345 ± 0.001 μs 1.02 ± 0.37
MonomialBasis/dim=2/deg=1 25.3 ± 13 ns 0.0353 ± 0.013 μs 0.717 ± 0.46
MonomialBasis/dim=2/deg=2 30 ± 13 ns 0.0413 ± 0.014 μs 0.726 ± 0.41
MonomialBasis/dim=3/deg=0 29.2 ± 14 ns 0.0361 ± 0.014 μs 0.81 ± 0.49
MonomialBasis/dim=3/deg=1 0.0367 ± 0.015 μs 0.0429 ± 0.014 μs 0.855 ± 0.44
MonomialBasis/dim=3/deg=2 0.038 ± 0.014 μs 0.0489 ± 0.013 μs 0.779 ± 0.36
Partial 2.43 ± 0.14 ms 2.68 ± 0.12 ms 0.909 ± 0.069
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∂ 9.68 ± 0.079 ns 9.84 ± 0.11 ns 0.984 ± 0.014
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∂² 10.1 ± 0.17 ns 10.2 ± 0.13 ns 0.99 ± 0.021
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∇ 17.1 ± 0.12 ns 17.1 ± 0.07 ns 0.999 ± 0.0081
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∇² 18.6 ± 0.04 ns 18.6 ± 0.031 ns 1 ± 0.0027
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∂ 9.68 ± 0.08 ns 9.81 ± 0.09 ns 0.987 ± 0.012
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∂² 10.2 ± 0.08 ns 10.1 ± 0.16 ns 1.01 ± 0.018
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∇ 17.1 ± 0.15 ns 17.1 ± 0.07 ns 0.999 ± 0.0097
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∇² 18.6 ± 0.04 ns 18.6 ± 0.041 ns 1 ± 0.0031
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∂ 9.68 ± 0.06 ns 9.89 ± 0.1 ns 0.979 ± 0.012
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∂² 10 ± 0.21 ns 10.1 ± 0.18 ns 0.995 ± 0.027
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∇ 17.1 ± 0.15 ns 17.1 ± 0.069 ns 0.999 ± 0.0096
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∇² 18.6 ± 0.031 ns 18.6 ± 0.061 ns 1 ± 0.0037
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∂ 6.32 ± 0.08 ns 6.14 ± 0.33 ns 1.03 ± 0.057
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∂² 14.2 ± 0.02 ns 14.2 ± 0.031 ns 1 ± 0.0026
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∇ 8.53 ± 0.23 ns 8.67 ± 0.24 ns 0.984 ± 0.038
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∇² 16 ± 0.16 ns 15.8 ± 0.11 ns 1.01 ± 0.012
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∂ 6.32 ± 0.01 ns 6.5 ± 0.37 ns 0.972 ± 0.055
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∂² 14.2 ± 0.08 ns 14.2 ± 0.071 ns 1 ± 0.0075
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∇ 8.54 ± 0.13 ns 8.63 ± 0.29 ns 0.99 ± 0.037
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∇² 16 ± 0.16 ns 16.1 ± 0.09 ns 0.991 ± 0.011
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∂ 6.32 ± 0.08 ns 6.14 ± 0.27 ns 1.03 ± 0.047
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∂² 14.2 ± 0.08 ns 14.2 ± 0.031 ns 1 ± 0.006
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∇ 8.6 ± 0.08 ns 8.62 ± 0.33 ns 0.997 ± 0.039
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∇² 16 ± 0.099 ns 15.8 ± 0.13 ns 1.01 ± 0.01
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 0/0/∂ 3.42 ± 0.001 ns 3.72 ± 0.01 ns 0.919 ± 0.0025
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 0/0/∂² 4.7 ± 0.01 ns 4.7 ± 0.01 ns 1 ± 0.003
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 0/0/∇ 5.62 ± 0.039 ns 5.69 ± 0.011 ns 0.988 ± 0.0071
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 0/0/∇² 3.11 ± 0 ns 3.11 ± 0 ns 1 ± 0
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 1/1/∂ 3.42 ± 0.001 ns 3.72 ± 0.01 ns 0.919 ± 0.0025
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 1/1/∂² 4.7 ± 0.01 ns 4.7 ± 0.011 ns 1 ± 0.0032
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 1/1/∇ 5.61 ± 0.041 ns 5.7 ± 0.02 ns 0.984 ± 0.008
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 1/1/∇² 3.11 ± 0 ns 3.11 ± 0 ns 1 ± 0
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 2/2/∂ 3.42 ± 0.01 ns 3.72 ± 0.01 ns 0.919 ± 0.0037
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 2/2/∂² 4.7 ± 0.01 ns 4.7 ± 0.01 ns 1 ± 0.003
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 2/2/∇ 5.62 ± 0.049 ns 5.69 ± 0.02 ns 0.988 ± 0.0093
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 2/2/∇² 3.11 ± 0 ns 3.11 ± 0 ns 1 ± 0
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 0/0/∂ 4.27 ± 0.01 ns 4.27 ± 0.01 ns 1 ± 0.0033
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 0/0/∂² 5.58 ± 0.08 ns 5.54 ± 0.021 ns 1.01 ± 0.015
