Bestfit value doesn't match with the plotted value

Question

Vaswati Biswas 2021-2-23

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https://ww2.mathworks.cn/matlabcentral/answers/754039-bestfit-value-doesn-t-match-with-the-plotted-value

评论： dpb 2021-2-23

采纳的回答： dpb

I am using nlinfit to fit a gaussian square function in my data. My code is shown below:

initGuess=[max(g1),500,100]

g1 is my data that needs to be fitted.

gaussian_fn= @(q,x) (q(1)^2.*exp(-2.*((x-q(2)).^2)/q(3).^2));
[bestfit,resid]=nlinfit(x1,g1,gaussian_fn,initGuess);
scatter(x1,g1,'.');
hold on;
A2=gaussian_fn(bestfit,x1);
plot(x1,gaussian_fn(bestfit,x1),'r');

My code gives me the result shown above but the bestfit value shown in the workspace (maked with yellow highlighter ) is different from the value shown in the graph. In graph it shows me 0.9065 whereas bestfit value is 0.9522. Why it is different? why it is not giving me the samevalue shown as bestfit value?

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Answer 1

dpb 2021-2-23

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编辑：dpb 2021-2-23

Because you used

gaussian_fn= @(q,x) (q(1)^2.*exp(-2.*((x-q(2)).^2)/q(3).^2));

as your fitting function -- in which q(1) is squared --

>> q=[0.9522,559.2633,425];         % from your screenshot
>> q(1)^2
ans =
    0.9067
>> 

For comparison,

>> gaussian_fn(q,q(2))          % at peak center is max value
ans =
    0.9067
>> gaussian_fn(q,555)           % where you evaluated on plot
ans =
    0.9065
>> 

Use

gaussian_fn= @(q,x) (q(1).*exp(-2.*((x-q(2)).^2)/q(3).^2));

if you want the peak amplitude to be same as coefficient.

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Vaswati Biswas 2021-2-23

Your answer helped me a lot to understand the thing. Thank you so much. I am trying to fit the function with the laser intensity data. So I simply applied the concept that intensity is proportional to E^2 and thus I just squared the function. But I should have thought a bit before doing that. Thanks again!

dpb 2021-2-23

Glad to try to help...

I was going to comment that the Gaussian doesn't do a great job; your peak is flattened and broadened noticeably from a pure Gaussian altho it is pretty-good on a symmetry basis.

Some transformation or alternate distribution form would seem reasonable to use, agreed.

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