Why do I get Cannot fit Power functions to data where X has nonpositive values when using the curve fitting tool?

Dear community,

Maybe my question is obvious, but I am trying to estimate a curve with negative values for x using the "power1" type curve fitting tool. However, Matlab shows me the following error: "Cannot fit Power functions to data where X has nonpositive values".

My question is, is there a way to get rid of this error, or by mathematical construction is it impossible?

I attach my x and y values.

Thank you in advance!

[Torsten]

A negative number, raised to a noninteger power, gives a complex number. And I guess your y-values are not complex, are they ?

Maybe using

y = a*abs(x)^b

already fits your needs as fitting function.

[Angelavtc]

@Torsten thank you for your prompt response. Indeed, y is not a complex number, and it is between -300 and 300. Unfortunately, the absolute value does not solve my problem, as my original x goes from -4500 to 3000 in an increasing direction. Thus, the absolute value distorts the order and fit. Any other ideas? Thank you very much in advance!

[Torsten]

Maybe you could include a .png file to see the measurement curve.

[Angelavtc]

Of course @Torsten! x_y.png is the graph with the original data, and absx_y.png is the absolute value graph. Thank you!

[Torsten]

At a first glance, I'd suggest

y = a*exp(b*x)

or

y = a/(b-x)

[Angelavtc]

@TorstenThanks for the hint :) However, how do I transform an x to include the coefficients before estimating? Because to use the fit "power1," I must specify the x and y in advance. On the other hand, would this transformation affect the estimation of the coefficients?

[Torsten]

You only have to pass the x and y values to the fit function that you used to make the plot.

Take a look at the examples provided under

de.mathworks.com/help/curvefit/fit.html

[Angelavtc]

@Torsten Thanks for the answer. From what I notice, the only thing I could do is to define my own fit type with the command:

ft = fittype('a*exp(b*x)');

But this is something I would not want :/

because from what I think, the estimation would not be as accurate as if I use the "power1" fit. Or is it?

Also, will my function transformation change the results of my estimation? I guess it does. Thank you very much!

[Torsten]

I'm not aware that a power function tends to 0 as x approaches -Inf and at the same time tends to +Inf as x approaches +Inf. So the last thing I would choose as fitting function is the power function.

I'm not sure what you mean by" function transformation". Could you clarify ?

[Angelavtc]

@TorstenThank you very much for all your help. I understand that you mean that an exponential function is a better fit for the data. With the transformation of the function, I meant just this. The answer is clear, the parameters will be different because we fit another function. I'm sorry for the obviousness of my question. Could your comment be an answer to accept it?

Answer 1

[Matt J]

Torsten's idea for an exp1 fit works pretty well.

load myfile 
f=fit(x,y,'exp1');

plot(f,x,y)

[Angelavtc]

I see :) thank you @Matt J!