MultiStart with lsqcurvefit error: FUN must have two input arguments

Hello folks,

I'm trying to fit a nonlinear curve from solving the advection-diffusion-adsorption PDE equation.

%Initial condition
IC=zeros(1,Nz)+1E-9;
%Initial guess
Lamdag=0.51;Kfg=1.0E+4;Ng=0.65;
g=[Lamdag;Kfg;Ng];
lb=[0.5,1E+3,0.3];
ub=[0.9,1E+5,1];
[P,SSE]=lsqcurvefit(@fun2,g,time,conc,lb,ub,[],IC,eps,V,De,Nz,dz,Cw,Jw);

I can use lsqcurvefit to fit my experimental data to the PDE eqaution and get the values of parameters successfuly. But it does not fit very well and I would like to try to use MultiStart to find the global optimization.

Therefore, I followed the example from this website https://www.mathworks.com/help/gads/multistart-using-lsqcurvefit-or-lsqnonlin.html. My script for the MultiStart is below:

problem = createOptimProblem('lsqcurvefit','x0',g,'objective',@fun2,...
    'lb',lb,'ub',ub,'xdata',time,'ydata',conc);  %lsqcurvefit

ms=MultiStart('PlotFcn',@gsplotbestf);
[x,fval,eflag,output,manymins]=run(ms,problem,50);

And I got the error: Error using lsqcurvefit (line 229)

FUN must have two input

arguments.

Error in globaloptim.multistart.fmultistart

Error in MultiStart/run (line 257)

globaloptim.multistart.fmultistart(problem,startPointSets,msoptions);

Error in DNP_NF270_fit (line 72)

[x,fval,eflag,output,manymins]=run(ms,problem,50);

Caused by:

Failure in call to the local solver with supplied problem structure.

I have searched the similar questions other people have asked and did not found what to do for my case. I have attached my .m script in the attachment if anyone need it.

Very appreciated if anyone can help me diagnose the problem. Thank you very much.

Answer 1

[Torsten]

problem = createOptimProblem('lsqcurvefit','x0',g,'objective',@(p,xdata)fun2(p,xdata,IC,eps,V,De,Nz,dz,Cw,Jw),...
                             'lb',lb,'ub',ub,'xdata',time,'ydata',conc);  %lsqcurvefit

[Alan Weiss]

In addition to the syntax issue that Torsten fixed for you, there remains the potential issue of inappropriately small finite difference steps. If you find that your least-squares problems are not being solved accurately, see the description and fix suggested in Optimizing a Simulation or Ordinary Differential Equation.

Alan Weiss

MATLAB mathematical toolbox documentation

[Zerui Hao]

Thank you Torsten. It solved successfully. Can I ask why is that? I am wondering when we could use @fun2, and when I need to use @(p,xdata) fun2(p.xdata,IC....).

[Zerui Hao]

Thank you Alan. I try to use different finite difference steps and even using MultiStart. The fitting result is actually my intial guess, and it did not change at all. It's weired.

[Torsten]

@Zerui Hao

Since you don't call "lsqcurvefit" directly by using

[P,SSE]=lsqcurvefit(@fun2,g,time,conc,lb,ub,[],IC,eps,V,De,Nz,dz,Cw,Jw);

how should MATLAB know by the setting

problem = createOptimProblem('lsqcurvefit','x0',g,'objective',@fun2,...
    'lb',lb,'ub',ub,'xdata',time,'ydata',conc);  %lsqcurvefit

that you also want to supply IC,eps,V,De,Nz,dz,Cw,Jw in the function "fun2" ?

Every time the actual list of input parameters to a function differs from the list MATLAB expects, you have to use

[P,SSE]=lsqcurvefit(@fun2,g,time,conc,lb,ub,[],IC,eps,V,De,Nz,dz,Cw,Jw);

or better

[P,SSE]=lsqcurvefit(@(p,xdata)fun2(p,xdata,IC,eps,V,De,Nz,dz,Cw,Jw),g,time,conc,lb,ub,[]);