Implizit surface fit of SMA Model; better way possible ?

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Moritz 2013-10-8

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/89527-implizit-surface-fit-of-sma-model-better-way-possible

Dear all,

i am using lsqnonlin for this purpose. It works. I would like to know if there is a better way to do that? E.g using the fit function. I tried it but it gave me an error and said that my independent variable x is not used in the equation.

q is z ( Adsorption capacity) Cna is y (Sodium concentration) C is x (inbound Protein ) p are some parameters q0 is the surface charge of the adsorbent; also a parameter FUNCTION defining fitobject:

function q=SMAexplizit(C,Cna,q0,p)
%%solves the SMA model near the point 0.001 and makes an explizit
%%expression for every data point C.
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

MAKE THE FIT:

%%Makes a set of test data
p=[0.2 5.7 9.1]';
q0=635;
Cna=linspace(25,100,4)';
C=linspace(0.01,2,20)';
tic
q=SMAexplizit(p,C,q0,Cna)
toc
tic
Testfit=lsqcurvefit(@(p,C)SMAexplizit(p,C,q0,Cna),p,C,q,[0.001 0.001 1],[100 50 50])
toc