Calculate residuals as a single number in lsqnonlin function

I solve a nonlinear curve fitting problem using the lsqnonlin Matlab function.

I am interested to check the residual of my fitting each time so I am returning the residual each time I call the lsqnonlin function. I wanted to calculate a single number of the residual to see if the fits gets better after doing some changes in my data. My data are 3D images. Each time I calculated the sum of residuals using the sum() function. I ended up though with very large numbers, e.g. 7.3507e+04. Is there a better way to represent the residual in a single number than calculating the sum?

[Matt J]

It is not clear why you think you need a "better" way. If you want the numbers to be smaller just scale down your objective function, e.g.,

objfun_new =@(x) objfun_old(x)/1e4;

Answer 1

[Rik]

Yes, the sum of squares or the RMS:

SSq=sum(res.^2);
RMS=sqrt(mean(res.^2));

The downside of using the plain sum is that a large negative and a large positive will cancel out, which is clearly not what you want. Whether or not a number is large should not be a factor in your decision, just that you want to minimize it.

[Rik]

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Answer 2

[Torsten]

If you use the usual naming conventions of lsqnonlin, the residual is "sum(F.^2)"

Best wishes

Torsten.