Help with a fit

Hello! I have a set of data (x,y) which describes a function y=f(x). I would like to fit this function with a biexponential function made like this : f(x) = a*exp(-x/b)+c*exp(-x/d)+e and retrieve the values of a,b,c,d,e. Can you help me to do this? Thank you!

Answer 1

[Mischa Kim]

Aurc89, does this help?

 a = 1; b = 1; c = 1; d = 1; e = 1;
 x = (0:0.1:2)';
 y = a*exp(-x/b)+c*exp(-x/d)+e + 0.1*rand(length(x),1);
 f = fit(x,y,'exp2');
 plot(f,x,y)

The fitting coefficients are accessed, e.g., via

 f.a

[aurc89]

Sorry, maybe I couldn't explain well... I already have both x and y data which describes a generic function y(x), different from f(x). Then I want to fit my data y=y(x) with the function f(x) = a*exp(-x/b)+c*exp(-x/d)+e and retrieve a,b,c,d,e coefficients.

[Mischa Kim]

I got that, I just made up x- and y-values to show the feature in action. So essentially you only need the fit command. Coefficients are retrieved as outlined above, f.a, f.b, etc.

[aurc89]

Ok, but there is something I don't understand: I write this code, where x and y are my data I want to fit:

---------------------------------------------------

x=[1 2 3 4 5 6 7 8 9];

y=[0.4 0.6 0.8 0.9 0.92 0.94 0.96 0.98 0.989];

plot(x,y)

a=1; b=1; c=1; d=1; f=1;

x=x';

y = a*exp(-x/b)+c*exp(-x/d)+f+0.1*rand(length(x),1);

f = fit(x,y,'exp2');

figure

plot(f,x,y)

-----------------------------------------------------

This is the (x,y) plot (first plot)

while this is the fit (second plot)

which is not a fit of the first curve, i.e. of the raw data... what's wrong?

[Mischa Kim]

As mentioned above, if you have x- and y-values you only need the fit command:

 x = [1 2 3 4 5 6 7 8 9];
 y = [0.4 0.6 0.8 0.9 0.92 0.94 0.96 0.98 0.989];
 f = fit(x',y','exp2');
 plot(f,x,y)

[John D'Errico]

Note that in your examples, adding error created from rand is a terribly poor thing to do, as rand produced uniform deviates with a mean of 0.5. To generate random noise, use randn.

[aurc89]

Ah ok, so I don't need to specify the expression of the biexponential function... Thank you very much!

[Mischa Kim]

Aurc89: You're welcome.

John: I was not trying to generate random noise, thanks for the polite pointer, though.

[aurc89]

Sorry, the last question: this kind of command gives me the fit with the function f(x) = a*exp(b*x) + c*exp(d*x). Instead, I woud like to have a fit with this kind of function: f(x) = a*exp(b*x) + c*exp(d*x) + g. I need the constant term g also, because the time constants of the biexponential changes with g (because I am differently close to zero axis by changing 'g', so b and d are different). Is there an authomatic way to do this? Thank you very much in advance