Wrote

However, AlgLib Solver works faster and depends little on X0 matrix.

Thanks Ber7 for recasting this project, thanks to all contributors.
Algib solver gives a new dimension to Smath. I have no immediate
applications wrt my own discipline [Process Control], but that
kind of solver may find more applications.
The attached document is in my own Smath style for uniformity,
i.e: 'x' is uniquely reserved for the independent variable rather
than often used as parameter.

Jean

Solve al_nleqsolve Ber7_Nicolas.sm (38 KiB) downloaded 47 time(s).

Thanks to Jean, thanks to Uni, AlgLib is really a wonderful solver!

Wrote

Thanks to Jean, thanks to Uni, AlgLib is really a wonderful solver!

Yes Sir ! We didn't have a hint of such a solver Mathcad/Mathsoft.
Just need more applications from "Russia for ever" !

Cheers all.

Hello.

Wrote

However, AlgLib Solver works faster and depends little on X0 matrix.See # 29
https://en.smath.info/forum/yaf_topics32_Extensions.aspx
Overdetermined.sm (15 KiB) downloaded 49 time(s).

I'm sorry, but again I have problems using this type of algorithm - see the attached image.

Wrote

I'm sorry, but again I have problems using this type of algorithm - see the attached image.

Just open and run my latest work sheet, posted today.
If you run 6671, your al_nleqsolve(,,,) needs be updated as well.
"Out of index..." => too many equalities wrt parameters.

Jean

Hello.

There are no updates for my 6671. For my SMath directory, I still have errors.

Nicolas

Wrote

There are no updates for my 6671. For my SMath directory, I still have errors.

My Smath is as well in C:\Program
But all the work sheets are in C:\Smath 6179
.........
Where you have all your Smath work sheets, add a New Folder,
name it "SmathFile" [typical or else]
address CWD:=CurrentDirectory(......)

Hello.

What do you call SMath Worksheet? I searched for these two words across my computer and I have no results. Is there a folder where you store all SMath files? I do not have a single folder for this purpose. I store sm files for each domain and I therefore have a whole library of sm files stored in folders with different names. That's why I do not store these folders in the C partition of the system, but in a D partition structured by domains of interest.

... Is OK. I have entered the address of one of these folders, where I stored the examples from Ber7. I see it works. Perhaps that address should be the folder where the file is stored.

Nicolas.

Hello.

I think I understood the maneuver explained by Jean Giraud, but I still can not get a goal, in the case of the file attached by Ber7 to post # 120. Probably the link is more subtle and I can not achieve it.

Nicolas.

Wrote

What do you call SMath Worksheet? I searched for these two words across my computer and I have no results. Is there a folder where you store all SMath files? I do not have a single folder for this purpose. I store sm files for each domain and I therefore have a whole library of sm files stored in folders with different names. That's why I do not store these folders in the C partition of the system, but in a D partition structured by domains of interest.

=======================
When you click on the Samth icon from the task bar, what does it do ?
It opens a work sheet of the number pages needed to complete the project.
All my work sheets are stored in a single folder C:\Smath 6179 [about 1600]
A global single file where to store/transit some reference modules, transit
some data to avoid re-computation, store images ...etc is all what I need
and this file is in C:\SmathFile ... from CWD:= CurrentDirectory("C:\SmathFile")
then, I address whatever can be filed for purpose.

My C:\Smath6179 contains 1554 work sheets, all categorized mnemonic,
easy to retrieve, for instance: Solve is a large category [101 work sheets].
Much easier to glance top to bottom through 1554 than having about 50 different
folders according to projects categories.
In < 2 sec, I retrieve any of my specific project [Instrumentation],
just the time to scan down 101 items.

BTW, you don't have to spool to file 'sol' ... just = but wise to
copy/paste in β:= as an independent/isolate vector.

Cheers

I believe that the function:





does not exactly represent the values of the Triode ECC83 graph (Tesla Graph).

Here is a comparison:



Levenberg_Marquardt_Code_CBG_Jean_Tesla_Test.sm (1 MiB) downloaded 42 time(s).

