Fitting a 4 variable nonlinear equation using lsqcurvefit

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JayD
JayD 2015-9-30
评论： Star Strider 2015-10-1
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)

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Star Strider
Star Strider 2015-9-30
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.)
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JayD
JayD 2015-10-1
Thank you so much. It works for me. Appreciate your comments.
Star Strider
Star Strider 2015-10-1
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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