Fitting implicit surface equation

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Moritz 2013-12-13

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/109698-fitting-implicit-surface-equation

Dear all,

following problem: I do have a 5x4 Matrix q(C,Cna) and would like to fit the implicit expression defined in the funktion SMAexplizit. I use lsqcurvefit, but i also tried fminunc fminsearch etc. I would like to use fit but i do not understand how to construct a fittype object with my function.

I do get results and the plot of the fit looks ok but i never come close to the inital parameters.

Any Suggestions why this happens ?

clear all
close all
clc
%%Makes a set of test data
p=[10 3 12]';
q0=635;
Cna=linspace(50,500,4)'; %Salt concentration
C=linspace(0.01,2,5)';   % Protein concentration
q=SMAexplizit(q0,p,C,Cna) % Calculated Isotherm Data for parameter p
qmeasured=q+5*rand(size(q,1),size(q,2)); % add noise
Testfit=lsqcurvefit(@(p,C)SMAexplizit(q0,p,C,Cna),p,C,qmeasured,[0.001 0.001 1],[100 50 50])
function q=SMAexplizit(q0,p,C,Cna)
%%solves the SMA model near the point 0.001 and makes an explizit
%%expression for every data point C.
% global q0
Ke=p(1);
sigma=p(2);
z=p(3);
q=zeros(size(C));
NN=length(C);
opt = optimset('display','off');
  for n=1:length(Cna)
      for i=1:NN
          q(i,n)=fsolve(@(q)Ke*(q0-(z+sigma).*q).^z.*C(i)./(Cna(n).^z)-q,0.001,opt);
      end
  end
end