MATLAB: Non-linear curvefitting in MATLAB

Question

Hey guys! I'm some given some huge set of data. I am trying to fit a set of data into a model of functional form as described below:

z(x, y) = c0. * x^0 * y^2 + c1. * x^1 * y^1 + c2. * x^2 *y^1

where c0, c1, c2 are the coefficients to be found.

My attempt is to use the nlinfit function to solve it.

So far I have tried:

% i have just added a small portion of my data

a= [ 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001,0.011, 0.011, 0.011, 0.011, 0.011, 0.011, 0.011, 0.011, 0.011, 0.011];

x = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10];

y = x.* a;

z = [ -.304860225, .170315374, .343019354, .370114906, .373180536, .36719579, .363397853, .363417755, .366962504, .379710865, -.304860225, .170315374, .343019354, .370114906, .373180536, .36719579, .363397853, .363417755, .366962504, .379710865];

model= c0.* (x(:).^0).* (y(:).^2) + c1.* (x(:).^1).* (y(:).^1) + c2.* (x(:).^2).* (y(:).^0)

[c0 c1 c2] = [0.001 0.007 0.788]

C= nlinfit( [x,y], z, 'model', [0.001 0.007 0.788])

% Here x,y are independent variables and z is dependent variable.

How can one set these initial values for the coefficients? I'm not getting how to pass the arguments. I'm getting this error "??? Undefined function or variable 'c0' ". Please help!!!

Thanks in advance, Syeda

Answer 1

The solution is trivial because you have a linear system of equations for the 3 coefficients

 A*c = b;
c = A\b

Hope this helps

Thank you for formally accepting my answer

Greg