오리진 Nonlinear Fitting - olijin Nonlinear Fitting

Good afternoon, I'm posting this question because I'm not able to find a satisfactory result of a non-linear fit with Matlab. On the contrary, OriginLab returns a good fit together with errors for fit parameters. Here my x and y data: x = [177600,961200, 2504000, 4997000, 8884000]; y = [6.754, 24.416, 58.622, 107.980, 154.507]; yErr = sqrt(y);

The fitting function is the following: y = V + (A-V)*S*x*EXP(-S*x) where V, A and S are the parameters which I need to calculate from the fit. OriginLab gives me the following:

• V = 1.978 ± 0.889
• A = 585 ± 64
• S = 4.392E-8 ± 6.771E-9

On Matlab I tried all the possible form of non-linear regression: fitnlm, lsqcurvefit, nlinfit etc... every time the same warning:The Jacobian is ill conditioned. Here is an example:

Nonlinear regression model:

y ~ a1 + (a2 - a1)*a3*x*exp( - a3*x)

Estimated Coefficients:

Estimate SEtStatpValue

__________ _______________________________

a1 -0.67892.9104e-19-2.3327e+182.0265e-73

a2 530.788.0894e-206.5614e+213.2371e-87

a3 5.2511e-08 5.1865e-10101.255.7063e-08

Of course such small standard errors are not reliable, but still I'm not able to reproduce the Origin results. Any suggestions?

Accepted Answer

Edited: Matt J on 14 Sep 2018

Well, I guess I would credit OriginLab with knowing how to pre-scale the x,y data appropriately. If you do this manually, then lsqcurvefit works fine, and gives a slightly better fit (according to resnorm) than OriginLab,

c=10*max(x);

a0=[1.9780 ,585, 4.3920e-08*c];

F=@(a,x) a(1)+(a(2)-a(1)).*a(3).*x/c.*exp(-a(3).*x/c);

[a,resnorm,~,~,~,~,J]=lsqcurvefit(F,[1,100,1],x,y,[],[],...

optimoptions('lsqcurvefit','Display','iter'));

solution=[a(1), a(2), a(3)/c]

resnorm

condJ = cond(full(J))

plot(x,y,'x',x,F(a,x),'--'); xlabel 'x', xlabel 'y';

More Answers (2)

Another frustrating scenario.. simple polynomial fit y = a+bx+cx^2 I get another error on Matlab "Polynomial is badly conditioned". On the other hand Origin does it better.. why? To me this is really embarrassing.

The global solution looks like below:

Root of Mean Square Error (RMSE): 1.42818042380826

Sum of Squared Residual: 10.1984966147457

Correlation Coef. (R): 0.999655170571204

R-Square: 0.999310460049744

Adjusted R-Square: 0.998620920099487

Determination Coef. (DC): 0.999310460049744

Chi-Square: 0.212210508410738

F-Statistic: 1449.24229503583

Parameter Best Estimate

---------- -------------

v 0.665211685653936

a 544.888484613983

s 4.9628897712431E-8

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