Best Regards


Carlos

Quite right, Carlos.

The proposed function fails to fit the data sets.
Tentatively, al_nleqsolve and Levenberg-Marquardt do find a set of parameters.
As applied to fit all curves, then do not fit .
If there is an eventual compatibility, the problem is to initialize.
I tried quite a few with the most robust al_nleqsolve, not to avail.

Of all the models that were tried, I have conserved the 2 constants + 2 parameters
Genfit Minimize Tesla(5) Auto_Iterate
No matter how much maths one can invent, it is not true an invented 6 parameters
will fit 8 data sets each having his own set of 2 parameters. If such miraculous
maths would exist, I bet it would have been explored/exploited in Mathcad/Mathsoft.

Jean

Solve al_nleqsolve Ber7_Nicolas Copy.sm (55 KiB) downloaded 40 time(s).
Genfit Minimize Tesla(5) Auto_Iterate.sm (238 KiB) downloaded 42 time(s).
Page2 Tesla.sm (178 KiB) downloaded 32 time(s).

Hello.

You're right Carlos. In fact, this was the first challenge, which was actually missed. Jean Giraud is not right. MatCAD has solved the problem, so mathematical tools exist. Proof is the chart I brought in the first post. Perhaps they will be in SMath in a while too. Until then, I accepted the second challenge, that of studying in detail the current mathematical tools that SMath puts at my disposal. From this point of view, it was a very useful experience. I thank you all for your help.

Nicolas.

Wrote

Jean Giraud is not right. MatCAD has solved the problem, so mathematical tools exist.

OK, Nicolas ... then plot the fitted family of results over the data sets.
Or, attach enough information so that I can spare some times in Mathcad 11.
This is paramount wrt Smath designers, especially from so much efforts.

Cheers Nicolas ... Jean

Wrote

OK, Nicolas ... then plot the fitted family of results over the data sets.
Or, attach enough information so that I can spare some times in Mathcad 11.
This is paramount wrt Smath designers, especially from so much efforts.

1. Checked the Mathcad 7 param model is same in Smath
2. if so => run that 7 parameters in attached document.
3. if it solves => attach in forum so it can be tried

Jean

Solve al_nleqsolve Ber7_Nicolas [6671].sm (21 KiB) downloaded 38 time(s).

The values of beta4 and beta5 strongly depend on vector of guesses

Solve al_nleqsolve Ber7_Nicolas 1.sm (18 KiB) downloaded 41 time(s).

Wrote

The values of beta4 and beta5strongly depend on vector of guesses

The reformated model is now robust.
The native beta's fit exceptionally well the first data set !
Slightly modified for the remaining data sets.
The Mathcad coefficients are given as well for comparing.
Puzzling why the same coefficients produced crappy Mathcad plots ?
All in all, a very interesting project exploiting exp(,) reflexive.
Smath solves decently this 7 parameters project.
Thanks Collabs contributors.

Jean

Solve al_nleqsolve Ber7_Nicolas [6179] READ 1rst.sm (73 KiB) downloaded 41 time(s).

This Smath document reconciliates this entire thread [137].
At this point, one may want to redefine the equalities for where a more accurate fit
may reveal so wrt the region of interest of the family. This kind of exercise looks
superfluous [IMHO], considering the data sets represent poorly a family of information
which family of information deviates from a real family of functions. All in all, the
productive recovering model depends upon only one variable => the grid voltage 'b'.

Same result from Levenberg-Marquardt but awfully slow !
The model may be overkilled, RemToDo from refitted data sets.

Comments/suggestions will be appreciated ... cheers, Jean

Solve al_nleqsolve TESLA [6 x 6].sm (7 KiB) downloaded 42 time(s).
Solve al_nleqsolve TESLA [7 x 7].sm (8 KiB) downloaded 37 time(s).
Solve al_nleqsolve Ber7_Nicolas [6179] RECONCILIATION Copy.sm (80 KiB) downloaded 39 time(s).