Fitting a 4 variable nonlinear equation using lsqcurvefit

I tried to fit my data to a multi-exponential function using "lsqcurvefit" and to find out the coefficients. It gives an unexpected error, "The Levenberg-Marquardt algorithm does not handle bound constraints and the trust-region-reflective algorithm requires at least as many equations as variables; aborting."

As for matlab examples given for simple exponential function, it works fine. Any idea to figuring this out?

xdata=[50 400 800];
ydata=[350 200 90];

ff=@(x,b) x(1)*(x(2)*exp(-(x(3)+x(4))*b)+(1-x(2))*exp(-x(4)*b)); 

x0=[1,0.2,0.01,0.001]; %guess values

lb=[0, 0, 0.005, 0]; 

ub=[1500, 1, 0.1, 0.005];

options = optimset('Algorithm','levenberg-marquardt','MaxFunEvals',1e9,'MaxIter',1e9,'TolFun', 1e-8, 'TolX', 1e-8);

X=lsqcurvefit(ff,x0,xdata,ydata,lb,ub,options); 
disp(X)

Answer 1

[Star Strider]

You are estimating four parameters with three data pairs. You cannot uniquely estimate more parameters than you have data. (Consider estimating a line — defined by two parameters — when you have only one point. An infinite number of lines could be drawn through that point.)

[JayD]

That makes sense now. Thank you so much. Since I cannot add more data to this specific problem, I will have to come up with another technique to use this model function. Any suggestions on that?

[Star Strider]

My pleasure.

A simple sum-of-exponentials is rarely a good model anyway. It is best that you derive a mathematical model your system and develop an objective function to fit that model to your data, so that the parameters have physical meaning.

In the interim, a single exponential would likely work with the data you have. I’d use something like this:

f = @(x,b) x(1) + x(2).*exp(x(3).*b);

(This is untested code.)

[JayD]

Thank you so much. It works for me. Appreciate your comments.

[Star Strider]

My pleasure.

The most sincere expression of appreciation here on MATLAB Answers is to Accept the Answer that most closely solves your problem.