Complex value computed by model function, fitting cannot continue. ... (2024)

The expression a+b*exp((-(x/c))^d cannot become complex-valued. My guess is that you use a different expression in your code.

We do not know what you tried (no code is shown), so we cannot guess what went wrong. I will point out though that the model is over-parametrized. It is enough to use 3-parameters y=a+b*exp(-c*x). No custom equation is needed for this - it falls within the 'exp2' fitType of the fit() command.

Because of the error message and the overfitting, I suspect

instead of

is meant.

@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!

[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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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]);

a_sol = sol(1)

b_sol = sol(2)

c_sol = sol(3)

d_sol = sol(4)

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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