fitting implicit function to data

Dear all,

i am fitting an implicit function (SMA Isotherm) z(x,y) with lsqcurvefit but i wonder if there is a better solution. My data is of different size z.B x(10x1) y(7x1)!

i make an explicit expression with fsolve by looping over x and y like:

    for n=1:length(x)
        for i=1:length(y)
            z(i,n)=fsolve(@(z)SomeExpression-z,0.001);
        end
    end

I then call it like

fitParam=lsqcurvefit(@(param,x)explizit_function(param,x,y),param,xmeasured,zmeasured)

Any hints are appreciated.

Kind regards

Moritz

Answer 1

[Matt J]

If your implicit equation is

 F(params,x,y,z)=0

and you have known data points (X(i),Y(i),Z(i)) that you want to fit, I think you would just use FSOLVE to solve the system of N equations

F(params,X(i),Y(i),(i))=0, i=1...N

for params.

Answer 2

[Moritz]

Yes, you are right. I did not see the forest because of all the trees. Actually it is a lot faster this way.

I use fmincon with constraints in order to avoid complex values. Instead of 16 seconds it now takes 0.6 seconds.

Thank you for this eye opener...