chrisbrahms / hankel.jl Goto Github PK

Thanks for a great package!

Since this package depends on FunctionZeros, it suffers from JuliaMath/FunctionZeros.jl#10 (that package doesn't work for orders larger than a few) and thus Hankel.jl cannot set up a plan for those orders. For example, here's a quick selection of nodes,

using Hankel
R = 1.0
N = 32
q = QDHT(10, R, N)
print(q.r[4:7])

[0.21586560553503556, 0.3827577984254705, 3.847210992460738, 0.24445021648591286]

These nodes aren't monotonically increasing!

I imagine this can be fixed by using a more reliable source of zeros, perhaps GSL? FunctionZeros is a very tiny package, so maybe a pure Julia replacement using more robust methods might be helpful.

It looks like v0.2 failed to register because the v0.2.0 tag already existed. v0.1.1 is the current version in the registry.

Bumping to v0.2.1 and registering would work, else the v0.2.0 tag would need to be deleted.

Thank you for this package! I remember using it tangentially for research last year and found it very helpful.

One thing I was curious about is if Bessels.jl would provide any added benefit here? In general, the besselj and gamma functions are several times faster than the ones provided by SpecialFunctions.jl (we also provide spherical Bessel functions). An advantage is that besselj doesn't allocate so that should be a very helpful memory boost.

I went ahead and cloned the library and swapped in Bessels.jl instead and it did pass all the tests except the ones for BigFloat. That is a current limitation as we only provide single and double precision so far. Are there any particular features that would be helpful here that we could add at Bessels? Or is there a nice example that I could try out to test any performance improvements?

Best,
Michael

Nice package!

I'm planning to implement a discrete spherical Hankel transform, also following the pattern of AbstractFFTs. Since you have the Hankel package name in the registry, would your package be a good place to contribute this (else I would create a SphericalHankel.jl)? It would be nice if the interfaces were similar.

I noticed you currently implement only the zero-order DHT. There's also @jagot's package https://github.com/jagot/Hankel.jl, which is stale but implements additional orders, seemingly following the same papers.

you may want to export besselj_zero or change your example in the documentations such that the function can be found.
It took me quite long to realize that this function is provided by this package, but not exported ;-)

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@chrisbrahms when tagging a new release (JuliaRegistries/General#38708 (comment)) it came to light that this package doesn't have a license. Any issues with me adding an MIT license here, which is highly permissive and also standard for Julia packages?

Hi! I used the QDHT to calculate the convolution of two radially symmetric functions via multiplication in Fourier space and then transforming back. What I am now interested in is the derivative of the convolution result with respect to the radial variable. Math-wise it should be something like this I think:

$$ \frac{d}{dr}f(r) = \frac{d}{dr}H_0^{-1}(F(k)) = \frac{d}{dr} \int_0^\infty F(k) J_0(kr)k\ dk = - \int_0^\infty F(k) J_1(kr)k^2\ dk = -H_1^{-1}(kF(k))$$

Question: Is there a nice way to obtain the result using QDHT? So far I think no, as $H_0$ and $H_1$ use different discretizations of the real and reciproke space, but I'd be happy if there's a workaround.