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

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Basil Eldeeb
Basil Eldeeb 2021-2-25
评论： Basil Eldeeb 2021-3-2
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')
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Basil Eldeeb
Basil Eldeeb 2021-2-26
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 2021-2-26
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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Matt J
Matt J 2021-2-25
编辑：Matt J 2021-2-25
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) );
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Matt J
Matt J 2021-3-1
编辑：Matt J 2021-3-1
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 2021-3-2
I appreciate it, thank you for the help!.

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