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 0/0/∇ 8.6 ± 0.1 ns 6.85 ± 0.01 ns 1.26 ± 0.015
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 0/0/∇² 4.27 ± 0.01 ns 4.27 ± 0.01 ns 1 ± 0.0033
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 1/1/∂ 4.27 ± 0.01 ns 4.27 ± 0.01 ns 1 ± 0.0033
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 1/1/∂² 5.58 ± 0.06 ns 5.52 ± 0.03 ns 1.01 ± 0.012
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 1/1/∇ 7.04 ± 0.27 ns 6.85 ± 0.01 ns 1.03 ± 0.039
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 1/1/∇² 4.27 ± 0.01 ns 4.27 ± 0.01 ns 1 ± 0.0033
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 2/2/∂ 4.27 ± 0.01 ns 4.27 ± 0.01 ns 1 ± 0.0033
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 2/2/∂² 5.58 ± 0.08 ns 5.54 ± 0.03 ns 1.01 ± 0.015
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 2/2/∇ 6.97 ± 0.27 ns 6.85 ± 0.01 ns 1.02 ± 0.04
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 2/2/∇² 4.27 ± 0.01 ns 4.27 ± 0.01 ns 1 ± 0.0033
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 0/0/∂ 4.96 ± 0.001 ns 5.26 ± 0.01 ns 0.943 ± 0.0018
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 0/0/∂² 4.65 ± 0.01 ns 4.65 ± 0.01 ns 1 ± 0.003
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 0/0/∇ 6.19 ± 0.011 ns 6.11 ± 0.079 ns 1.01 ± 0.013
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 0/0/∇² 3.42 ± 0.001 ns 3.42 ± 0.001 ns 1 ± 0.00041
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 1/1/∂ 4.96 ± 0.001 ns 5.26 ± 0.01 ns 0.943 ± 0.0018
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 1/1/∂² 4.65 ± 0.01 ns 4.65 ± 0.01 ns 1 ± 0.003
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 1/1/∇ 6.19 ± 0.011 ns 6.1 ± 0.071 ns 1.01 ± 0.012
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 1/1/∇² 3.42 ± 0.001 ns 3.42 ± 0.001 ns 1 ± 0.00041
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 2/2/∂ 4.96 ± 0.001 ns 5.26 ± 0.01 ns 0.943 ± 0.0018
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 2/2/∂² 4.65 ± 0.01 ns 4.65 ± 0.01 ns 1 ± 0.003
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 2/2/∇ 6.19 ± 0.011 ns 6.11 ± 0.07 ns 1.01 ± 0.012
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 2/2/∇² 3.42 ± 0.01 ns 3.42 ± 0.001 ns 1 ± 0.0029
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 0/0/∂ 10.4 ± 0.081 ns 10.3 ± 0.11 ns 1.01 ± 0.013
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 0/0/∂² 4.96 ± 0.01 ns 4.96 ± 0.01 ns 1 ± 0.0029
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 0/0/∇ 12.5 ± 0.071 ns 12.5 ± 0.081 ns 1 ± 0.0086
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 0/0/∇² 8.08 ± 0.09 ns 8.05 ± 0.071 ns 1 ± 0.014
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 1/1/∂ 10.4 ± 0.089 ns 10.3 ± 0.11 ns 1.01 ± 0.014
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 1/1/∂² 4.96 ± 0.001 ns 4.96 ± 0.01 ns 1 ± 0.002
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 1/1/∇ 12.5 ± 0.091 ns 12.6 ± 0.091 ns 0.995 ± 0.01
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 1/1/∇² 8.08 ± 0.09 ns 8.06 ± 0.08 ns 1 ± 0.015
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 2/2/∂ 10.4 ± 0.09 ns 10.2 ± 0.16 ns 1.01 ± 0.018
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 2/2/∂² 4.96 ± 0.001 ns 4.96 ± 0.01 ns 1 ± 0.002
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 2/2/∇ 12.5 ± 0.1 ns 12.5 ± 0.1 ns 1 ± 0.011
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 2/2/∇² 8.08 ± 0.07 ns 8.05 ± 0.062 ns 1 ± 0.012
time_to_load 0.646 ± 0.0014 s 0.806 ± 0.0054 s 0.802 ± 0.0056

Benchmark Plots

A plot of the benchmark results have been uploaded as an artifact to the workflow run for this PR.
Go to "Actions"->"Benchmark a pull request"->[the most recent run]->"Artifacts" (at the bottom).

@kylebeggs kylebeggs merged commit 0089df9 into main Feb 17, 2026
25 of 26 checks passed
@kylebeggs kylebeggs deleted the perf/reduce-allocations-solve-hotpaths branch February 20, 2026 20:02
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perf: optimize memory allocations in solve system hot paths

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