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 (30,28 KiB) scaricato 1673 volta(e).

splines_integral_data1.sm (31,52 KiB) scaricato 1649 volta(e).

Hello

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



Javier_fit_CBG.sm (37,14 KiB) scaricato 1639 volta(e).


Best Regards

Carlos

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

Thanks in advance,

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 (27,68 KiB) scaricato 1687 volta(e).

Wrote

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 (27,68 KiB) scaricato 1687 volta(e).

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.



It is always important to draw the curve

Javier fit.sm (24,31 KiB) scaricato 1625 volta(e).

Best Regards

Carlos

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 (32,85 KiB) scaricato 1667 volta(e).
LevenbergMarquardt_solver.pdf (233,35 KiB) scaricato 1004 volta(e).

Best regards.
Alvaro.

Wrote

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 (30,28 KiB) scaricato 1673 volta(e).

splines_integral_data1.sm (31,52 KiB) scaricato 1649 volta(e).

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



splines_integral_data.sm (85,66 KiB) scaricato 1666 volta(e).

splines_integral_data.pdf (180,67 KiB) scaricato 938 volta(e).

Best regards.
Alvaro.

.. refreshed/augmented.
Cheers ... Jean.

Inst_Frechet GAUSSIAN.sm (92,39 KiB) scaricato 1724 volta(e).