
From:  Patrick Alken 
Subject:  Re: [Buggsl] bugs when using gsl_sf_hyperg_U 
Date:  Tue, 11 Mar 2014 16:23:29 0600 
Useragent:  Mozilla/5.0 (X11; Linux x86_64; rv:24.0) Gecko/20100101 Thunderbird/24.3.0 
Just wanted to forward this to the list so it is archived On 03/11/2014 03:42 PM, Feng Gao wrote:
Hi Ray and Patrick,Thanks for your help so much thus far. I have included a simple cpp file which demonstrates several cases that will invoke bugs. I put the gsl folder in the same current folder and usedg++ Wall o gsl_sf_hyperg_U_bug_report gsl_sf_hyperg_U_bug_report.cpp lgsl lgslcblas lmto compile. Thanks again! Best Regards, Feng20140311 15:13 GMT04:00 Raymond Rogers <address@hidden <mailto:address@hidden>>:Hi Feng, Take the writing below as coming from somebody who had just a brush with the subject matter; numerical approximatioin of special function.s. I think that somebody on the GSL mailing list is an expert and could actually help. I didn't have much luck but that was years ago. I do suggest giving actual c (or some such) code you are trying to run. A simple program. Let me know I if I can help further.  No joy in my searh but I did look at the DLMF. In particular http://dlmf.nist.gov/13.2#vii To change b to +b (and +a) and http://dlmf.nist.gov/13.8 for Asymptotic expansions. Unfortunately I didn't find your case where the a,b go to infinity; but I did find an earlier paper: http://www.sciencedirect.com/science/article/pii/S0377042796001331 Which directly that covers b> inf equation 3. Unfortunately it solves the problem in terms of Bessel functions :) So some work has to be done. When I worked with large negative a I used a recursive form to walk a up to positive. One of the relations on http://dlmf.nist.gov/13.3 In particular 13.3.8 walks b and leaves a, z fixed. I did it in a matrix form because I am simpleminded but a straight recursion would work. Be aware that there are two ways to work recursions one explodes errors (the dominant recursion) and the other smooths them out (the minimall one). If you have access to a library or have "Numerical Methods for Special Functions" Gil,Segura, Temme chapter 4 covers recurrence theory. It's really not very hard. If needed I could copy that chapter and email it or you might get a preview on Google books I did email Pr Temme (who is a scholar on numerical approximations and Special functions) at: http://homepages.cwi.nl/~nicot/ <http://homepages.cwi.nl/%7Enicot/> He was very helpful and came back in 1 day with an answer to my question about large negative a; a simple formula that worked with a<1000 to astounding accuracy. I imagine asking him for a pointer instead of just asking for the formula would be more diplomatic. I did go out and buy one of his books after he answered and read some parts. Ray On 03/11/2014 12:15 PM, Feng Gao wrote:Hi Ray, Thanks very much for your effort! Best Regards, Feng 20140311 11:56 GMT04:00 Raymond Rogers <address@hidden <mailto:address@hidden>>: Okay, let me look around on my computer. I have to find it; the original email I had got extinguished by difficult manuever. It's hard but you _can_ erase all of your old emails onn gmail if you really try (or are really dumb!). Anyhow.... I will check now. Ray On 03/11/2014 11:01 AM, Feng Gao wrote:Hi Ray, Thanks for your response! These would be helpful indeed. Please notice that all the problems I had were for negative b. Actually in my case the value of a is fixed at 1 (so I don't need to worry about large negative a); the value of b is (inf, 2) and the value of x is > 0. If you have anything that works for this scenario, that will be extremely helpful. Best Regards, Feng 20140311 9:03 GMT04:00 Raymond Rogers <address@hidden <mailto:address@hidden>>: Hello, I had a similar problem with negative a (Lamm'sequation) and developed some programs that worked. That was about three years ago and I would have to findit. In addition the program blows up for large negative a; but I got in touch with a professional in these things and he gave me a asymptotic formula. I also have his book that explains a lot about doing these calculations. Let me know if I can help along this line. I probably have a bunch of links for asymptotic analysis. Ray On 03/10/2014 10:38 PM, Feng Gao wrote: Hi, Sorry for so many emails... I also tried the GSL SHELL software and it seemse that sf.hypergU(1, 500, 0.1) can be calculated correctly. However, I found that any negative nonintegers of b for U(a, b, x) cannot be calculated. These negative nonintegers should be suitable arguments and the manual states that b is of type double. Thanks very much for your attention and I will be very grateful if you can resolve these problems. Best Regards, Feng 20140310 21:01 GMT04:00 Feng Gao <address@hidden <mailto:address@hidden>>: Sorry for the typo but for example 1) listed in the previous email: gsl_sf_hyperg_U(1, 500, 0.1) gives the correct value: ~1.99e3. The problem happens when calculating gsl_sf_hyperg_U(1, 500, 40): gsl: gsl: hyperg.c:165: ERROR: overflow. The value should be ~0.00184 so I suppose this is a bug. Again, thanks very much if you can help me solve this problem since I very much need it in my research. Best Regards, Feng 20140310 19:53 GMT04:00 Feng Gao <address@hidden <mailto:address@hidden>>: Hi, I have been using the gsl_sf_hyperg_U function for a while and I found several bugs when calculating normal values. For example, 1) gsl_sf_hyperg_U(1, 500, 0.1) gives incorrect value: 9.3246e+03, which actually should be around 0.19. 2) Many domain error bugs. For example, gsl_sf_hyperg_U(1, 6.67, 1) should have value ~0.128 but will invoke domain error for gsl. Hope that you can further investigate this and come up with solutions. Thanks! Best Regards, Feng Act IV, Sc. IVWhat is a man, If his chief good and profit of his time Be to sleep and feed. Be a beast, no more Act IV, Sc. IVWhat is a man, If his chief good and profit of his time Be to sleep and feed. Be a beast, no more Act IV, Sc. IVWhat is a man, If his chief good and profit of his time Be to sleep and feed. Be a beast, no more
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