curve fitting with fminsearch

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Hello all,
I'm trying to learn MATLAB and take a course for that, and i have a homework that i can't solve. I have experimental datas for x and y variables(total 11 each) and the question asks me to fit the datas by using 'fminsearch' .
Can anyone help me how can i find the best curve and write a proper code? Thank you
x=[3, 5, 7, 10, 13, 17, 20, 23, 25, 29, 31];
y=[1.1 , 2.0 , 3.7 , 9.0 , 22.2 , 73.8 , 181.5,446.5 , 813.6 , 2701.3 , 4922.1];
  2 Comments
Ameer Hamza
Ameer Hamza on 18 May 2020
Edited: Ameer Hamza on 18 May 2020
Can you show what you have already tried? Even if you don't have a code, can you write down your understanding about solving this problem?
Burak Akayoglu
Burak Akayoglu on 18 May 2020
Well, i've tried to write those, but i know it's false.
In the question, x vs y datas are going to be fitted a curve (i think it's gonna be y= a*exp(bx) ) by using fminsearch, and find the parameters. I did it by using "cftool" but i couldnt do it with fminsearch. It would be great if you tell me how can i do that? thanks
f=@(x) a*exp(b*x);
x0=[2,1];
options = optimset('PlotFcns',@optimplotfval, 'Display','iter');
x = fminsearch(f,,x0,options)

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Accepted Answer

Ameer Hamza
Ameer Hamza on 18 May 2020
Study this example
x = [3, 5, 7, 10, 13, 17, 20, 23, 25, 29, 31];
y = [1.1 , 2.0 , 3.7 , 9.0 , 22.2 , 73.8 , 181.5,446.5 , 813.6 , 2701.3 , 4922.1];
f = @(a,b,x) a*exp(b*x);
obj_fun = @(params) norm(f(params(1), params(2), x)-y);
sol = fminsearch(obj_fun, rand(1,2));
a_sol = sol(1);
b_sol = sol(2);
figure;
plot(x, y, '+', 'MarkerSize', 10, 'LineWidth', 2)
hold on
plot(x, f(a_sol, b_sol, x), '-')
  3 Comments
Ameer Hamza
Ameer Hamza on 18 May 2020
That a very useful observation. Many times differences in scale of the data points also make it difficult for optimizers to find an optimal solution. Such modifications can make things easy for the optimizer.
Burak Akayoglu
Burak Akayoglu on 18 May 2020
Thankyou very much Ameer and John. Your answers help me a lot both solve the question and understand the concept. Thank you for your time and effort again.

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More Answers (1)

Ang Feng
Ang Feng on 18 May 2020
Hi Burak,
This link is certainly helpful
Matlab has very good documentation.
Good luck
  1 Comment
Burak Akayoglu
Burak Akayoglu on 18 May 2020
Hi Ang,
Thanks for your answer. I will check this documentation

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