Fit returns Imaginary Coefficients

I am fitting a complex function to complex data, but the coefficients must be real. However, when fitting I get complex valued coefficients. Most of the time its fine, because the complex part is several orders of magnitude smaller than the real part, but sometimes beta(1) has a complex part that is of the same order of magnitude as the real part. I have tried using both nlinfit and lsqcurvefit. What fitting function and options can I use to force the coefficients to stay real? I cannot just ignore the complex data because it is important, and I cannot fit the imaginary and real data separately because the coefficients must be the same for the real and imaginary part.

F = @(beta,k) beta(1)*beta(2)*exp(-beta(2)^2/2*(k - beta(3)).^2 - 1i*beta(4)*(beta(3) - k))

[Matt J]

You haven't mentioned what code you're using to perform the fit.

[Chris]

I have tried nlinfit and lsqcurvefit. Both yield the same result.

Answer 1

[Matt J]

Change F to

 model= @(beta,k) beta(1)*beta(2)*exp(-beta(2)^2/2*(k - beta(3)).^2 - 1i*beta(4)*(beta(3) - k))

 F=@(beta,k) [real(model(beta,k)); imag(model(beta,k))];

and split your ydata into real and imaginary parts similarly.

[Chris]

and then just fit the real part?

[Matt J]

No, as you can see from my modification of F, the imaginary part is included as well

imag(model(beta,k))

Answer 2

[Miranda Jackson]

Use real() on all the coefficients in the fitting function so the imaginary part won't have any effect on the solution. Then use real() on the resulting coefficients you get from lsqcurvefit. Even if the coefficients go complex, only the real part will affect the result of the fit.

[Matt J]

Note that with this approach, you will not be able to apply bounds on the coefficients.