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Offline Jean Giraud  
#21 Posted : 05 October 2020 03:30:34(UTC)
Jean Giraud


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Originally Posted by: hanskl Go to Quoted Post
The plots of N.γ(0.9,atan(x)) and N.γ(0.95,atan(x)) has an odd shape when they approach x=1. It turns out there are some complex solutions in this area.

Is there anything to be done about this, to make the graph closer resemble the diagram?

This is a good observation, I did catch it but didn't mention.
Yes the system generates some complex values, can't track it back
in the generating algo. Will have another look.
The atan(,) from numerical libraries does not generate complex.
That's why you had no plot initially, complex blinds the Quick plot.
Cheers ... Jean
Offline hanskl  
#22 Posted : 05 October 2020 09:09:48(UTC)
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Originally Posted by: Jean Giraud Go to Quoted Post

This is a good observation, I did catch it but didn't mention.
Yes the system generates some complex values, can't track it back
in the generating algo. Will have another look.
The atan(,) from numerical libraries does not generate complex.
That's why you had no plot initially, complex blinds the Quick plot.
Cheers ... Jean


Another interesting observation is that j.lim in the even Numbers generates values in the areas mentiod that are far too big, while odd j.lims generate conservatively small values.

I really appreciate all the help I can get with this.

Cheers.
Offline hanskl  
#23 Posted : 05 October 2020 10:16:25(UTC)
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Originally Posted by: Jean Giraud Go to Quoted Post
Is there anything to be done about this, to make the graph closer resemble the diagram?

This is a good observation, I did catch it but didn't mention.
Yes the system generates some complex values, can't track it back
in the generating algo. Will have another look.
The atan(,) from numerical libraries does not generate complex.
That's why you had no plot initially, complex blinds the Quick plot.
Cheers ... Jean


Take a look at this sheet, where every factor of the equation has been ploted separately.

It seems the complex numbers starts with X.c before the iterations start, due to c going negative.

EDIT: It seems in order to produce a plot similar to that of the diagram, dc/dx can not be allowed to be negative. How would I be able to manipulate this?

Cheers.

problem_complex_separated_5.sm (320kb) downloaded 3 time(s).

c derivate.PNG

Edited by user 05 October 2020 15:05:10(UTC)  | Reason: New attachment

Offline Jean Giraud  
#24 Posted : 05 October 2020 18:55:36(UTC)
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From your last report, you are right and wrong.
In many more projects, residuals complex have been observed
where the maths do not generate complex. The numerical Smath
engine is in cause. In other applications Smath 32 bits is too granular.
Your project is a two time constants XFR [Transfer Function],
associated wrt the composite process gain Kp. That is much different
than XFR in Process Control Techniques. Maybe the model is ill posed.
In the mean time, by pushing j 1..99 we get a much better recovery.
Cheers ... Jean

Project Hanski Soil Drainage.sm (517kb) downloaded 6 time(s).
Offline Jean Giraud  
#25 Posted : 05 October 2020 23:12:00(UTC)
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... this version is suggestive of completing the project.

Project Hanski Soil Drainage.sm (518kb) downloaded 3 time(s).
Offline hanskl  
#26 Posted : 06 October 2020 02:01:07(UTC)
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Originally Posted by: Jean Giraud Go to Quoted Post
... this version is suggestive of completing the project.

Project Hanski Soil Drainage.sm (518kb) downloaded 3 time(s).


JMG - great tip to put eval() on all the lines inside the function, sped up the computation considerably, far beyond just right clicking and choosing numeric evaluation.

I think unless someone on the forum can find a way to differentiate c, I will stop pursuing this further.

I have attached a new sheet with my final findings of this function. In my furter application of N.gamma i will have the function output only real values of the solution, and use deltaX = 0,0001 and j.lim = 99.

Thanks to everyone for the help.

Cheers.

problem_complex_separated_6.sm (281kb) downloaded 7 time(s).

problem_complex_separated_6.PNG
Offline Jean Giraud  
#27 Posted : 06 October 2020 20:56:19(UTC)
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This project is nicely concluded.
j.lim 39 is as good as j.lim 99 ... much faster.
Should be same in your machine and SS version.
Cheers, thanks ... Jean.

Project Hanski Soil Drainage Ng.sm (296kb) downloaded 9 time(s).
Offline hanskl  
#28 Posted : 25 October 2020 01:58:07(UTC)
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Hi guys,

Back at it again, I am now trying to plot these functions in Zedgraph with a log scale.

I've found that "if" within the function is not supported by Zedgraph ("x is not defined"Wink and "cases" breaks the iteration process.

Is there any way to make zedgraph plot my function?
Offline Jean Giraud  
#29 Posted : 25 October 2020 21:03:09(UTC)
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Originally Posted by: hanskl Go to Quoted Post
Is there any way to make zedgraph plot my function?

log scale 'y' deteriorates the reality. The project is in two different plots.
Easy to add labels for the part of large deviations, like this demo.
IMHO, much better for publishing the reality. You can label part two as well.
Cheers ... Jean

HanskiLabels.PNG

Project Hanski Soil Drainage Ng.sm (314kb) downloaded 3 time(s).
thanks 1 user thanked Jean Giraud for this useful post.
on 25/10/2020(UTC)
Offline hanskl  
#30 Posted : 25 October 2020 21:58:57(UTC)
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Originally Posted by: Jean Giraud Go to Quoted Post
Originally Posted by: hanskl Go to Quoted Post
Is there any way to make zedgraph plot my function?

log scale 'y' deteriorates the reality. The project is in two different plots.
Easy to add labels for the part of large deviations, like this demo.
IMHO, much better for publishing the reality. You can label part two as well.
Cheers ... Jean



Thanks Jean for your reply, but it doesnt quite solve my problem.

Attached is a sheet showing what I want to achieve, and explaining the troubles I have trying to do that.

Best regards,

problem_log.sm (692kb) downloaded 3 time(s).
Offline Jean Giraud  
#31 Posted : 26 October 2020 03:40:07(UTC)
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X_Y plots reject conditional. Try to remove them in the program.
You can log scale the calculated ordinates, example attached.
Cheers ... Jean

Project Hanski Soil Drainage Ng.sm (322kb) downloaded 0 time(s).
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