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Offline Javier Ochoa  
#1 Posted : 16 May 2023 02:34:26(UTC)
Javier Ochoa


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Hi,

These two examples solve the problem calculations for the total biomass formed in a batch bioreactor and the pattern flow of a reactor with a pulse of some tracer. The splines method and the Simpson integration formula found in the forum let me solve both problems.


Kind regards,


splines_integral_data.sm (31kb) downloaded 27 time(s).

splines_integral_data1.sm (32kb) downloaded 20 time(s).
thanks 1 user thanked Javier Ochoa for this useful post.
on 26/05/2023(UTC)

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Offline CBG  
#2 Posted : 22 May 2023 21:02:07(UTC)
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Hello

Fitting Javier's data to the Gauss function by the Levenberg-Marquardt Algorithm

Fit_Javier_LMA.png

Javier_fit_CBG.sm (38kb) downloaded 19 time(s).


Best Regards

Carlos
thanks 1 user thanked CBG for this useful post.
on 22/05/2023(UTC)
Offline Javier Ochoa  
#3 Posted : 22 May 2023 21:56:44(UTC)
Javier Ochoa


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Hi Jean and Carlos,
These worksheets help me to better understand the problem which I tried to solve.

Thanks in advance,

Offline Javier Ochoa  
#4 Posted : 23 May 2023 22:29:20(UTC)
Javier Ochoa


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Hi Jean and Carlos,

I am curious about your thoughts for the result I found using the al_nlqsolve routine from ALGLIB.

May be I was lucky to find a similar solution.

Kind regards,


LevenbergMarquardt_solver.sm (28kb) downloaded 15 time(s).
Offline CBG  
#5 Posted : 24 May 2023 06:30:27(UTC)
CBG


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Originally Posted by: Javier Ochoa Go to Quoted Post
Hi Jean and Carlos,

I am curious about your thoughts for the result I found using the al_nlqsolve routine from ALGLIB.

May be I was lucky to find a similar solution.

Kind regards,


LevenbergMarquardt_solver.sm (28kb) downloaded 15 time(s).


Hi Javier
As you can see in the graph, the green line is that of your solution,
and it is not correct, since it does not fit the data.

javier_fit2.png

It is always important to draw the curve

Javier fit.sm (25kb) downloaded 9 time(s).

Best Regards

Carlos

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on 24/05/2023(UTC)
Offline Razonar  
#6 Posted : 24 May 2023 09:41:54(UTC)
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Hola Javier. Your Levenberg Marquardt algorithm works pretty well, but you choose a bad guess starting point, with a very high tolerance. BTW, I made some few modifications and use also other target function.

LevenbergMarquardt_solver.sm (33kb) downloaded 15 time(s).
LevenbergMarquardt_solver.pdf (234kb) downloaded 12 time(s).

Best regards.
Alvaro.
thanks 2 users thanked Razonar for this useful post.
on 24/05/2023(UTC),  on 24/05/2023(UTC)
Offline Razonar  
#7 Posted : 24 May 2023 21:52:25(UTC)
Razonar


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Originally Posted by: Javier Ochoa Go to Quoted Post
Hi,

These two examples solve the problem calculations for the total biomass formed in a batch bioreactor and the pattern flow of a reactor with a pulse of some tracer. The splines method and the Simpson integration formula found in the forum let me solve both problems.


Kind regards,


splines_integral_data.sm (31kb) downloaded 27 time(s).

splines_integral_data1.sm (32kb) downloaded 20 time(s).


Hola Javier. You can also use this code for integrate and differentiate tabulated data.

Click to enlarge

splines_integral_data.sm (86kb) downloaded 14 time(s).

splines_integral_data.pdf (181kb) downloaded 7 time(s).

Best regards.
Alvaro.

Edited by user 24 May 2023 21:55:06(UTC)  | Reason: Not specified

thanks 1 user thanked Razonar for this useful post.
on 29/05/2023(UTC)
Offline Jean Giraud  
#8 Posted : 25 May 2023 19:16:26(UTC)
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.. refreshed/augmented.
Cheers ... Jean.

Inst_Frechet GAUSSIAN.sm (93kb) downloaded 9 time(s).
thanks 1 user thanked Jean Giraud for this useful post.
on 29/05/2023(UTC)
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