I need the 3rd-order Debye function in a Julia routine and wonder which is the best way to use/implement it. Searching for it in different repositories, I found various implementations, some of which based on simply solving the integral with Gauss quadrature (FewSpecialFuntions.jl), some of them im…

[image] PeterSimon: Even though the code is freely available on Netlib? Does it come with a license, and which one, is the question.

[image] PeterSimon: Even though the code is freely available on Netlib? Freely available ≠ open source . The Netlib TOMS page specifically says Use of ACM Algorithms is subject to the ACM Software Copyright and License Agreement which is only “free for noncommercial use” (≠ free/open-sour…

[image] PeterSimon: Here is a translation of the TOMS 757 Fortran algorithm to Julia. NB: the accuracy suddenly becomes much worse after 4 (as x increases, there’s a huge jump in relative error when it passes 4), but slowly improves thereafter.

Thanks to everybody for the replies. In the meantime, I have written a module that comprises an implementation based mostly on the Abramowitz & Stegun formulas. I have compared it with the TOMS method as given by Steven and with the quadrature-based version from FewSpecialFunctions.jl, and to my dis…

For the tests, I evaluated the 3rd-order Debye function at x=0.2 and at x=4.2, as I found that the first option in the if block corresponds to smaller x and the second to larger ones. The TOMS-derived function seems to perform vastly differently between the two values: for x=4.2 it took two orders o…

[image] trg818: For the tests, I evaluated the 3rd-order Debye function at x=0.2 and at x=4.2, as I found that the first option in the if block corresponds to smaller x and the second to larger ones. The TOMS-derived function seems to perform vastly differently between the two values: for x=4.2 …

I agree that recurrence relations are a great way to save time, but I don’t see how to make one here. bernum is used only once per call to nDebye to calculate a single Bernoulli number. I only noticed that the function should have been written more compactly as function bernum(n) # based on formul…

For example, you shouldn’t need to call binomial for each term in the sum, but rather compute each ten from the previous term. (And allocating an array and them calling sum is also terribly inefficient.) But if bernum isn’t performance critical, of course it doesn’t matter.

[image] trg818: nD+=(B2n[k]*x^k2)/((k2+n)*factorial(big(k2))) But this loop body is in your performance critical function, right? The same advice applies: compute the factorials and powers iteratively from the previous summand, not separately for each term. By doing so you can also avoid spur…

Best way to use/implement Debye function in Julia?

General Usage

stevengj March 4, 2024, 9:16pm 16

This is a slow way to implement a power series. You always want to compute each term as a recurrence from the next. See also And Julia keeps amazing me: high precision computation - #6 by stevengj

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Best way to use/implement Debye function in Julia?

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