exp(-b/x) fit, inf problem when fitting

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I am trying to fit some data with the model: exp(-b/x); When x goes to zero, y should go to zero as well since anything power negative infinity is zero. However Matlab sees the infinity and terminates everything. Here is my code:
vv=data(:,1);
ii=data(:,2);
g = fittype('exp(-b/x)');
f0 = fit(vv,ii,g);
xx = linspace(-1,1);
plot(vv,ii,'o',xx,f0(xx),'r-');
grid('on')
  5 Comments
Basil Eldeeb
Basil Eldeeb on 26 Feb 2021
supposedly when the exponent is quite small it will behave linearly to a first order. The model is more complex, actually, I am just facing a problem with the exp(-b/x) term. I want matlab to evaluate exp(-Inf) without giving error. The other answer shows promise. However it gave an error, you can see it in my response
Mathieu NOE
Mathieu NOE on 26 Feb 2021
not sure it's really a good model...
data = readmatrix('data.txt');
x = data(:,1);
y = data(:,2);
% exponential fit method
% model : y = exp(-b/x)
f = @(b,x) exp(b./x);
obj_fun = @(params) norm(f(params(1), x)-y);
sol = fminsearch(obj_fun, -0.1);
b_sol = sol(1)
y_fit = f(b_sol, x);
figure
plot(x,y,'r',x,y_fit,'-.k');
legend('data','exp fit');

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Accepted Answer

Matt J
Matt J on 25 Feb 2021
Edited: Matt J on 25 Feb 2021
When x goes to zero, y should go to zero as well since anything power negative infinity is zero.
Only if b>=0.
g = fittype('exp(-b/x)', 'options', fitoptions('Lower',0) );
  5 Comments
Matt J
Matt J on 1 Mar 2021
Edited: Matt J on 1 Mar 2021
You should divide the data into two sets and fit each one separately, e.g.,
pos=vv>0; neg=~pos;
fpos = fit(vv(pos),ii(pos),gpos,options);
fneg = fit(vv(neg),ii(neg),gneg,options);
Basil Eldeeb
Basil Eldeeb on 2 Mar 2021
I appreciate it, thank you for the help!.

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