How to fit a desired function form to a set of data in MATLAB?

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Homayoon 2015-11-7

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/253698-how-to-fit-a-desired-function-form-to-a-set-of-data-in-matlab

评论： Unai San Miguel 2018-10-16

Dear All,

I just installed the curve fitting toolbox and have been trying to get familiar with how it works. Although my question is specifically addressing a real problem, it could be a general question with any arbitrary choice of functional form. Assume I have a desired functional form such as :

f(x) = D*(1 - exp(-a*x))^2

And I have the following data set of:

 X  Y
-0.55  2.3386639
-0.5  -15.554354
-0.45  -31.500773
-0.4  -45.661997
-0.35  -58.182891
-0.3  -69.179367
-0.25  -78.728997
-0.2  -86.859606
-0.15  -93.532515
-0.1  -98.620664
-0.05  -101.89666
-103.08067
05  -102.01361
1  -98.879876
15  -94.172935
2  -88.344847
25  -81.576677
3  -73.851215
35  -65.088782
4  -55.255995
45  -44.56707
5  -33.717314
55  -23.724423
6  -15.329395
65  -8.7090074
7  -3.7387088
75  -0.25488612
8  1.9270662
85  3.0617316
9  3.4563882
95  3.405915
3.1230416
05  2.706436
1  2.3402943
15  2.018794
2  1.7367674
25  1.4896294
3  1.2733121
35  1.0842074
4  0.91911626
45  0.77520246
5  0.64995259

I want to know how I can fit the given functional form to the provided set of data and find the coefficients a and D. Even though I know how to use polyfit, and simple exponential fitting in MATLAB, when it comes to complicated functional forms, I stuck in mug!!

I hope by your helps and assistance I will be able to follow a general strategy to fit any arbitrary functional forms to a given set of data. Thank you so much.