How are initial values chosen for either lsqcurvefit or nlinfit functions?

I want to fit my experimental data to a theoretical model which contains an exponential. I've attached a copy of the code I'm using. I've tried various x0 matrix values, but the same error message keeps popping up:

Caused by: Failure in initial objective function evaluation. LSQCURVEFIT cannot continue.

[Walter Roberson]

The code did not get attached.

Answer 1

[Torsten]

There must be some mathematical operation within your objective function that gives Inf, NaN or something similar (e.g. division by zero, log or sqrt of a negative number, exponentiation of a negative number ...).

Best wishes

Torsten.

Answer 2

[Ken Mathai]

So if I have the following:

xdata=cranialStrain
ydata=cranialStress
fun=@(x,xdata)(x(1)*xdata+x(2)*xdata*xdata);
x0 = [0.1 0.1 0];
x = lsqcurvefit(fun,x0,xdata,ydata)

I should be careful that my data does not include negative numbers for ydata, as that would cause issues for the model equation?

[Torsten]

Here the error is that

fun=@(x,xdata)(x(1)*xdata+x(2)*xdata.*xdata);

must be used instead of

fun=@(x,xdata)(x(1)*xdata+x(2)*xdata*xdata);

Furthermore, y=p1*x+p2*x^2 is a linear parameter estimation problem. No need to use "lsqcurvefit" here.

What I mean is: Look for expressions in your function that evaluate to Inf or NaN (e.g. p(1)/xdata where some of the xdata are zero or log(x(1)) (the parameter vector can become negative), or ...)

Best wishes

Torsten.

[Ken Mathai]

hmm. I'm not sure why you say this is a linear parameter estimation problem. Isn't the fact that the xdata is being squared make the model a quadratic?

Also, I made the proposed change to xdata in the multiplication and I reformatted the axes to not include negative numbers. This allowed me to run the code without error!

[Torsten]

Linear means: The equation is linear in the parameters.

It is irrelevant how "xdata" enters the equation.

Thus in your case x(1) and x(2) are simply given by

x = [xdata xdata.^2]\ydata

where xdata and ydata are your respective column vectors.

Best wishes

Torsten.

Answer 3

[Ken Mathai]

Ah, ok. But what other way is there to fit the data to my model equation? I also do not have the cftool box.

[Torsten]

It should suffice to have the Optimization Toolbox (lsqcurvefit, fmincon,...)