refactor(basis): replace operator closures with functor types by kylebeggs · Pull Request #64 · JuliaMeshless/RadialBasisFunctions.jl

kylebeggs · 2026-01-05T19:28:52Z

Summary

This PR addresses both Issue #62 and Issue #63.

Issue #62: Functor pattern for RBF operators

Add ∂, ∇, ∂², ∇², D, D² callable structs in basis.jl
Replace closure-returning functions with call methods for all RBF types
Update PHS1/3/5/7, Gaussian, IMQ implementations
Use D functor in assembly.jl instead of dot(n, ∇(...))

Issue #63: Unified operator construction

Add unified RadialBasisOperator(ℒ, data; eval_points, basis, k, adjl, hermite) constructor
Refactor all operator files to use thin wrappers delegating to unified constructor
Add hermite keyword argument as NamedTuple alternative
Maintain full backward compatibility

Benefits:

Proper Julia multiple dispatch instead of runtime branching
Better type inference and potential performance improvements
Reduced code duplication across operator files
More idiomatic Julia code

Closes #62
Closes #63

Test plan

All existing tests pass
New tests for D functor added (PHS, Gaussian, IMQ)
460 total tests passing

🤖 Generated with Claude Code

This refactoring addresses Issue #63 by introducing a unified constructor for RadialBasisOperator that uses keyword arguments, reducing code duplication across operator files. Changes: - Add unified `RadialBasisOperator(ℒ, data; eval_points, basis, k, adjl, hermite)` constructor in operators.jl - Refactor all operator files (laplacian, partial, custom, jacobian, gradient, directional, regridding) to use thin wrappers - Old positional constructors now delegate to the unified constructor - Maintain full backward compatibility with existing API - Add hermite keyword argument as NamedTuple alternative to positional args - Improve documentation with examples The new keyword-based API is now the primary interface: ```julia op = laplacian(data; basis=PHS(5), k=30) op = jacobian(data; eval_points=pts, hermite=(is_boundary=..., bc=..., normals=...)) ``` Closes #63 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

- Add ∂, ∇, ∂², ∇², D, D² functor structs in basis.jl - Replace closure-returning functions with callable structs - Update PHS, Gaussian, IMQ implementations - Use D functor in assembly.jl instead of dot(n, ∇(...)) 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

codecov · 2026-01-05T19:31:33Z

Codecov Report

❌ Patch coverage is 99.14530% with 4 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/operators/gradient.jl	60.00%	2 Missing ⚠️
src/operators/monomial/partial.jl	96.66%	1 Missing ⚠️
src/utils.jl	66.66%	1 Missing ⚠️

Files with missing lines	Coverage Δ
src/RadialBasisFunctions.jl	`100.00% <ø> (ø)`
src/basis/basis.jl	`100.00% <100.00%> (ø)`
src/basis/gaussian.jl	`100.00% <100.00%> (ø)`
src/basis/inverse_multiquadric.jl	`100.00% <100.00%> (ø)`
src/basis/monomial.jl	`100.00% <100.00%> (ø)`
src/basis/polyharmonic_spline.jl	`100.00% <100.00%> (ø)`
src/interpolation.jl	`100.00% <100.00%> (ø)`
src/operators/custom.jl	`100.00% <100.00%> (+66.66%)`	⬆️
src/operators/directional.jl	`100.00% <100.00%> (ø)`
src/operators/jacobian.jl	`100.00% <100.00%> (ø)`
... and 14 more

🚀 New features to boost your workflow:

❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

github-actions · 2026-01-05T19:39:08Z

Benchmark Results

	main	`f675246`...	main / `f675246`...
Directional	2.42 ± 0.14 ms	2.42 ± 0.09 ms	1 ± 0.069
Directional (per point)	2.42 ± 0.13 ms	2.4 ± 0.094 ms	1.01 ± 0.067
Gradient	8.16 ± 0.43 ms	8.29 ± 0.31 ms	0.984 ± 0.064
MonomialBasis/dim=1/deg=0	0.0469 ± 0.012 μs	0.0457 ± 0.012 μs	1.03 ± 0.38
MonomialBasis/dim=1/deg=1	0.0753 ± 0.012 μs	0.075 ± 0.0099 μs	1 ± 0.21
MonomialBasis/dim=1/deg=2	0.0856 ± 0.013 μs	0.0851 ± 0.019 μs	1.01 ± 0.27
MonomialBasis/dim=2/deg=0	0.035 ± 0.012 μs	0.0363 ± 0.011 μs	0.965 ± 0.43
MonomialBasis/dim=2/deg=1	0.0356 ± 0.012 μs	0.037 ± 0.012 μs	0.962 ± 0.46
MonomialBasis/dim=2/deg=2	0.0424 ± 0.011 μs	0.0425 ± 0.011 μs	0.997 ± 0.37
MonomialBasis/dim=3/deg=0	0.0364 ± 0.012 μs	0.034 ± 0.011 μs	1.07 ± 0.5
MonomialBasis/dim=3/deg=1	0.0424 ± 0.011 μs	0.0428 ± 0.012 μs	0.99 ± 0.39
MonomialBasis/dim=3/deg=2	0.0487 ± 0.011 μs	0.0484 ± 0.011 μs	1.01 ± 0.33
Partial	2.43 ± 0.14 ms	2.36 ± 0.086 ms	1.03 ± 0.07
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∂	10.1 ± 0.09 ns	10.1 ± 0.11 ns	1 ± 0.014
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∂²	10.6 ± 0.091 ns	10.5 ± 0.16 ns	1.01 ± 0.018
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∇	17.3 ± 0.06 ns	17.3 ± 0.06 ns	1 ± 0.0049
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∇²	18.3 ± 0.09 ns	18.2 ± 0.081 ns	1 ± 0.0067
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∂	10.1 ± 0.09 ns	10.1 ± 0.09 ns	0.999 ± 0.013
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∂²	10.6 ± 0.08 ns	10.5 ± 0.19 ns	1.01 ± 0.02
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∇	17.3 ± 0.06 ns	17.3 ± 0.06 ns	1 ± 0.0049
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∇²	18.3 ± 0.08 ns	18.2 ± 0.08 ns	1 ± 0.0062
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∂	10.1 ± 0.1 ns	10.1 ± 0.11 ns	1 ± 0.015
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∂²	10.6 ± 0.1 ns	10.6 ± 0.11 ns	1 ± 0.014
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∇	17.3 ± 0.06 ns	17.3 ± 0.06 ns	1 ± 0.0049
RBF/Gaussian, exp(-(ε*r)²)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∇²	18.2 ± 0.071 ns	18.2 ± 0.072 ns	1 ± 0.0056
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∂	6.32 ± 0.011 ns	6.73 ± 0.14 ns	0.939 ± 0.02
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∂²	14.1 ± 0.029 ns	14.1 ± 0.2 ns	1 ± 0.014
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∇	8.64 ± 0.05 ns	8.53 ± 0.26 ns	1.01 ± 0.031
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 0/0/∇²	16.3 ± 0.06 ns	16.4 ± 0.081 ns	0.996 ± 0.0062
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∂	6.32 ± 0.011 ns	6.8 ± 0.15 ns	0.929 ± 0.021
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∂²	14.1 ± 0.02 ns	14.1 ± 0.23 ns	1 ± 0.017
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∇	8.65 ± 0.03 ns	8.53 ± 0.26 ns	1.01 ± 0.031
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 1/1/∇²	16.3 ± 0.06 ns	16.4 ± 0.081 ns	0.994 ± 0.0061
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∂	6.32 ± 0.011 ns	6.8 ± 0.09 ns	0.929 ± 0.012
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∂²	14.1 ± 0.02 ns	14.1 ± 0.23 ns	1 ± 0.016
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∇	8.65 ± 0.039 ns	8.62 ± 0.15 ns	1 ± 0.018
RBF/Inverse Multiquadrics, 1/sqrt((r*ε)²+1)
├─Shape factor: ε = 1
└─Polynomial augmentation: degree 2/2/∇²	16.3 ± 0.06 ns	16.4 ± 0.081 ns	0.996 ± 0.0062
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 0/0/∂	3.42 ± 0.001 ns	3.42 ± 0.001 ns	1 ± 0.00041
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 0/0/∂²	4.7 ± 0.011 ns	4.7 ± 0.01 ns	1 ± 0.0032
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 0/0/∇	5.43 ± 0.02 ns	5.59 ± 0.05 ns	0.971 ± 0.0094
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 0/0/∇²	3.11 ± 0 ns	3.11 ± 0.001 ns	1 ± 0.00032
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 1/1/∂	3.42 ± 0.001 ns	3.42 ± 0.001 ns	1 ± 0.00041
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 1/1/∂²	4.7 ± 0.02 ns	4.7 ± 0.01 ns	1 ± 0.0048
