Incorrect lsqcurvefit fitting, stays in initial guess

Question

hg song 2022 年 6 月 24 日

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この質問への直接リンク

https://jp.mathworks.com/matlabcentral/answers/1747040-incorrect-lsqcurvefit-fitting-stays-in-initial-guess

コメント済み: hg song 2022 年 6 月 26 日

採用された回答: Matt J

MATLAB Online で開く

hello all,

I am trying to fitting the data with the following function:

y = a*exp(-x/b)+c*exp(-x/d) , where a,b,c,d are 4 free parameters.

a range from (1e9,5e10), b range from (0,100) ,c range from (5e8,5e9), d range from (100,500);

x range from (1e-5, 1.2e-3)

Saying b = 20, the (-x*1e6/b) could range vastly.

This problem might be similar to this post:https://ww2.mathworks.cn/matlabcentral/answers/255480-lsqcurvefit-does-not-change-the-initial-values

After applied the method in my code, it barely improved the performance.

Here are the codes:

xdata =[2.00E-05 2.45E-05 3.00E-05 3.70E-05 4.55E-05 5.55E-05 6.75E-05 8.25E-05 1.01E-04 ...

1.24E-04 1.51E-04 1.85E-04 2.26E-04 2.76E-04 3.37E-04 4.12E-04 5.03E-04 6.15E-04 7.52E-04 9.19E-04 1.12E-03];

ydata =[2.51E+10 1.68E+10 1.24E+10 8.10E+09 6.33E+09 4.73E+09 3.28E+09 1.88E+09 1.26E+09 ...

7.77E+08 5.17E+08 3.45E+08 2.34E+08 1.57E+08 9.70E+07 5.35E+07 2.94E+07 1.53E+07 7.77E+06 3.89E+06 1.82E+06];

a0=[5; 1; 2; 1.5];

options = optimset('TolFun',1e-28);

lb = [0 ; 0; 1; 1];

ub = [10;10;10;10];

fun=@(x,xdata)(x(1)*1e10)*exp(-xdata*1e6/x(3)/10)+(x(2)*1e9)*exp(-xdata*1e6/x(4)/100);

for i = 1:100

x = lsqcurvefit(fun,a0,xdata,ydata,lb,ub,options);

a0 = x;

end

Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. 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Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance. Local minimum possible. lsqcurvefit stopped because the size of the current step is less than the value of the step size tolerance.

semilogy(xdata,fun(x,xdata),xdata,ydata,'+');

And the best fit could be （5.5e10, 26, 1e9, 160)

Is there anybody with a suggestion for improvement?

Best wishes