Complex value computed by model function, fitting cannot continue. Try using or tightening upper and lower bounds on coefficients.

Question

Daniel Jiao 2024-6-3

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评论： Matt J 2024-6-4

200ms_SD.xlsx

Hello, I really need some help on data fitting. I would like to fit my data custom equation:a+b*exp((-(x/c))^d. I try to use upper and lower bounds on coefficients but it does not work.If anyone can tell me what to do to resolve this I would greatly appreciate it.

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Torsten 2024-6-3

在 MATLAB Online 中打开

@Matt J

Because of the error message and the overfitting, I suspect

a+b*exp(-(x/c)^d)

instead of

a+b*exp((-(x/c))^d

is meant.

Daniel Jiao 2024-6-4

@Torsten Thanks lot, I'll check it. This equation is given by an article, so it's a theoretical formula, but yeah, I'll check whether it's correct, thanks so much!

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Answer 1

Matt J 2024-6-3

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编辑：Matt J 2024-6-3

在 MATLAB Online 中打开

200ms_SD.xlsx

fminspleas from this FEX download,

https://www.mathworks.com/matlabcentral/fileexchange/10093-fminspleas

is helpful for these kinds of models.

[x,y]=readvars('200ms_SD.xlsx');

flist={1,@(c,x) exp(-c*x)};

[c,ab]=fminspleas(flist,+1,x,y);

a=ab(1);

b=ab(2);

f=@(x)a+b*exp(-c*x);

xf=linspace(min(x),max(x));

plot(x,y,'.c',xf,f(xf)); axis padded; legend Data Fit

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Daniel Jiao 2024-6-4

Thanks a lot for this answer, it really give me some ideas and confidence, as the comment you mentioned above, I just try to use fit() and fittype(), like:

ft = fittype( 'a+b*exp((-(x/c))^d)', 'independent', 'x', 'dependent', 'y' );

fitobject = fit(x,y,ft,'lower',[-1,0,0.002,0],'upper',[0,3,0.005,1]);

and I also use the curve fitting toolbox. Just some basic way, since it was first time I try to do curve fitting.

Anyway that's really helpful! Thanks so much for that, and I'll try it!

Matt J 2024-6-4

You're welcome, but when you've decided upon a solution, please Accept-click the appropriate answer.

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Answer 2

Mathieu NOE 2024-6-3

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https://ww2.mathworks.cn/matlabcentral/answers/2124786-complex-value-computed-by-model-function-fitting-cannot-continue-try-using-or-tightening-upper-and#answer_1466616

在 MATLAB Online 中打开

200ms_SD.xlsx

hello

a very basic code using only fminsearch (no toolbox required )

I preferred to smooth a bit your data (otherwise it looks more like a cloud) but it's not absolutely needed - but you end up with other parameters after the fit

hope it helps !

data = readmatrix('200ms_SD.xlsx');

x = data(:,1);

y = data(:,2);

[x,ia,ic] = unique(x);

y = y(ia);

ys = smoothdata(y,'gaussian',100);

% curve fit using fminsearch

% model a+b*exp((-(x/c))^d

f = @(a,b,c,d,x) a + b.*exp(-(x/c).^d);

obj_fun = @(params) norm(f(params(1), params(2), params(3), params(4),x)-ys);

sol = fminsearch(obj_fun, [ys(end),(max(ys)-ys(end)),1,1]);

Exiting: Maximum number of function evaluations has been exceeded - increase MaxFunEvals option. Current function value: 1.159572

a_sol = sol(1)

a_sol = 0.0903

b_sol = sol(2)

b_sol = 0.5209

c_sol = sol(3)

c_sol = 0.0028

d_sol = sol(4)

d_sol = 0.1143

y_fit = f(a_sol, b_sol, c_sol, d_sol, x);

R2 = my_R2_coeff(ys,y_fit); % correlation coefficient

plot(x,y, 'k.',x,ys,'r',x, y_fit,'b-')

title([' Fit / R² = ' num2str(R2) ], 'FontSize', 15)

legend('raw data','smoothed','fit');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function R2 = my_R2_coeff(data,data_fit)

% R2 correlation coefficient computation

% The total sum of squares

sum_of_squares = sum((data-mean(data)).^2);

% The sum of squares of residuals, also called the residual sum of squares:

sum_of_squares_of_residuals = sum((data-data_fit).^2);

% definition of the coefficient of correlation (R squared) is

R2 = 1 - sum_of_squares_of_residuals/sum_of_squares;

end

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Daniel Jiao 2024-6-4

Hello,thanks a lot for the answer, it's really helpful! I'll try to read and try the code you offered! My original code is much more basic, since I'm just a beginner.

Thanks again that I really got some knowledge from you!

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