multi-vari​able-param​etric data fitting

Hello,

I try to fit the following polynomial to a set of data:

myfun =fittype(@(a,b,c,d,e,f,x,y) y.^3-a*x*y.^2-b*y.^2+c*y*x.^2+d*x*y+e*y-f*x, 'ind', {'x' 'y'},'dep','z')

After I ask matlab to fit the function to my data:

myfit = fit([data(:,1),data(:,2)],z,myfun)

I get the following error.

Warning: Start point not provided, choosing random start point. 
> In Warning>Warning.throw at 31
  In fit>iFit at 320
  In fit at 109 
Error using fit>iFit (line 415)
Error while trying to evaluate FITTYPE function :

Inner matrix dimensions must agree.

Error in fit (line 109)
[fitobj, goodness, output, convmsg] = iFit( xdatain, ydatain, fittypeobj, ...

Caused by:
    Failure in initial user-supplied objective function evaluation. LSQCURVEFIT cannot continue.

What I am doing wrong? data is a matrix of 25x2. which my x is the first column and y is the second. z is defined as

z=zeros(25,1);

Which simply means the coefficients should be obtained in a way to get a flat surface... Any idea why I get such error?

[Matt J]

Why not simply,

   myfit = fit(data,z,myfun)

Answer 1

[Matt J]

Make sure all operations are elementwise,

    >> fun=@(a,b,c,d,e,f,x,y) y.^3-a*x*y.^2-b*y.^2+c*y*x.^2+d*x*y+e*y-f*x;
    >> vectorize(fun)

    ans =

    @(a,b,c,d,e,f,x,y)y.^3-a.*x.*y.^2-b.*y.^2+c.*y.*x.^2+d.*x.*y+e.*y-f.*x

[Shazux Gharasoo]

Hi, thank you for your comment and answer. It still makes the same error!

my dependent variable is actually 'y'! Since my function is not y=f(x) but it is f(x,y)=0, I did it this way assuming z=f(x,y)=0. is this way of doing it correct at all? any hint on how to do it? Or shall I do it in a completely different way?

I tried:

myfun =fittype(@(a,b,c,d,e,f,x,y) y.^3-a*x*y.^2-b*y.^2+c*y*x.^2+d*x*y+e*y-f*x, 'ind', {'x'},'dep','y')

but it didnt work in Matlab