How to prevent complex solutions from lsqnonlin

I am trying to determine the parameter of an equation using lsqnonlin.

y = x.^a

Where x and y are input and output data, and a is the parameter to be solved for.

This is the part of my code:

Y_fn = @(apara) ((X_meas).^(apara(1))-Y_meas);
apara = lsqnonlin(Y_fn,init,LB,UB,Y_meas);

Running the script yields solutions for a such as -0.1771 + 1.1983i. How do I prevent obtaining complex solutions?

Thanks

Answer 1

[Walter Roberson]

If any of your X_meas are negative then you are likely to get complex results unless you use a lower bound of 0 for apara. A negative value raised to a non-integral exponent using .^ is going to return a complex value.