How to constrain the lower and upper bounds in lsqcurvefit?

Hi,

For a data set (x, y), I am trying to fit a function f(m, x) using lsqcurvefit. I write as follow:

x=xdata;
y=ydata;
fun=f(m,x);
m0=[m01; m02; m03]; %these are real numbers
lb=[0; 0; 0];
ub=[ub1; ub2; ub3]; %these are real numbers
m=lsqcurvefit(fun, m0, xdata, ydata, lb, ub);

However, sometimes it obeys the bounds and sometimes it does not while fitting. Could anyone please help me if there is any way of constraining the bounds?

Thank you very much in advance!

Kind regards,

Arun

[Viren Gupta]

Is the column vector - 'xdata' having the same dimensions as the column vector - lb and ub i.e 3*1?

[Arun Kumar Bar]

No, they are not same.

[Torsten]

sometimes it obeys the bounds and sometimes it does not while fitting

This might happen during the fitting process. Usually, the parameters only respect the prescribed bounds after fitting.

[Arun Kumar Bar]

Even after fitting, the final output parameters are ouside the bounds. Thtat's my concern . If it does not obey during fitting process and if the final output parameters obey the bounds, then it could be perfect.

Anyway, thanks Torsten!

Wish you a very happy new year!

Regards,

Arun

[Matt J]

To investigate this, we need to be given what is needed to run the fit ourselves (xdata, ydata, and code for f(m,x)).

[Arun Kumar Bar]

Hi Matt,

Glad to see that you would like to chek yourself. I did not provide initially in details as the equation is a complex one. Anyway, I am providing here a small set of data, particularly where I face problem.

The rlprt is a 24x2 double, see the attached file, same is the imprt.

In the equation (see below), there are three independent parameters m1, m2 and m3.

Notably, all m(i) must be > 0;

When I fit individually (i.e. using xdata=rlprt(:, 1) and ydata=imprt(:, 1)), it results out all m(i) > 0. But when I run in loop, see bellow for the code I use, m(2) come out as negative values.

Thanks and regards,

Arun

-

--------
figure()
for i=1:2
xdata=rlprt(:, i);
ydata=imprt(:, i);
fun=@(m,xdata) ((((m(2)-m(1)).*tan(pi.*m(3)/2))/2)+((sqrt((((m(2)-m(1)).*tan(pi.*m(3)/2)).^2)-(4.*((xdata.*xdata)-(xdata.*(m(1)+m(2)))+(((m(1)+m(2)).^2)/4)-(((m(2)-m(1)).^2)/(4.*((sin(pi.*(m(3)-1)/2)).^2)))+(((m(2)-m(1)).^2).*((tan(pi.*m(3)/2)).^2)/4)))))/2));
m0=[0.45; 0.1815; 0.0735];
lb=[0; 0; 0];
ub=[2, 0.75, 0.25];
m=lsqcurvefit(fun, m0, xdata, ydata, lb, ub);
plot(xdata, ydata, 'o', 'linewidth', 1.5); hold on;
plot(xdata, fun(m, xdata), '-', 'linewidth', 1.5);
output(i, 1:3)=m(1:3, 1);
end
hold off;

--------

[Matt J]

I don't get negative values when I run this code. I get complex ones,

output =

   0.3528 + 0.0001i  -3.5428 - 1.5825i   0.2693 + 0.0047i
   0.3698 + 0.0000i  -0.0523 - 0.0029i   0.2063 + 0.0017i   

Your function is not real-valued at certain m in the search space.

Answer 1

[Matt J]

This seems to work okay,

for i=1:2
    [xdata,is]=sort(realpart(:, i));
    ydata=imaginarypart(is, i);
    fun=@(m,xdata) ((((m(2)-m(1)).*tan(pi.*m(3)/2))/2)+((sqrt((((m(2)-m(1)).*tan(pi.*m(3)/2)).^2)-(4.*((xdata.*xdata)-(xdata.*(m(1)+m(2)))+(((m(1)+m(2)).^2)/4)-(((m(2)-m(1)).^2)/(4.*((sin(pi.*(m(3)-1)/2)).^2)))+(((m(2)-m(1)).^2).*((tan(pi.*m(3)/2)).^2)/4)))))/2));
    m0=[0.45; 0.1815; 0.0735];
    lb=[0; 0; 0];
    ub=[2, 0.75, 0.25];
    [m,resnorm,residual,exitflag,stats]=lsqcurvefit(@(m,xd) abs(fun(m,xd)), m0, xdata, ydata, lb, ub);
    plot(xdata, ydata, 'o', 'linewidth', 1.5); hold on;
    plot(xdata, fun(m, xdata), '-', 'linewidth', 1.5);
    output(i, 1:3)=m(1:3, 1);
end

output =

    0.3522    0.0000    0.1771
    0.3676    0.0239    0.1444

[Arun Kumar Bar]

Hi Matt,

Thank you very much for your efforts to reply so promptly!

Yes, these codes do work for this data set. Notably, It appears quite surprising to me now. For the data sets where I used to get -ve values of the real parts of the output m(i) using the codes I provided in my previous comment, now I get better fittings and more reliable outputs through the way you suggested. However, the data sets which give better fitting and more reliable outputs through the way I used to use, now result out very poor fitting and unrliable outputs through the way you suggested. It appears strange to me, at least at the moment. Let me see if I can figure out where it's going wrong.

Thanks a lot once again!

Kind regards,

Arun.

[Arun Kumar Bar]

Thanks a lot, dear Matt! It's working fine now.

Kind regards,

Arun