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) downloaded 1328 time(s).

splines_integral_data1.sm (31.52 KiB) downloaded 1301 time(s).

Hello

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



Javier_fit_CBG.sm (37.14 KiB) downloaded 1289 time(s).


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) downloaded 1333 time(s).

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) downloaded 1333 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.



It is always important to draw the curve

Javier fit.sm (24.31 KiB) downloaded 1259 time(s).

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) downloaded 1320 time(s).
LevenbergMarquardt_solver.pdf (233.35 KiB) downloaded 759 time(s).

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) downloaded 1328 time(s).

splines_integral_data1.sm (31.52 KiB) downloaded 1301 time(s).

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



splines_integral_data.sm (85.66 KiB) downloaded 1305 time(s).

splines_integral_data.pdf (180.67 KiB) downloaded 683 time(s).

Best regards.
Alvaro.

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

Inst_Frechet GAUSSIAN.sm (92.39 KiB) downloaded 1371 time(s).