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 1/1/∇	5.43 ± 0.021 ns	5.59 ± 0.079 ns	0.971 ± 0.014
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 1/1/∇²	3.11 ± 0 ns	3.11 ± 0.001 ns	1 ± 0.00032
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 2/2/∂	3.42 ± 0.001 ns	3.42 ± 0.001 ns	1 ± 0.00041
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 2/2/∂²	4.7 ± 0.14 ns	4.7 ± 0.01 ns	1 ± 0.03
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 2/2/∇	5.43 ± 0.021 ns	5.59 ± 0.06 ns	0.971 ± 0.011
RBF/Polyharmonic spline (r³)
└─Polynomial augmentation: degree 2/2/∇²	3.11 ± 0 ns	3.11 ± 0.001 ns	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	5.78 ± 0.01 ns	5.82 ± 0.011 ns	0.993 ± 0.0025
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 0/0/∇	6.78 ± 0.02 ns	7.27 ± 0.031 ns	0.932 ± 0.0048
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 0/0/∇²	4.52 ± 0.01 ns	4.27 ± 0.01 ns	1.06 ± 0.0034
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	5.77 ± 0.4 ns	5.82 ± 0.021 ns	0.991 ± 0.069
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 1/1/∇	6.78 ± 0.02 ns	7.27 ± 0.021 ns	0.932 ± 0.0038
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 1/1/∇²	4.52 ± 0.01 ns	4.27 ± 0.01 ns	1.06 ± 0.0034
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	5.78 ± 0.011 ns	5.82 ± 0.02 ns	0.993 ± 0.0039
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 2/2/∇	6.78 ± 0.021 ns	7.27 ± 0.051 ns	0.933 ± 0.0071
RBF/Polyharmonic spline (r¹)
└─Polynomial augmentation: degree 2/2/∇²	4.52 ± 0.01 ns	4.27 ± 0.01 ns	1.06 ± 0.0034
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 0/0/∂	5.26 ± 0.01 ns	5.26 ± 0.01 ns	1 ± 0.0027
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 0/0/∂²	4.96 ± 0.01 ns	4.96 ± 0.01 ns	1 ± 0.0029
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 0/0/∇	6.03 ± 0.09 ns	6.23 ± 0.09 ns	0.968 ± 0.02
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 0/0/∇²	3.73 ± 0.01 ns	3.42 ± 0.001 ns	1.09 ± 0.0029
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 1/1/∂	5.26 ± 0.01 ns	5.26 ± 0.01 ns	1 ± 0.0027
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 1/1/∂²	4.96 ± 0.01 ns	4.96 ± 0.01 ns	1 ± 0.0029
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 1/1/∇	6.04 ± 0.09 ns	6.23 ± 0.089 ns	0.97 ± 0.02
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 1/1/∇²	3.73 ± 0.01 ns	3.42 ± 0.001 ns	1.09 ± 0.0029
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 2/2/∂	5.26 ± 0.01 ns	5.26 ± 0.01 ns	1 ± 0.0027
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 2/2/∂²	4.96 ± 0.01 ns	4.96 ± 0.01 ns	1 ± 0.0029
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 2/2/∇	6.03 ± 0.081 ns	6.22 ± 0.081 ns	0.97 ± 0.018
RBF/Polyharmonic spline (r⁵)
└─Polynomial augmentation: degree 2/2/∇²	3.73 ± 0.01 ns	3.42 ± 0.001 ns	1.09 ± 0.0029
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 0/0/∂	10.6 ± 0.11 ns	10.1 ± 0.21 ns	1.04 ± 0.024
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 0/0/∂²	5.27 ± 0.01 ns	4.96 ± 0.01 ns	1.06 ± 0.0029
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 0/0/∇	12.4 ± 0.06 ns	12.8 ± 0.18 ns	0.967 ± 0.014
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 0/0/∇²	8.12 ± 0.11 ns	8.4 ± 0.03 ns	0.967 ± 0.014
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 1/1/∂	10.6 ± 0.16 ns	10.2 ± 0.2 ns	1.04 ± 0.026
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 1/1/∂²	5.27 ± 0.01 ns	4.96 ± 0.01 ns	1.06 ± 0.0029
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 1/1/∇	12.4 ± 0.06 ns	12.8 ± 0.19 ns	0.968 ± 0.015
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 1/1/∇²	8.12 ± 0.11 ns	8.4 ± 0.03 ns	0.967 ± 0.014
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 2/2/∂	10.6 ± 0.02 ns	10.1 ± 0.16 ns	1.05 ± 0.017
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 2/2/∂²	5.27 ± 0.01 ns	4.96 ± 0.01 ns	1.06 ± 0.0029
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 2/2/∇	12.4 ± 0.061 ns	12.8 ± 0.18 ns	0.968 ± 0.014
RBF/Polyharmonic spline (r⁷)
└─Polynomial augmentation: degree 2/2/∇²	8.12 ± 0.11 ns	8.4 ± 0.03 ns	0.967 ± 0.014
time_to_load	0.605 ± 0.0021 s	0.61 ± 0.0053 s	0.992 ± 0.0092

