lsqcurvefit fitting not good

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Zuyu An
Zuyu An on 17 Oct 2019
Edited: Alex Sha on 22 Oct 2019
>> xdata = ...
[0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 0.08];
ydata = ...
[-1.5641 4.331 10.226 10.328 10.43 9.2075 7.9845 6.9538 5.9227 4.7857 3.6488 2.1603 0.67176 0.22867 -0.21442 -0.10787];
fun = @(x,xdata)x(1)+x(2).*sqrt(x(3)./((2.*pi.*x(4).*(xdata+x(5))).^3)).*exp(-x(3).*((x(4).*(xdata+x(5))-x(6)).^3)./(2.*x(4).*(xdata+x(5)).*x(6).^2));
x0 = [0,8,0.9,13,0.01,0.9];
x = lsqcurvefitlsqcurvefit(fun,x0,xdata,ydata)
options = optimoptions('lsqcurvefit','Algorithm','levenberg-marquardt');
lb = [];
ub = [];
times = linspace(xdata(1),xdata(end));
plot(xdata,ydata,'ko',times,fun(x,times),'b-')
legend('Data','Fitted exponential')
title('Data and Fitted Curve')
it should mindestens so:
but in my Matlab it is so:
what should i do? and where am i wrong?

Accepted Answer

Star Strider
Star Strider on 17 Oct 2019
Choose different values for ‘x0’.
I used these:
x0 = [-2.6; 17; 0.7; 7; 0.0001; -0.7; 0.7];
to get this result:
x =
-4.324990458427486
29.118149115959035
0.816104607520526
6.992507999448133
0.003331267566044
-0.774459180826721
0.700000000000000
and this plot:
#lsqcurvefit fitting not good.png
I began with a random vector, and used fminsearch to produce the new ‘x0’ vector. It gave a good fit after about 10 initial starts. A better approach would have been to use the ga funciton.
  11 Comments
Star Strider
Star Strider on 21 Oct 2019
I posted an Answer to your new Question.

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More Answers (1)

Alex Sha
Alex Sha on 18 Oct 2019
Edited: Alex Sha on 22 Oct 2019
whether fminsearch or lsqcurvefit in Matlab use local optimization algorithms, it is why the initial start values are so important, unfortunately, guessing good initial start values is nightmare for most of users, although GA toolbox in Matlab use global algorithm, but the effect of GA in Matlab is far below expectations。The follow results are calculated from one of other software by using global optimization, no need to guess initial start values:
Root of Mean Square Error (RMSE): 0.448475537821338
Sum of Squared Residual: 3.21808492838621
Correlation Coef. (R): 0.993866542618332
R-Square: 0.987770704536117
Adjusted R-Square: 0.98588927446475
Determination Coef. (DC): 0.987770704536117
Chi-Square: 0.0996829655505242
F-Statistic: 161.541718751279
Parameter Best Estimate
---------- -------------
x1 -4.32518017924354
x2 1.5161832530864
x3 0.816035356312747
x4 0.139454519659979
x5 0.00333139106331274
x6 -0.015446312666105

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