Objective function is returning Inf or NaN values at initial point. lsqcurvefit cannot continue.

Hi guys, I tried to fitting my data with following code

k0= 3.5e+05; % (s-1)
lamda=7.5e-10; % (m)
n=0.92e-20;

KbT=4.11e-21; % (J)

p=[k0, lamda, n];
func=@(p,ydata)2*p(1)*p(2)*sinh((0.072*cosd(70)-0.0623.*cosd(ydata))/(2*KbT*p(3)));
lb=[1e+1; 1e-12; 1e-15]; % lower bound
ub=[1e+9; 1e-6; 1e-25]; % upper bound

f=lsqcurvefit(func, p, ydata, xdata, lb,ub);


plot(xdata,ydata,'ko',xdata,func(f,ydata),'b-')

But, when I ran, the code results in:

Error using lsqncommon
Objective function is returning Inf or NaN values at initial point. lsqcurvefit cannot continue.

Error in lsqcurvefit (line 274)
    lsqncommon(funfcn,xCurrent,lb,ub,options,defaultopt,optimgetFlag,caller,...

Error in mkt (line 21)
f=lsqcurvefit(func, p, ydata, xdata, lb,ub);

I tried to look at my data, but it looks find to me. Please see the attachment for the data reference, column 1 is xdata, column 2 is ydata.

Thanks for suggestion.

Answer 1

[Torsten]

Before you call lsqcurvefit, you should call your function "func" with the initial guess values for the parameters to see what it returns. So insert the command

test = func(p,ydata)

before the line

f=lsqcurvefit(func, p, ydata, xdata, lb,ub);

Further it is usual that you have a function ydata = func(p,xdata). You reversed the roles of xdata and ydata: xdata = func(p,ydata). You should check whether this is really what you want.

Further your model depends on only one parameter, not three. The expression

2*p(1)*p(2)/(2*KbT*p(3))

can be seen as one parameter P you try to estimate. It's not possible to distinguish between p(1), p(2) and p(3) because they are subsummed in one expression.

To understand this, imagine you try to fit a model

ydata = p(1)*p(2)*xdata

If the optimizer returns p(1) = 2, p(2) = 5, would this in any way be better than p(1) = 1, p(2) = 10 or p(1) = 2.5, p(2) = 4 ?