Using custom fit equation for surface

If I do a fittype for a cruve like this

ft = fittype('a + b*x + c *x^2')

it works fine, but if i want to do a surface fit with a custom equation like with y as a variable like this (just an example not the equation im using)

ft = fittype('a + b*x + c x^2 + d*y^2')

it gives me this error

"The name y cannot be used for both a coefficient and the dependent variable"

How do I work around this.

Answer 1

[Torsten]

ft = fittype('a + b*x + c x^2 + d*y^2','dependent',{'z'},'independent',{'x','y'},'coefficients'{'a','b','c','d'})

[Riccardo Scorretti]

Torsten is right. The documents of ftitype reads: "fittype assumes x is the independent variable, y is the dependent variable, and all other variables are coefficients of the model. x is used if no variable exists.", Basically, it is mandatory to set a different name for the dependent variable, which is y by default.

Hereis a full example:

% Generate some noisy data
a0 = 1 ; b0 = 3 ; c0 = -2 ; d0 = 2;
[x, y] = meshgrid(-3:3, -3:3);
data = a0 + b0*x + c0*x.^2 + d0*y.^2;
data = data + 2*randn(size(data));

% fittype assumes x is the independent variable, y is the dependent variable, 
% and all other variables are coefficients of the model. x is used if no variable exists.
opt = fitoptions('Method','NonlinearLeastSquares', 'StartPoint', [0 0 0 0]);
fun = fittype('a + b*x + c*x^2 + d*y^2', ...
  'independent', {'x', 'y'}, ...
  'dependent', 'f', ...
  'options', opt);
myfit = fit([x(:) y(:)], data(:), fun)

     General model:
     myfit(x,y) = a + b*x + c*x^2 + d*y^2
     Coefficients (with 95% confidence bounds):
       a =      0.5926  (-0.5208, 1.706)
       b =       3.125  (2.835, 3.416)
       c =      -1.996  (-2.164, -1.828)
       d =       2.103  (1.935, 2.271)

% Let's check
hndl = plot(myfit, [x(:) y(:)], data(:));
hndl(1).FaceAlpha = 0.5;

[Xymbu]

Aw, hey its you again. hahah Thanks. I appreciate it.