Add LaguerreGaussKernel #893
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## main #893 +/- ##
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- Coverage 65.94% 65.88% -0.06%
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Files 113 113
Lines 7852 7880 +28
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+ Hits 5178 5192 +14
- Misses 2674 2688 +14
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The normal smoothing kernel test that we have doesn't work here since the truncation error is too large. |
The Gauss kernel is also truncated. Why can't you run the same tests for this kernel? |
I can but the errors seem to be unreasonable because they are larger than 1. |
| Poly6Kernel, | ||
| LaguerreGaussKernel |
| # C' = 1 / (4 * pi * h^3 * integral) | ||
| # integral = (7 * sqrt(pi) / 32) * erf(2) - (77 / 24) * exp(-4) | ||
| return (1 / (4 * pi * ((7 * sqrt(pi) / 32) * erf(2) - (77 / 24) * exp(-4)))) / h^3 |
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- Why not write it like in the comment? This is easier to read and avoids the division by
h^3. erfis expensive:julia> @b erf(2) 19.637 ns
| # C' = 1 / (4 * pi * h^3 * integral) | |
| # integral = (7 * sqrt(pi) / 32) * erf(2) - (77 / 24) * exp(-4) | |
| return (1 / (4 * pi * ((7 * sqrt(pi) / 32) * erf(2) - (77 / 24) * exp(-4)))) / h^3 | |
| erf2 = 0.9953223f0 | |
| sqrt_pi = sqrt(oftype(h, pi)) | |
| integral = (7 * sqrt_pi / 32) * erf2 - 77 * exp(-4) / 24 | |
| return 1 / (pi * h^3 * 4 * integral) |
Same with the other normalization factors.
| return ifelse(s < 2, val, zero(val)) | ||
| end | ||
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| @muladd @inline function kernel_deriv(kernel::LaguerreGaussKernel, r::Real, h) |
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| @muladd @inline function kernel_deriv(kernel::LaguerreGaussKernel, r::Real, h) | |
| @inline function kernel_deriv(kernel::LaguerreGaussKernel, r::Real, h) |
There is no muladd used anywhere in this function. Same for the one above.
| s = r * invh | ||
| if s >= 2 | ||
| return zero(s) | ||
| end | ||
| # dg/ds = (s/3)*(-s^4 + 5s^2 - 9) * exp(-s^2) | ||
| poly = ((-s^2 + 5) * s^2 - 9) * (s / 3) | ||
| return normalization_factor(kernel, h) * exp(-s^2) * poly * invh |
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- Please avoid branching
- Please use
qlike in all other kernels.
| s = r * invh | |
| if s >= 2 | |
| return zero(s) | |
| end | |
| # dg/ds = (s/3)*(-s^4 + 5s^2 - 9) * exp(-s^2) | |
| poly = ((-s^2 + 5) * s^2 - 9) * (s / 3) | |
| return normalization_factor(kernel, h) * exp(-s^2) * poly * invh | |
| q = r * invh | |
| # dg/dq = (q/3)*(-q^4 + 5q^2 - 9) * exp(-q^2) | |
| poly = ((-q^2 + 5) * q^2 - 9) * (q / 3) | |
| return ifelse(q < 2, normalization_factor(kernel, h) * exp(-q^2) * poly * invh, zero(q) |
| Truncated Laguerre–Gauss kernel (fourth-order smoothing) as defined in | ||
| [Wang2024](@cite). Its radial form uses | ||
| `s = r/h` and is truncated at `s = 2` (compact support `2h`): |
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Please fix the equation below and use math here instead of code.
| with normalization constants | ||
| α₁ = 8/(5√π), α₂ = 3/π, α₃ = 8/π^{3/2}. | ||
| Recommended practical choice from the paper: use h ≈ 1.3Δx and the same |
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| Recommended practical choice from the paper: use h ≈ 1.3Δx and the same | |
| Recommended practical choice from the paper: use ``h \approx 1.3Δx`` and the same |
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| Any Kernel with a stability rating of more than '+++' doesn't suffer from pairing-instability. | ||
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| ```julia |
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Is this supposed to be a doctest to generate a plot?
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| [default.extend-words] | ||
| ba = "ba" | ||
| Comput = "Comput" |
2 participants
In my quick testing this didn't show the claimed accuracy improvement vs Wendland and Quintic.