docs refresh by kylebeggs · Pull Request #87 · JuliaMeshless/RadialBasisFunctions.jl

kylebeggs · 2026-02-18T15:21:39Z

No description provided.

Expand Quick Start to show operator algebra, regrid, and second derivatives. Remove Advanced Features section (outdated Hermite API, niche custom operators). Add TIP callout pointing to docs for configuration. Expand Documentation links with Autodiff page.

Clarify that both Enzyme and Mooncake have native AD rules. Add note about Interpolator construction requiring Mooncake via DifferentiationInterface. Update compatibility table with Interpolator construction row.

Replace generic hero/feature cards with problem-first messaging, use README's Quick Start example, add "Best For" column to RBF table, cut filler prose from getting_started/quickref/autodiff.

github-actions · 2026-02-18T15:33:59Z

Benchmark Results

	main	`2f5f095`...	main / `2f5f095`...
Directional	2.38 ± 0.14 ms	2.4 ± 0.15 ms	0.993 ± 0.083
Directional (per point)	2.43 ± 0.15 ms	2.46 ± 0.15 ms	0.986 ± 0.083
Gradient	7.74 ± 0.42 ms	8.34 ± 0.41 ms	0.928 ± 0.068
MonomialBasis/dim=1/deg=0	0.0471 ± 0.016 μs	0.0465 ± 0.013 μs	1.01 ± 0.44
MonomialBasis/dim=1/deg=1	0.0816 ± 0.018 μs	0.0762 ± 0.021 μs	1.07 ± 0.38
MonomialBasis/dim=1/deg=2	0.0875 ± 0.022 μs	0.0851 ± 0.022 μs	1.03 ± 0.37
MonomialBasis/dim=2/deg=0	0.0392 ± 0.0086 μs	0.039 ± 0.0013 μs	1.01 ± 0.22
MonomialBasis/dim=2/deg=1	25.3 ± 14 ns	0.0356 ± 0.014 μs	0.709 ± 0.49
MonomialBasis/dim=2/deg=2	0.0404 ± 0.014 μs	0.0413 ± 0.015 μs	0.977 ± 0.49
MonomialBasis/dim=3/deg=0	0.0352 ± 0.014 μs	0.0362 ± 0.013 μs	0.971 ± 0.52
MonomialBasis/dim=3/deg=1	0.0467 ± 0.014 μs	0.0471 ± 0.013 μs	0.993 ± 0.41
MonomialBasis/dim=3/deg=2	0.0425 ± 0.014 μs	0.0446 ± 0.015 μs	0.952 ± 0.44
Partial	2.38 ± 0.12 ms	2.62 ± 0.18 ms	0.908 ± 0.078
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∂	9.69 ± 0.09 ns	9.67 ± 0.06 ns	1 ± 0.011
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∂²	10.1 ± 0.17 ns	10.1 ± 0.2 ns	1 ± 0.026
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∇	17.1 ± 0.04 ns	17 ± 0.06 ns	1.01 ± 0.0043
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∇²	18.6 ± 0.28 ns	18.1 ± 0.06 ns	1.03 ± 0.016
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∂	9.66 ± 0.18 ns	9.67 ± 0.051 ns	0.999 ± 0.019
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∂²	10.2 ± 0.17 ns	10.1 ± 0.21 ns	1.01 ± 0.027
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∇	17.2 ± 0.13 ns	17.2 ± 0.15 ns	0.998 ± 0.012
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∇²	18.6 ± 0.29 ns	18.1 ± 0.069 ns	1.03 ± 0.017
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∂	9.66 ± 0.18 ns	9.67 ± 0.05 ns	0.999 ± 0.019
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∂²	10.1 ± 0.15 ns	10.1 ± 0.2 ns	1 ± 0.025
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∇	17 ± 0.051 ns	17 ± 0.051 ns	1 ± 0.0043
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∇²	18.6 ± 0.28 ns	18.1 ± 0.06 ns	1.03 ± 0.016
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∂	6.32 ± 0.011 ns	6.32 ± 0.06 ns	1 ± 0.0096
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∂²	14 ± 0.09 ns	14.2 ± 0.1 ns	0.986 ± 0.0095
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∇	8.41 ± 0.18 ns	8.6 ± 0.25 ns	0.978 ± 0.035
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∇²	15.9 ± 0.14 ns	15.8 ± 0.07 ns	1.01 ± 0.01
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∂	6.32 ± 0.01 ns	6.27 ± 0.079 ns	1.01 ± 0.013
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∂²	14 ± 0.03 ns	14.2 ± 0.071 ns	0.987 ± 0.0054
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∇	8.35 ± 0.3 ns	8.63 ± 0.21 ns	0.967 ± 0.042
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∇²	15.9 ± 0.11 ns	15.8 ± 0.089 ns	1.01 ± 0.0091
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∂	6.32 ± 0.019 ns	6.33 ± 0.07 ns	0.999 ± 0.011
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∂²	14 ± 0.071 ns	14.2 ± 0.15 ns	0.987 ± 0.012
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∇	8.34 ± 0.31 ns	8.63 ± 0.25 ns	0.966 ± 0.046
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∇²	15.9 ± 0.14 ns	15.8 ± 0.099 ns	1.01 ± 0.011
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 0/0/∂	3.4 ± 0.039 ns	3.73 ± 0.01 ns	0.911 ± 0.011
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 0/0/∂²	4.7 ± 0.01 ns	4.71 ± 0.001 ns	0.998 ± 0.0021
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 0/0/∇	5.71 ± 0.02 ns	5.61 ± 0.041 ns	1.02 ± 0.0082
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 0/0/∇²	3.42 ± 0.001 ns	3.11 ± 0 ns	1.1 ± 0.00032
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 1/1/∂	3.4 ± 0.039 ns	3.73 ± 0.01 ns	0.911 ± 0.011
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 1/1/∂²	4.7 ± 0.01 ns	4.71 ± 0.01 ns	0.998 ± 0.003
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 1/1/∇	5.71 ± 0.02 ns	5.61 ± 0.039 ns	1.02 ± 0.0079
