How to fit multiple data sets?

Question

Ionut Anghel 2013-6-17

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https://ww2.mathworks.cn/matlabcentral/answers/79309-how-to-fit-multiple-data-sets

Dear all, I have the following question: I need to determine some coefficients(A,B,C,D,E):

    ydata=[1:1:10];
    xdata=[0.1:0.1:1];
    zdata=[10:10:100];
    Y=[A+B*X+C*X^2+D*X^3]*Z^E;
    the code look as:
    xx=xdata'; % X
    yy=ydata'; % Y
    zz=zdata'; % Z
    vect_ones=(10,1);
    %declare function 
    functionfit=@(x,a)x(1)*vect_ones+x(2)*a(1,:)+x(3)*power(a(1,:),2)+x(4)*power(a(1,:),3))*power(b(1,:),x(5));
    initial values;
    x0=[1 1 1 1 1]; % how arbitrary should be this value? 
    [x] = lsqcurvefit(functionfit,x0,XX,ZZ,XX);

Questions:

Why "b" is not recognized as variable as "a" is? Can lsqcurvefit function really work with two (multiple) sets of data)?

Thank you

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Answer 1

Matt J 2013-6-17

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https://ww2.mathworks.cn/matlabcentral/answers/79309-how-to-fit-multiple-data-sets#answer_89035

编辑：Matt J 2013-6-17

在 MATLAB Online 中打开

Why "b" is not recognized as variable as "a" is?

Because you didn't designate it as a variable. You only designated x and a

functionfit=@(x,a)...

That's the way Anonymous Functions work.

Can lsqcurvefit function really work with two (multiple) sets of data)?

It's not clear what you mean by multiple sets of data. As long as ydata has the same dimensions as the output of functionfit, it should be fine.

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Ionut Anghel 2013-6-17

在 MATLAB Online 中打开

The speed seems to be higher (I have about 600 data in one set). However I replace as follow: aa=[xx,zz];

 functionfit=@(x,a)((x(1)*vect_ones+x(2)*a(:,1)+x(3)*power(a(:,1),2)+x(4)*power(a(:,1),3))*power(a(:,2)^x(5)));
%
[x] = lsqcurvefit(functionfit,x0,aa,yy);

Still troubles for the "inner matrix dimensions"

Matt J 2013-6-17

编辑：Matt J 2013-6-17

在 MATLAB Online 中打开

I think you want this:

    xx=xdata'; % X
    yy=ydata'; % Y
    zz=zdata'; % Z
    M=bsxfun(@power,xx(:), 0:3);
    functionfit=@(p,z) (  M*p(1:4)  ).*(z.^p(5));
    p0=[1 1 1 1 1].';
    p = lsqcurvefit(functionfit,p0(:),zz,yy);