Lsqcurvefit - multiple parameters - two variables

Hello,

I'm currently working on a function of two variables of the type z=f(x,y), controlled by 4 parameters, and I would like to fit data I obtained to my theoretical function. I read detailed post about how to dit with lsqcurvefit, but a problem remains. This is how I did :

function Sigma = Sigma_funct(p,Var)

Sigma = f(p(1),p(2),p(3),p(4), x,y)

end

with lets say Var(1) = x and Var(2) = y. Then, I'm supposed to use the following syntax :

    p0 = [3,1,2,10] ;
    x = lsqcurvefit(@Sigma_funct,p0,[x y],Sigma_data) ;

However, my problem is that x and y have different size, meaning that Sigma_data isn't a squared matrix : I can't concatenate x and y. How am I supposed to do ?

Thanks for your answers !

P.S : Just to say it, f is linear neither in parameters nor in variables.

[Torsten]

It's not clear what the size of the matrix "Sigma_data" is and what it contains.

Best wishes

Torsten.

[Cyril GADAL]

You're right. So I have a vector x of size N and y of size M such that Sigma_data is of size N*M : I would then have for the theoretical values Sigma(i,j) = f(xi, xj) and then would like to fit this to Sigma_data using lsqcurvefit.

Answer 1

[Torsten]

p0 = [3,1,2,10] ;
xdata = zeros(numel(x)*numel(y),1);
ydata = reshape(Sigma_data,[numel(x)*numel(y),1]);
p_sol = lsqcurvefit(@(p,xdata)Sigma_funct(p,xdata,x,y),p0,xdata,ydata);

function Sigma = Sigma_funct(p,xdata,x,y)
Sigma_mat = f(p(1),p(2),p(3),p(4),x,y)
Sigma = reshape(Sigma_mat,[numel(x)*numel(y),1]);
end

Best wishes

Torsten.

[Cyril GADAL]

Oh right. So everything has to be column vectors. I just do not understand why xdata is full of zeros ?

[Torsten]

Because in your case, there is no senseful "xdata" vector.

Sigma_data depends on x and y, but what scalar value could you choose that Sigma_mat(i,j) depends on ?

Anyway, you can define "xdata" to be an arbitrary N*M-vector - it has no influence on the parameter estimation.

Best wishes

Torsten.

[Cyril GADAL]

I'm sorry, I don't get it ... Are xdata not supposed to be representing the variables leading to ydata ? As the time for example if I look at a time serie, or the distance if I look at a 2D topography ?

Thank you for your answers by the way, that was really helpfull !

[Torsten]

The only thing that matters for "lsqcurvefit" is how the ydata-vector depends on the parameter vector.

The xdata-vector is only introduced to make things easier for you if the relationship between parameter vector and ydata-vector can be established easily by an equation of the form

ydata(i) = func(p,xdata(i)) (i=1,...,N*M)

e.g. for linear regression ydata(i) = p(1)+p(2)*xdata(i).

But this is not the case for your problem - so don't worry about the "xdata"-vector.

Best wishes

Torsten.

[Cyril GADAL]

Understood.

Thank you very much for your time !