http://www.mapleprimes.com/posts/41466-BesselK1-And-BesselK0-Purely-Numerical en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Sat, 13 Jun 2026 09:56:25 GMT Sat, 13 Jun 2026 09:56:25 GMT The latest comments added to the Post, BesselK1 and BesselK0 purely numerical http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/posts/41466-BesselK1-And-BesselK0-Purely-Numerical http://www.mapleprimes.com/posts/41466-BesselK1-And-BesselK0-Purely-Numerical?ref=Feed:MaplePrimes:BesselK1 and BesselK0 purely numerical:Comments#comment77271 The readme.txt file in <a href=http://www.kurims.kyoto-u.ac.jp/~ooura/bessel.tar.gz>bessel.tar.gz</a> says, "copyright Copyright(C) 1996 Takuya OOURA (email: ...). You may use, copy, modify this code for any purpose and without fee. You may distribute this ORIGINAL package." Is that what was in the source that you translated, may I ask, Axel? I couldn't see from it whether one it gives permission to distribute the code in modified or translated form. I know very little about the legalities of such things; perhaps someone here could explain it to me... acer The latest comments added to the Post, BesselK1 and BesselK0 purely numerical 77271 Thu, 26 Apr 2007 23:45:58 Z acer acer http://www.mapleprimes.com/posts/41466-BesselK1-And-BesselK0-Purely-Numerical?ref=Feed:MaplePrimes:BesselK1 and BesselK0 purely numerical:Comments#comment77265 Thanks very much, Axel, for the explanation. The timings in the worksheet indicate that your maple-language implementations, the translations, might be 4-5 times faster than Maple's own when run outside of evalhf, is that right? And far more importantly, your implementations are evalhf'able! The BesselK1 implementation seems to be quite accurate, except perhaps for very small arguments, judging by the graph. I find this to be very exciting. acer The latest comments added to the Post, BesselK1 and BesselK0 purely numerical 77265 Fri, 27 Apr 2007 01:12:51 Z acer acer http://www.mapleprimes.com/posts/41466-BesselK1-And-BesselK0-Purely-Numerical?ref=Feed:MaplePrimes:BesselK1 and BesselK0 purely numerical:Comments#comment77266 Acer, yes, that's the source. I am not a lawyer, but care for the legal afairs and contracts at our software company and so will try to answer your implicitely stated inhibitions (if i got you right): According to the legal situation in the European Community (and guess also US) I am the author of the modification and thus have the rights for it (BTW: anybody can use it for free and ... [2 formal pages of text ... I think covered by signing to MaplePrimes]). The point is: you can not transfer the rights, only the ((un)restricted) usage and his text says not even that, but allows even more. However it would not be enough for a patent (that would be a mess, it would miss originality)), so in plain words his (c) says: use it, even distribute it. For the inhibitions: the double expontential integration method (used in Maple, Mathematica and other commercial software) is due to him and his teacher (you find it on his page as well). Does that hit the very point? Axel -------------------------------------------- Edited to add a citation: Dear Axel Vogt, > > I hope usage is ok according to your copyright? It is ok. Please distribute the modified code freely. Takuya Ooura Research Institute for Mathematical Sciences The latest comments added to the Post, BesselK1 and BesselK0 purely numerical 77266 Fri, 27 Apr 2007 13:44:16 Z Axel Vogt Axel Vogt http://www.mapleprimes.com/posts/41466-BesselK1-And-BesselK0-Purely-Numerical?ref=Feed:MaplePrimes:BesselK1 and BesselK0 purely numerical:Comments#comment85617 Yes it is ~ 5 times faster, however evalhf'able is the essential point and then it is ~ 1000 faster. It is just the following observation: for numeric approximation you will usually need coefficients given in arrays. Put them into a global array of double floats. Then you can make the code evalhf'able (at the cost of having globals - holding them local in the proc makes it slower, I do not know the exact reason - may be Maple's remember tables?). To be fair: it is only absolute exactness (as almost all numerical code not relative as Maple does), only integer index and real arguments and it covers no symbolics. And the Bessel Family is large ... But for many things that's just needed and enough. The latest comments added to the Post, BesselK1 and BesselK0 purely numerical 85617 Fri, 27 Apr 2007 15:36:22 Z Axel Vogt Axel Vogt