# Using Levenberg-Marquardt algorithm in the optimization

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RAPHAEL OWENS on 22 Apr 2020
Commented: Robert U on 5 May 2020
How can I use the optimization tool preferable to find a given value in an equation. This is the main equation I=i_ph-Is.*(exp(U./(m_1*Ut))-1) and I have a IU curve, but i want to get the value of 'c_01' in the sub equation Is=c_01*T^(3)*exp((-e_g*eV)/(k*T)).

Robert U on 23 Apr 2020
Hi RAPHAEL OWENS,
there are several solvers and methods available. One of the available functions in Matlab is lsqcurvefit(). Below there is a sketch of how to apply the function on your (supposedly) available data.
% known parameters
T
e_g
eV
k
i_ph
m_1
Ut
% underlying equation
Is = @(c_01) c_01 * T^3 * exp((-e_g*eV)/(k*T));
I = @(c_01,U) i_ph - Is(c0_1) .* (exp(U./(m_1*Ut))-1);
% start value(s) for optimization
c_01_guess = 1;
% choose algorithm, and possibly other options for optimization solver
opt = optimoptions('lsqcurvefit');
opt.Algorithm = 'levenberg-marquardt';
% run optimization
c_01_opt = lsqcurvefit(I,c_01_guess,U_measured,I_measured,[],[],opt);
Kind regards,
Robert
Robert U on 5 May 2020
Hi RAPHAEL OWENS,
I am not sure whether I understood your question correctly: Where do I acquire xdata and ydata on real data?
Usually you are measuring the U-I-curve by supplying U and measuring I. In that case the real data are "U" (xdata) and "I" (ydata). The grid does not matter since you are trying to fit the data to a model function. It just needs to be fine enough to cover the overall model function characteristics.
In a nutshell:
1. Supply U (xdata)
2. Measure I (ydata)
3. Give known parameters
4. Fit to model funcion.
Kind regards,
Robert

R2020a

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