SMath Studio Forum
»
SMath Studio
»
Bugs & Problems
»
Different Results of Integration in 7219 & 7250 (Gamma Function)
Rank: Guest
Groups: Registered
Joined: 04/07/2015(UTC) Posts: 6,866 Was thanked: 981 time(s) in 809 post(s)
|
|
|
|
|
Rank: Advanced Member Groups: Registered
Joined: 05/06/2014(UTC) Posts: 348 Location: Colombo Was thanked: 125 time(s) in 82 post(s)
|
Originally Posted by: ndtma Still I get errors in SS 7251. After I got this error with 7251, again I did a Clean re-installation, and all issues posted later occurred consequent to this. Furthermore, a similar Clean re-installation of 7251 was done in my second laptop today, but errors continued to occur with same test worksheets except Jean's "Test_Gamma_7251_[6179].sm". Therefore, I have no alternative but leave it to the developers to decide. Edited by user 13 November 2019 14:03:33(UTC)
| Reason: Not specified |
Look within!... The secret is inside you. Best Regards Eng. NDTM Amarasekera - Sri Lanka |
|
|
|
Rank: Guest
Groups: Registered
Joined: 04/07/2015(UTC) Posts: 6,866 Was thanked: 981 time(s) in 809 post(s)
|
Originally Posted by: ndtma Therefore, I have no alternative but leave it to the developers to decide. Wait and see what Grand Doctors have to say. Frechet PDF is another one that Simpson rejects. In the attached, rescued in two ways. When compatible, dn_GearsBDF is hyperfast, known accurate. Thanks Collab for your contribution, most interesting. Cheers ... jean Integrate Frechet.sm (22kb) downloaded 16 time(s).
|
|
|
|
Rank: Guest
Groups: Registered
Joined: 04/07/2015(UTC) Posts: 6,866 Was thanked: 981 time(s) in 809 post(s)
|
Originally Posted by: Jean Giraud When compatible, dn_GearsBDF is hyperfast, known accurate. It carries parameters as well, following a fitting session. Integrate Frechet.sm (29kb) downloaded 16 time(s).
|
|
|
|
Rank: Advanced Member Groups: Registered
Joined: 05/06/2014(UTC) Posts: 348 Location: Colombo Was thanked: 125 time(s) in 82 post(s)
|
Observed same problems even after a second Clean re-installation of 7251. Consequently, I noticed that the Vectorize operator works correctly when eval() function is used to evaluate alpha and beta of the Gamma function. Otherwise, it gives incompatible results. Has anybody experienced this issue? Thank you Jean for the inspiration and encouragement. Thank you Alvaro. Any comments? New_Test_Gamma.sm (15kb) downloaded 17 time(s).Edited by user 15 November 2019 00:17:56(UTC)
| Reason: Not specified |
Look within!... The secret is inside you. Best Regards Eng. NDTM Amarasekera - Sri Lanka |
|
|
|
Rank: Advanced Member Groups: Registered
Joined: 28/08/2014(UTC) Posts: 1,356 Was thanked: 815 time(s) in 516 post(s)
|
Originally Posted by: ndtma Any comments?
New_Test_Gamma.sm (12kb) downloaded 12 time(s).Hi Nugegodage. I slightly modify your file, putting eval only where Mean appear. What I see rigth now, with your new file using eval, not before, is that there are not bug, and the "bad results" are because Mean can't be vectorized (or better say, isn't a good idea vectorize them), like any other function that take vectors or matrices as arguments. Edited by user 15 November 2019 01:41:51(UTC)
| Reason: Upload the smath file.
|
|
|
|
Rank: Guest
Groups: Registered
Joined: 04/07/2015(UTC) Posts: 6,866 Was thanked: 981 time(s) in 809 post(s)
|
Originally Posted by: ndtma Otherwise, it gives incompatible results. Not clear what's incompatible in the yellow/red brace.
|
|
|
|
Rank: Advanced Member Groups: Registered
Joined: 05/06/2014(UTC) Posts: 348 Location: Colombo Was thanked: 125 time(s) in 82 post(s)
|
Originally Posted by: ndtma Observed same problems even after a second Clean re-installation of 7251. Gamma CDF function error revisited. Following issues observed while trying to calculate SPI for a different set of data. 1. Gamma CDF function fails if 0 <'alpha' < 12. Even Razonar's method fails in such a situation. 3. According to the literature on calculation of SPI, the Gamma function is valid for all 'alpha' values > 0. 4. No such issues in Excel or Mathcad. 5. Attached example is only to demonstrate the issue. For the attention of authorities. Gamma_CDF_Error_with_Alpha less than 1_.sm (14kb) downloaded 10 time(s).Edited by user 12 May 2020 19:01:05(UTC)
| Reason: Not specified |
Look within!... The secret is inside you. Best Regards Eng. NDTM Amarasekera - Sri Lanka |
1 user thanked ndtma for this useful post.