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 1/1/∇²	3.42 ± 0.001 ns	3.11 ± 0 ns	1.1 ± 0.00032
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 2/2/∂	3.41 ± 0.04 ns	3.73 ± 0 ns	0.914 ± 0.011
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 2/2/∂²	4.7 ± 0.01 ns	4.71 ± 0.001 ns	0.998 ± 0.0021
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 2/2/∇	5.71 ± 0.02 ns	5.61 ± 0.049 ns	1.02 ± 0.0096
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 2/2/∇²	3.42 ± 0.001 ns	3.11 ± 0 ns	1.1 ± 0.00032
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	5.61 ± 0.01 ns	5.44 ± 0.01 ns	1.03 ± 0.0026
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 0/0/∇	6.82 ± 0.079 ns	7.12 ± 0.011 ns	0.958 ± 0.011
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 0/0/∇²	4.28 ± 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	5.61 ± 0.011 ns	5.44 ± 0.01 ns	1.03 ± 0.0028
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 1/1/∇	6.82 ± 0.069 ns	7.12 ± 0.011 ns	0.958 ± 0.0098
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 1/1/∇²	4.28 ± 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	5.61 ± 0.01 ns	5.44 ± 0.01 ns	1.03 ± 0.0026
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 2/2/∇	6.82 ± 0.1 ns	7.12 ± 0.011 ns	0.958 ± 0.014
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 2/2/∇²	4.28 ± 0.01 ns	4.27 ± 0.01 ns	1 ± 0.0033
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 0/0/∂	4.65 ± 0.001 ns	4.96 ± 0.01 ns	0.937 ± 0.0019
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 0/0/∂²	5.26 ± 0.01 ns	4.96 ± 0.011 ns	1.06 ± 0.0031
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 0/0/∇	6.24 ± 0.031 ns	6.11 ± 0.071 ns	1.02 ± 0.013
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 0/0/∇²	3.42 ± 0.001 ns	3.12 ± 0.01 ns	1.1 ± 0.0035
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 1/1/∂	4.65 ± 0.001 ns	4.96 ± 0.01 ns	0.937 ± 0.0019
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 1/1/∂²	5.26 ± 0.01 ns	4.96 ± 0.01 ns	1.06 ± 0.0029
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 1/1/∇	6.24 ± 0.041 ns	6.11 ± 0.071 ns	1.02 ± 0.014
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 1/1/∇²	3.42 ± 0.001 ns	3.12 ± 0.01 ns	1.1 ± 0.0035
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 2/2/∂	4.65 ± 0.001 ns	4.96 ± 0.011 ns	0.937 ± 0.0021
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 2/2/∂²	5.26 ± 0.01 ns	4.96 ± 0.011 ns	1.06 ± 0.0031
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 2/2/∇	6.24 ± 0.021 ns	6.11 ± 0.071 ns	1.02 ± 0.012
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 2/2/∇²	3.42 ± 0.001 ns	3.12 ± 0.01 ns	1.1 ± 0.0035
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 0/0/∂	10.2 ± 0.25 ns	10.3 ± 0.16 ns	0.986 ± 0.029
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 0/0/∂²	5.27 ± 0.01 ns	5.27 ± 0.01 ns	1 ± 0.0027
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 0/0/∇	13.1 ± 0.22 ns	12.5 ± 0.091 ns	1.04 ± 0.019
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 0/0/∇²	8.12 ± 0.059 ns	8.05 ± 0.072 ns	1.01 ± 0.012
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 1/1/∂	10.1 ± 0.25 ns	10.3 ± 0.16 ns	0.983 ± 0.029
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 1/1/∂²	5.27 ± 0.01 ns	5.27 ± 0.01 ns	1 ± 0.0027
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 1/1/∇	13 ± 0.14 ns	12.6 ± 0.1 ns	1.04 ± 0.014
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 1/1/∇²	8.13 ± 0.051 ns	8.05 ± 0.071 ns	1.01 ± 0.011
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 2/2/∂	10.2 ± 0.25 ns	10.1 ± 0.25 ns	1 ± 0.035
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 2/2/∂²	5.27 ± 0.01 ns	5.27 ± 0.01 ns	1 ± 0.0027
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 2/2/∇	13 ± 0.14 ns	12.5 ± 0.1 ns	1.04 ± 0.014
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 2/2/∇²	8.12 ± 0.059 ns	8.05 ± 0.08 ns	1.01 ± 0.012
time_to_load	0.846 ± 0.029 s	0.81 ± 0.005 s	1.04 ± 0.037

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 added 4 commits February 17, 2026 19:48

docs(autodiff): update implementation status and Interpolator caveats

1a8a166

Clarify that both Enzyme and Mooncake have native AD rules. Add note about Interpolator construction requiring Mooncake via DifferentiationInterface. Update compatibility table with Interpolator construction row.

docs: rewrite landing page and tighten prose to match README voice

be9fa39

Replace generic hero/feature cards with problem-first messaging, use README's Quick Start example, add "Best For" column to RBF table, cut filler prose from getting_started/quickref/autodiff.

spruce up docs

2f5f095

kylebeggs merged commit 9a38824 into main Feb 18, 2026
3 checks passed

kylebeggs deleted the docs branch February 20, 2026 20:02

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docs refresh#87

docs refresh#87
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