Wrote

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

Wrote

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.

Wrote

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 (319,66 KiB) scaricato 1159 volta(e).

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 (516,23 KiB) scaricato 1163 volta(e).

... this version is suggestive of completing the project.

Project Hanski Soil Drainage.sm (517,16 KiB) scaricato 1233 volta(e).

Wrote

... this version is suggestive of completing the project.

Project Hanski Soil Drainage.sm (517,16 KiB) scaricato 1233 volta(e).

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 (280,93 KiB) scaricato 1106 volta(e).

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 (295,27 KiB) scaricato 1147 volta(e).

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") and "cases" breaks the iteration process.

Is there any way to make zedgraph plot my function?

Wrote

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



Project Hanski Soil Drainage Ng.sm (313,4 KiB) scaricato 1127 volta(e).

Wrote

Wrote

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 (691,53 KiB) scaricato 1184 volta(e).

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 (321,38 KiB) scaricato 1137 volta(e).

Wrote

X_Y plots reject conditional. Try to remove them in the program.
You can log scale the calculated ordinates, example attached.
Cheers ... Jean

But the program needs the conditional due to the iteration process I think.

I will have a look into Maxima to see if that gives me what I want.

On the other hand, I have found another method to calculate Ngamma. I have tried to write a similar program to this method, but when I plot this method it differs vastly from the first method/original diagram. Can someone please have a look and check if the setup for method 2 is correct?

Thanks.

Method 1 vs Method 2.sm (459,04 KiB) scaricato 1170 volta(e).

Please, visit what I just posted under "Uni" ZedGraph.

Project Hanski Soil Drainage Ng User.sm (313 KiB) scaricato 1151 volta(e).

Wrote

Please, visit what I just posted under "Uni" ZedGraph.

Thanks Jean, and everyone else who has spent their time trying to figure this out with me.

I think I have come as far as I can on this project, and a lot of new cool smath stuff has been learned.

What an amazing program and community!

Cheers.

Wrote

What an amazing program and community!

Please visit the just posted latest brew in ZedGraph thread.
For our education: what are r, ρ, Nγ ???
'r' percolation factor ?
'ρ' the unary radius ?
'Nγ' some spread ?
No such thing as soil drainage function in the web !
Thanks, cheers ... Jean

Wrote

Please visit the just posted latest brew in ZedGraph thread.
For our education: what are r, ρ, Nγ ???
'r' percolation factor ?
'ρ' the unary radius ?
'Nγ' some spread ?
No such thing as soil drainage function in the web !
Thanks, cheers ... Jean

Nγ is a factor used in the following equation to calculate soil bearing capacity.

σ.v + a = N.q*(p' + a) + 0,5*N.γ*γ'*B.0

r = is roughness of the foundation surface, and ρ = internal friction angle of the soil.

https://www.geostru.eu/blog/2016/06/20/bearing-capacity-for-shallow-foundations/

Cheers.

Thanks for the details. As is, the project is complete.
You can create an interpolated blue track trace, read Nγ on the plot.
I'm not completely happy of the Y log, however immaterial for application.
Thanks Hanski for enriching the Smath Community
Jean ... last brew attached.

Project Hanski Soil Drainage Ng ZedGraph.sm (399,09 KiB) scaricato 1223 volta(e).

Wrote

Thanks for the details. As is, the project is complete.
You can create an interpolated blue track trace, read Nγ on the plot.
I'm not completely happy of the Y log, however immaterial for application.
Thanks Hanski for enriching the Smath Community
Jean ... last brew attached.

The whole business of ploting the function is just for documentation purposes, to make sure the function is correct (compared to the referenced diagrams).

In practical application, only the function will be used.

I think the whole problems is ill posed, as you suggested earlier, as evidenced by the complex results. I have made a modification to the function to combat this in my final version of this function.

Attached is the document I will be storing on my server for future reference/use on projects.

Best regards,

project_complete.sm (943,93 KiB) scaricato 1153 volta(e).

Wrote

I have made a modification to the function to combat this in my final version of this function.

I will visit later tomorrow.
In the mean time, if you like this ZedGraph plot ... attached.
Cheers ... Jean



Project Hanski Soil Drainage Ng ZedGraph.sm (519,73 KiB) scaricato 1258 volta(e).

Wrote

Attached is the document I will be storing on my server for future reference/use on projects.

Your latest "complete" does not calculate same values ?
Much shorter in real values. For the remaining of the project, all red SS 6179.
Can't even copy/paste algo in same document, neither export.