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).

Add H (Hessian) functor for all basis types to enable pre-construction of derivative operators outside hot loops in Hermite interpolation. Changes: - Add H struct to basis.jl for Hessian matrix computation - Implement H for PHS1, PHS3, PHS5, PHS7, Gaussian, IMQ - Add D² (directional second derivative) for Gaussian and IMQ - Add BasisOperators wrapper to bundle φ, ∇φ, Hφ operators - Update hermite_rbf_dispatch to use dot(n, ∇φ) and dot(ni, Hφ*nj) - Construct BasisOperators once before loop in _build_collocation_matrix! Performance: Avoids constructing D/D² functors per point pair in hot loop. Instead pre-constructs gradient and Hessian operators once and computes directional derivatives via dot products. Tests: Add Hessian and D² tests for all basis types verified against ForwardDiff. 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

kylebeggs and others added 4 commits January 5, 2026 07:57

rm md

71498dd

test(basis): add D functor tests for Gaussian and IMQ

1092302

🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

format

0a85edc

kylebeggs requested a review from Davide-Miotti January 5, 2026 19:36

kylebeggs and others added 5 commits January 5, 2026 18:27

some style updates

9801885

fix hessian

bb76344

style: apply JuliaFormatter

14781ff

🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

add some coverage for new constructors

f675246

kylebeggs force-pushed the refactor/issue-62-functor-operators branch from f789293 to f675246 Compare January 8, 2026 03:35

kylebeggs merged commit aa67750 into main Jan 8, 2026
32 of 51 checks passed

kylebeggs deleted the refactor/issue-62-functor-operators branch January 8, 2026 03:43

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refactor(basis): replace operator closures with functor types#64

refactor(basis): replace operator closures with functor types#64
kylebeggs merged 10 commits intomainfrom
refactor/issue-62-functor-operators

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Summary

Issue #62: Functor pattern for RBF operators

Issue #63: Unified operator construction

Test plan

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