How to modify built-in function tolerance for 'lsqcurvefit'?

Dear All,

I am trying to fit the appended data to a lognormal distribution using lsqcurvefit; however, the function is getting terminated because 'because the final change in the sum of squares relative to its initial value is less than the value of the function tolerance'. My code is as follows (data used for fitting is appended):

**********************************************************************************************************

clc; clear all; close all;

A = xlsread('Curve_fit_data_04102022_3');

xdata = A(:,1); ydata = A(:,2);

plot(xdata,ydata,'ro')

% Supply initial guess

x0 = [2 6];

% Function handle

F = @(x,xdata)(1./xdata/sqrt(2*pi)./log(x(2))).*exp(-0.5.*(log(xdata./x(1))./log(x(2))).^2)

[x,resnorm,~,exitflag,output] = lsqcurvefit(F,x0,xdata,ydata)

************************************************************************************************************

This code throws up an exitflag value of 3 with a resnorm value of 0.2089;

How do I modify the function tolerance such that resnorm is lowered; your inputs are much appreciated.

Regards,

KD

Answer 1

[Torsten]

FunctionTolerance and StepTolerance are the parameters in the options-structure you can play with.

[Kareemulla Dudekula]

Thanks, Torsten!

I added the following two lines to the code before calling 'lsqcurvefit'; I set lb and ub matrices to be empty.

options = optimoptions('lsqcurvefit')

options.FunctionTolerance = 1e-15

[x,resnorm,~,exitflag,output] = lsqcurvefit(F,x0,xdata,ydata,lb,ub,options)

I lowered the function tolerance until exitflag is 1; however, there is no change in resnorm (still is 0.2089) and so, no change in the final parameter values. Insights?

[Steven Lord]

Do you have a reason to believe that the residual norm can be lowered given the form of the equation that you're trying to fit?

If by "lowered the function tolerance" you meant you changed it to something smaller than eps you should read the Tip on this documentation page.

[Kareemulla Dudekula]

Do you have a reason to believe that the residual norm can be lowered given the form of the equation that you're trying to fit?

Not at the moment; I had happened to fit a different set of data to the same lognormal distribution and noticed residual norms in the order of e-5. So, I was expecting along the same lines.

If by "lowered the function tolerance" you meant you changed it to something smaller than eps you should read the Tip on this documentation page.

Thanks very much; I shall go through it!

Thanks a ton!