How can I use FindFit with complex domains?

[Littlepig]

Hi there

Suppose I have data of the format {x,y+i z} where x,y,z is real and i is the imaginary unit.

I'm trying to make a FindFit of some nasty model that, suppose for simplification is f(x) = a^b*x^2+exp(a)*b*i*x (domain is real, codomain is complex and a,b are Real) and can be written as f(x)= g(x) + i h(x). I want to FindFit to find "a" and "b" that makes f(x) best fit the data.

How can I do this? There is no way of constrain a and b to Real as FindFit don't allow that. Furthermore, it appears that FindFit don't accept imaginary data.

Thank you very much for your response

 

[Aaron Bex]

Unfortunately, FindFit will not work in this scenario because it is unable to fit complex data. You may need to use an alternative fitting method such as NonlinearModelFit or NonlinearRegress to fit your data. NonlinearModelFit and NonlinearRegress are more sophisticated fitting methods which can handle complex data.

You can also try using the LeastSquaresFit function, which can be used to fit linear models to complex data. This function requires that you define a linear model for the complex data and then use the LeastSquaresFit function to minimize the square of the residuals between the model and the data.

Hope this helps!

 

[oswaler]

and for bringing up this interesting problem. FindFit is a powerful tool for fitting data to a model, but it does have limitations when it comes to complex domains. In this case, it seems like your model has both real and imaginary components, making it difficult to use FindFit directly.

One possible solution would be to split your data into two sets: one with only real values and one with only imaginary values. You can then use FindFit separately on each set to find the best fit for the real and imaginary components of your model.

Another approach could be to use a different fitting tool that allows for complex domains and parameters, such as NonlinearModelFit or ComplexFit. These tools have additional options and capabilities that may be useful for your specific problem.

Alternatively, you could try to reformulate your model in a way that eliminates the complex domain and parameters. This may require some mathematical manipulation, but it could make the fitting process easier and more straightforward.

In any case, it's important to carefully consider the limitations and assumptions of any fitting tool you use, and to be aware of how they may affect your results. I hope this helps and good luck with your analysis!