How modelise (write a code ) of LSE model by matlab and how to do a fit of a experimental data with this model ?

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khouloud abiedh on 4 Jul 2018

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https://se.mathworks.com/matlabcentral/answers/408774-how-modelise-write-a-code-of-lse-model-by-matlab-and-how-to-do-a-fit-of-a-experimental-data-with

Commented: Walter Roberson on 7 Jul 2018

hello , i'm debutant in matlab and i need to do a fit of my experimental data by LSE model in matlab. the file below contain the article which describe this model. from the last comment i write the same code of the energetic position of a gaussian but i find a problem to do an exact fit of the data by matlab , also i need to do a fit of the LMH of the gaussian by this model in matlab . when i read the article i understand that it must resolve another equation numerically to find the LMH described in the LSE model. the file blow contain this equation, i use the same code which i find in the comment but i change the equation but it display an error. i need our help please help me and thank you in advance.

%%trouver x et tracer la position energetique
sigma = 13*10^-3;%eV
deltaE = -73e-3;%eV
E0 = 1.185;%eV
Ea = E0+75e-3;
tautr=0.027 ;
taur=250;
Kb = 8.617*10^-5;%eV/K
theta = 270; %K
alfa = 0.48e-3;%eV/K
T= 0:10:300;
X = zeros(size(T));
E2 = zeros(size(T));
E1= zeros(size(T));
a = zeros(size(T));
syms x
for i=1:numel(T)
      E1(i) = E0 -( alfa*T(i)^2)/(theta+T(i));
      X(i) = vpasolve(((sigma/(Kb*T(i)))^2 - x)*(taur/tautr)*exp(deltaE/(Kb*T(i)))-x*exp(x)==0,x);
      E2(i) = E0 -(alfa*T(i)^2)/(theta + T(i))-X(i)*Kb*T(i);
      a(i) = X(i)*Kb*T(i);    
  end
figure(1);plot(T,E1,'r.');
figure(2);plot(T,E2,'g')
hold on ;plot(T,E1,'r')
figure(3);plot(T,X,'k.','Markersize',5)
figure(4);plot(T,a,'k');
%%to find LMH i must resolve n(E0-X(T)*Kb*T,T)/2=n(E,T)

trouver n(E0-X(T)*Kb*T,T)/2

n(E,T)= exp(-(E(i)-E0)^2/(2*sigma^2)/(exp((E(i)-Ea)/(Kb*T(i)))+(tautr/taur)))

E = zeros(size(T));
n = zeros(size(T));
n1=zeros(size(T));
for i=1:numel(T)
     E(i)= E0-a(i);
      n(i)=exp(-(E(i)-E0).^2/(2*sigma^2))/(exp((E(i)-Ea)/(Kb*T(i)))+(tautr/taur));
     n1(i)=n(i)/2;
  end
figure (5)
plot(E1,n1)
X1=zeros(size(T));
   syms x1
for i=1:numel(T)
      X1(i) = vpasolve(exp(-(E(i)-E0)^2/(2*sigma^2))/(exp((E(i)-Ea)/(Kb*T(i)))+(tautr/taur))-n1(i)==0,x1);
end
figure(6);plot(T,X1,'r.');