Fitting a 4 variable nonlinear equation using lsqcurvefit

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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)

Accepted Answer

Star Strider
Star Strider on 30 Sep 2015
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.)
  4 Comments
JayD
JayD on 1 Oct 2015
Thank you so much. It works for me. Appreciate your comments.
Star Strider
Star Strider on 1 Oct 2015
My pleasure.
The most sincere expression of appreciation here on MATLAB Answers is to Accept the Answer that most closely solves your problem.

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