# How to fit complicated function with 3 fitting parameters using Least square regression

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Thi Na Le on 25 Mar 2020
Commented: Alex Sha on 27 Mar 2020
I want to fit below equation J(v). J and V data areavailable.
N=10^21
q=1.6x10^-19
Epsilon=26.5 x 10^-14
d=3x10^- 6
Initial values may be x0=[µ l H]=[10^-5 5 10^18]
3 fitting parameters are: µ, l and H. other parameters are known.
can some one help me to solve this?
I am not expert in Matlab
V is xdata:
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
J is ydata:
1.64544E-05
1.99822E-05
0.000032253
4.2623E-05
7.40498E-05
0.000660899
0.007578998
0.027109725
0.106353025
0.30299725
0.7332185
1.550115
2.98009
5.3102775
8.88175
14.0394325
21.163215

Alex Sha on 27 Mar 2020
Pleasure, congratulation！
Thi Na Le on 27 Mar 2020
thank you!
The only problem is that result for H value is always equal to the startpoint that I set for H. Is it my fitting has been fail?
Alex Sha on 27 Mar 2020
You may try to provide a little different start-value for H, and see the final result, if final H is still alway equaling to start-value of H, your fitting seems to have problem.

Alex Sha on 25 Mar 2020
Hi, you may try to use "lsqcurvefit" command or curve fitting tool box (cftool), it is also better if you post data as well as known constant values, so other persons may try for you.

#### 1 Comment

Thi Na Le on 26 Mar 2020

Jeff Miller on 25 Mar 2020
I assume you have vectors of values for V and J, in which case fminsearch might be a good choice. The basic steps are:
1. Write a function "predicted" to compute a predicted value of J for any given V, µ, l and H.
2. Write a function "error" that computes the sum of (predictedJ - actualJ)^2, summing across the J vector.
3. call fminsearch and pass it this error function as the function to be minimized. You will have to give it reasonable guesses for µ, l and H.

#### 1 Comment

Thi Na Le on 26 Mar 2020
Thank you for your comment. I will try this

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