Incorrect lsqcurvefit fitting, stays in initial guess

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hg song
hg song 2022 年 6 月 24 日
コメント済み: hg song 2022 年 6 月 26 日
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.
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. 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. 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. 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. 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. 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. 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. 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
  3 件のコメント
hg song
hg song 2022 年 6 月 25 日
Dear Torsten,
I've tried the method, unfortunately, the performance is less satisfactory.
I found it is better if the xdata & ydata is piecewisely fitted, same as the "fminspleas" suggests.

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採用された回答

Matt J
Matt J 2022 年 6 月 25 日
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];
xdata=xdata*1e5;
ydata=ydata/1e10;
funlist={@(bd,xd) exp(-bd(1)*xd), @(bd,xd) exp(-bd(2)*xd)};
lb=[1/100,1/500];
ub=[inf,1/100];
[bd,ac]=fminspleas(funlist,[1,10],xdata,ydata,lb,ub,1./ydata);
a=ac(1); c=ac(2);
b=1./bd(1); d=1./bd(2);
fun=@(x) a*exp(-x/b)+c*exp(-x/d);
x=linspace(min(xdata),max(xdata));
plot(x,fun(x),xdata,ydata,'+');
  1 件のコメント
hg song
hg song 2022 年 6 月 26 日
Dear Matt,
Thanks for your reply. It looks well in linear axis.

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