MATLAB: Problem with nonlinear curve fitting – lsqcurvefit

MATLAB

Hello!

I'm trying to fit a nonlinear curve with constrains, so I use lsqcurvefit to get the parameters of my function. After applying lsqcurvefit I obtain this output:

Local minimum possible.

So I use MultiStart in order to get the global minimum, but it is not able to obtain the parameters of the function. In this case the output is:

MultiStart encountered failures in the user provided functions. All 100 local solver runs failed in a user supplied function

Searching on Matlab answers I came across this post

http://www.mathworks.es/matlabcentral/answers/49057-nonlinear-curve-fitting-issue

They suggest patternsearch in situations where an objective function has many local minima. However, it is not clear how to use pattern search to fit a nonlinear curve.

How can I obtain an optimal fitting? How can I use pattern search when fitting a nonlinear curve?

Any help will be appreciated. Thanks!

Best Answer

Hi Alex, this link may help you get started:

http://www.mathworks.com/help/matlab/math/example-curve-fitting-via-optimization.html

Using optimization routines in MATLAB are very similar across functions. The idea in fitting a curve is to set up an error function usually sum of squared errors, and ask the optimization tool (your choice) to minimize it.

x = patternsearch(@err,x0)

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MATLAB: Matlab: Get the Hessian matrix using Multistart

MultiStart does not return the Hessian. But, if you really want the Hessian for computing confidence intervals, you shouldn't use the fmincon Hessian anyway, because, as documented, it is inaccurate.

I do not know what the confidence interval calculation is when there are active constraints in a maximum likelihood calculation. If, at the end of the calculation, there are no active constraints, then you can call fminunc on the function at the final point. As documented, fminunc Hessians are accurate.

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MATLAB: Problem with nonlinear curve fitting (lsqcurvefit and Multistart)

I am not sure why you wrote the function firstorderDSC1 like that, but reviewing it briefly, it appears that the ode function you have written inside it to fit the data is wrong. Check the differences of your code with this code

clc
clear all;
close all;
%xdata
T = 294:0.1:361;
T=T';
%ydata
for i=1:size(T,1)
    f1(i)=  0.2099*exp(-((T(i)-340.2)/2.439).^2);
end
f1=f1';
%Initial value for unknown coefficient
B0 =rand(1,3);
%find the local fit using lsqcurvefit
options = optimoptions('lsqcurvefit','FiniteDifferenceType','central','OptimalityTolerance',1e-12,'FunctionTolerance',1e-12, 'MaxFunctionEvaluations',1500);
lb = [-Inf];
ub = [Inf];
[B,Rsdnrm,Rsd,ExFlg,OptmInfo,Lmda,Jmat] = lsqcurvefit(@firstorderDSC1,B0,T,f1,lb,ub,options);
% Set up the problem for MultiStart
problem = createOptimProblem('lsqcurvefit','x0',B0,'objective',@firstorderDSC1,...
    'lb',lb,'ub',ub,'xdata',T,'ydata',f1);
ms = MultiStart('PlotFcns',@gsplotbestf);
[xmulti,errormulti] = run(ms,problem,50);
%plot the result
figure;
plot(T,f1,T,firstorderDSC1(xmulti,T),'LineWidth',3)
legend('Data','Fitted result')
function dndt2 = firstorderDSC1(B, T)
%my differential equation
    function denaturate = firstorderDSC(T, n)
        a= (exp(183.8)./1.5); %(1/s)
        dndT=B(1)*exp(-((T-B(2))/B(3)).^2);
        denaturate=dndT;
    end
%solving my differential equation
options = odeset('AbsTol', 1e-8,'RelTol',1e-8);%,'OutputFcn',@odeplot);
[temp,num] = ode23s(@firstorderDSC, T, 0, options);
dndt2 = firstorderDSC(temp,num);
end

Both lines overlap.

Best Answer

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MATLAB: Problem with nonlinear curve fitting (lsqcurvefit and Multistart)

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