lsqcurvefit : undefined values at initial point

a.mat contains the output of a ccd camera.

   y = transpose(mean(a));
    x = transpose(1:1280);
    x0 = [600 1e4 .01];
    parfit = lsqcurvefit(@fraunhof,x0,x,y)

    function F = fraunhof(x,xdata)
    beta = x(3).*(xdata-x(1));
    sinbeta = sin(beta);
    F = x(2).*sinbeta.^2./beta.^2;

Running this code returns the following error:

Error using snls (line 47)
Objective function is returning undefined values at initial point. lsqcurvefit cannot continue.

Error in lsqncommon (line 150)
    [xC,FVAL,LAMBDA,JACOB,EXITFLAG,OUTPUT,msgData]=...

Error in lsqcurvefit (line 253)
[xCurrent,Resnorm,FVAL,EXITFLAG,OUTPUT,LAMBDA,JACOB] = ...

[Matt J]

The meaning of the contents of a.mat is not clear (to me at least).

[G Guerrer]

Hi Matt, its a 960x1280 uint16 array. Ive attached the file.

Answer 1

[Star Strider]

You’re encountering a ‘sin(x)/x’ problem, where your function is undefined at 0. The solution is to have it defined at 0, although you have to fudge your function a bit to do it. I added 1E-8 to ‘beta’ to emulate L’Hospital’s rule, and got a good fit:

fraunhof = @(x,xdata)  x(2).*sin(x(3).*(xdata-x(1)) + 1E-8).^2./(x(3).*(xdata-x(1)) + 1E-8).^2;

x0 = [600 1E5 0.01];
parfit = lsqcurvefit(fraunhof,x0,x,y)

figure(1)
plot(x, y)
hold on
plot(x, fraunhof(parfit,x))
hold off
grid

parfit =

     649.6130e+000    47.9481e+003    10.3101e-003

[G Guerrer]

Thanks, it worked!

[Star Strider]

My pleasure!

[Josh Begale]

I am having a similar issue with my code and was wondering if you could assist me? Here is my code and following errors:

F1 = @(x,xdata)(x(1)*(xdata.^2 - xdata.^(-1))); %% Neo-Hookean

F2 = @(x,xdata)(2*(x(1)*(xdata.^2 - xdata.^(-1)) + x(2)*(xdata - xdata.^(-2)))); %% Mooney-Rivlin

F3 = @(x,xdata)((x(1)/x(2))*(xdata.^x(2) - xdata.^(-x(2)/2))); % Ogden

NH1 = lsqcurvefit(F1,[1,1,1],S,MP);

% NH2 = lsqcurvefit(F1,[1,1,1],S,LP);

% MR1 = lsqcurvefit(F2,[1,1,1],S,MP);

% MR2 = lsqcurvefit(F2,[1,1,1],S,LP);

% Og1 = lsqcurvefit(F3,[1,1,1],S,MP);

% Og2 = lsqcurvefit(F3,[1,1,1],S,LP);

Error using snls (line 47)

Objective function is returning undefined values

at initial point. lsqcurvefit cannot continue.

Error in lsqncommon (line 166)

snls(funfcn,xC,lb,ub,flags.verbosity,options,defaultopt,initVals.F,initVals.J,caller,

...

Error in lsqcurvefit (line 257)

lsqncommon(funfcn,xCurrent,lb,ub,options,defaultopt,caller,...

Error in Matlab_Code (line 5)

NH1 = lsqcurvefit(F1,[1,1,1],S,MP);

[Star Strider]

@Josh Begale — It would be best for you to post this as a new Question, then delete this Comment.

[Matt J]

@Josh Begale — Or better still, since you have the same issue, why don't you read the replies in this thread and apply them to your issue as well.

Answer 2

[Matt J]

When xdata(i)=x(1) or x(3)=0, then beta(i) will be zero and your expression for F

F = x(2).*sinbeta.^2./beta.^2

is undefined.

Similarly, if xdata is being assigned the uint16 variable "a" in your a.mat file, then any operation xdata(i)-x(1) will evaluate to 0 when x(1)>xdata(i). My guess is that this is what's happening, in which case you should cast a to double precision.

[Matt J]

I now see that your xdata=1:1280

This means that xdata(600)=600. Since x(1)=600 at your initial point, this will give F(600)=0/0=NaN in your objective function.

Presumably you want F=0 when beta=0? If so, add some post-processing

 F(beta==0)=0;

[G Guerrer]

The function is defined for beta->0 since sinbeta also goes to 0. I can plot it and see it is continuous.

[G Guerrer]

Tried to cast a to double. Still not working.

[Matt J]

Try this simple experiment at the command line.

    >> beta=0; sin(beta)/beta

    ans =

       NaN