|
|
|
Rank: Guest
Groups: Registered
Joined: 04/07/2015(UTC) Posts: 6,866 Was thanked: 981 time(s) in 809 post(s)
|
Originally Posted by: ndtma Gamma CDF function fails Your integration is ill posed ... "x_undefined" SMath native Gamma(x) 4 decimals and INT acc 50 have no impact. Try your own alpha/beta. Cheers ... Jean Page1 NDTMA.sm (14kb) downloaded 10 time(s).
|
1 user thanked Jean Giraud for this useful post.
|
|
|
Rank: Advanced Member Groups: Registered
Joined: 05/06/2014(UTC) Posts: 348 Location: Colombo Was thanked: 125 time(s) in 82 post(s)
|
Originally Posted by: Jean Giraud Try your own alpha/beta. Cheers ... Jean Thank you Jean. Your suggestion to introduce ε=10^{-15} as lower limit of integration solved my problem. But still the error persists if lower limit is zero. A beginner may be confused and/or discouraged in a similar situation. Gamma_CDF_Error_with_Alpha less than 1_SOLVED.sm (107kb) downloaded 16 time(s).Edited by user 13 May 2020 08:03:29(UTC)
| Reason: Not specified |
Look within!... The secret is inside you. Best Regards Eng. NDTM Amarasekera - Sri Lanka |
1 user thanked ndtma for this useful post.
|
|
|
Rank: Advanced Member Groups: Registered, Advanced Member Joined: 13/01/2012(UTC) Posts: 2,647 Location: Italy Was thanked: 1329 time(s) in 875 post(s)
|
I see the issue... when alpha < 1 and t = 0 smath has 1/(0^(1-alpha)) and the numerical integrator fails. I'm not sure about how ccould be fixed. Looking for improvements in the Gamma function... Lanczos.sm (70kb) downloaded 16 time(s). |
If you like my plugins consider to support SMath Studio buying a plan; to offer me a coffee: paypal.me/dcprojects |
2 users thanked Davide Carpi for this useful post.
|
on 14/05/2020(UTC), on 14/05/2020(UTC)
|
|
Rank: Guest
Groups: Registered
Joined: 04/07/2015(UTC) Posts: 6,866 Was thanked: 981 time(s) in 809 post(s)
|
Originally Posted by: Davide Carpi Looking for improvements in the Gamma function... Thanks Davide: sanity check [real/complex] vs Keisan/Casio
|
|
|
|
Rank: Guest
Groups: Registered
Joined: 04/07/2015(UTC) Posts: 6,866 Was thanked: 981 time(s) in 809 post(s)
|
All that is not as simple as the BigBang theory. If the first computed 'x' appears in data < 10^-15 the quick plot rejects, no complain ... didn't check X_Y plot. Thus: zero min value 10^-15. Just experimented on Bézier/Bernstein project. Cheers ... Jean
|
|
|
|
Rank: Advanced Member Groups: Registered
Joined: 05/06/2014(UTC) Posts: 348 Location: Colombo Was thanked: 125 time(s) in 82 post(s)
|
|
Look within!... The secret is inside you. Best Regards Eng. NDTM Amarasekera - Sri Lanka |
|
|
|
Rank: Guest
Groups: Registered
Joined: 04/07/2015(UTC) Posts: 6,866 Was thanked: 981 time(s) in 809 post(s)
|
Originally Posted by: ndtma A few more issues please.
Freak 7251 does not open ! You just have two values: α:=0.7352, β:=245.7456 That's enough to simulate/evaluate CDF. Cheers ... Jean CDF Gamma.sm (263kb) downloaded 15 time(s).
|
|
|
|
Rank: Advanced Member Groups: Registered
Joined: 05/06/2014(UTC) Posts: 348 Location: Colombo Was thanked: 125 time(s) in 82 post(s)
|
|
Look within!... The secret is inside you. Best Regards Eng. NDTM Amarasekera - Sri Lanka |
|
|
|
Rank: Guest
Groups: Registered
Joined: 04/07/2015(UTC) Posts: 6,866 Was thanked: 981 time(s) in 809 post(s)
|
Ordinary Simpson is inadequate [too steep PDF, too long X's] Romberg/Simpson algo style is just perfect. All done in gray attached. Cheers mon Ami from so far away ! CDF Gamma.sm (278kb) downloaded 13 time(s).
|
1 user thanked Jean Giraud for this useful post.
|
|
|
SMath Studio Forum
»
SMath Studio
»
Bugs & Problems
»
Different Results of Integration in 7219 & 7250 (Gamma Function)
Forum Jump
You cannot post new topics in this forum.
You cannot reply to topics in this forum.
You cannot delete your posts in this forum.
You cannot edit your posts in this forum.
You cannot create polls in this forum.
You cannot vote in polls in this forum.