Best tool to calculate the parameters of a custom equation fit

Question

Birsen Ayaz-Maierhafer 2022-7-7

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编辑： Matt J 2022-7-14

Hello,

There are quite a bit merhods/tools to fit an custom equation to the experimantal data. I am struggling to use the right one (I tried many of them and eventually decided to ask to an expert). My custom equation is (a+b/x^2)*exp(-x/c). What is the best way to find a,b and c if you really don't know what the starting parameter values are.

Thank you

Birsen

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Answer 1

Matt J 2022-7-7

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编辑：Matt J 2022-7-7

在 MATLAB Online 中打开

For your particular equation, I'd rcommend,

[a,b,c]=deal(3,2,1)

a = 3

b = 2

c = 1

x=linspace(1,2,30); %fake data

y=a+b./x.^2.*exp(-x/c);

funlist={1,@(c,x) exp(-x/c)./x.^2};

[c,ab]=fminspleas(funlist,2, x,y);

a=ab(1), b=ab(2),c %fitted values

a = 3

b = 2

c = 1.0000

yfit=a+b./x.^2.*exp(-x/c);

plot(x,y,'x',x,yfit); legend('Sample Data','Fit')

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Birsen Ayaz-Maierhafer 2022-7-11

Hi Matt,

Thank you, that seems very promising. My equation indeed is (I posted wrong but I corrected it immediatly after that)

y=(a+(b/x^2))*exp(-x/c);

I am trying to understand what you did with funlist below. Would it be the same with the updated equation? You are passing only one parameter c, not the others.

funlist={1,@(c,x) exp(-x/c)./x.^2 };

In the following you are passing funlist and the number "2". Is that c and ab?

[c,ab]=fminspleas(funlist,2, x,y);

Thank you

Birsen

Matt J 2022-7-11

编辑：Matt J 2022-7-14

Would it be the same with the updated equation?

I don't see any change in the equation since I posted. But yes, the fminspleas algorithm only iterates over c (and only requires an initial guess for c) in your case, because that is the only parameter that the model equation has a nonlinear dependence. on.

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Answer 2

Kevin Holly 2022-7-7

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Have you tried using the Curve Fitting Toolbox? You can fit your custom equation to a set of data and it will provide you with the coefficients that provide the best fit along with statistical metrics and a plot.

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Birsen Ayaz-Maierhafer 2022-7-7

Hi Kevin, thank you. i tried that tool. It really did not work.The curvefit tool box plot does not come with log scale and you really can't see if the fit is good or not. It gave me answers but when I used the parameters and plot outside of curve fitting tool box the data it was way out of fitting.

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