How can I create a modified curve fitting function?

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Christian 2017-3-19

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评论： Sung YunSing 2021-8-18

Hi,

i want to fit a recovery curve of my experiment to the following expression:

F(t)=k*exp(-D/2t)[I0(D/2t)+I1(D/2t)]

where I0 and I1 are the modified Bessel fundtions of the first kind of zero and first order. I want to determine D and k.

Is there any simple solution for this problem?

Thanks for helping

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Christian 2017-3-19

Okay, thank you. I'll try that.

Star Strider 2017-3-19

My pleasure.

If you have problems, post your code. We can help.

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回答（2 个）

John D'Errico 2017-3-19

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编辑：John D'Errico 2017-3-19

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Yes. Of course it is possible to do this. What toolbox do you have available? It sounds like the curve fitting TB is what you have. READ THE HELP. Look at the examples provided.

You said modified first kind Bessel, so you would use besseli. I'll get you started:

I0 = @(z) besseli(0,z);
I1 = @(z) besseli(1,z);
F = @(P,t) P(1)*exp(-P(2)/2*t).*(I0(P(2)/2*t)+I1(P(2)/2*t));

The curve fitting toolbox should be able to use this, as well as nlinfit and lsqcurvefit.

Note that I made the assumption that D/2t should be interpreted as (D/2)*t, NOT as D/(2*t).

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Christian 2017-3-20

I think the fitting function is okay. Maybe the results are so confusing because the upper and lower limits of the Parameters are not defined correctly?